Methods : Modelling Dichotomous Categorical Responses for Prediction
John Pauline Pineda
December 3, 2022
- 1.
Table of Contents
- 1.1 Sample Data
- 1.2 Data Quality Assessment
- 1.3 Data Preprocessing
- 1.4 Data Exploration
- 1.5 Predictive Model
Development
- 1.5.1 Logistic Regression (LR)
- 1.5.2 Linear Discriminant Analysis (LDA)
- 1.5.3 Flexible Discriminant Analysis (FDA)
- 1.5.4 Mixture Discriminant Analysis (MDA)
- 1.5.5 Naive Bayes (NB)
- 1.5.6 Nearest Shrunken Centroids (NSC)
- 1.5.7 Averaged Neural Network (AVNN)
- 1.5.8 Support Vector Machine - Radial Basis Function Kernel (SVM_R)
- 1.5.9 Support Vector Machine - Polynomial Kernel (SVM_P)
- 1.5.10 K-Nearest Neighbors (KNN)
- 1.5.11 Classification and Regression Trees (CART)
- 1.5.12 Conditional Inference Trees (CTREE)
- 1.5.13 C5.0 Decision Trees (C50)
- 1.5.14 Random Forest (RF)
- 1.5.15 Bagged Trees (BTREE)
- 1.5.16 Model Evaluation Summary
- 1.6 References
1. Table of Contents
This document presents a non-exhaustive list of modelling techniques for predicting dichotomous categorical responses using various helpful packages in R.
1.1 Sample Data
The Solubility dataset from the AppliedPredictiveModeling package was used for this illustrated example. The original numeric response was transformed to simulate a dichotomous categorical variable.
Preliminary dataset assessment:
[A] 1267 rows (observations)
[A.1] Train Set = 951 observations
[A.2] Test Set = 316 observations
[B] 229 columns (variables)
[B.1] 1/229 response = Log_Solubility_Class variable (factor)
[B.1.1] Levels = Log_Solubility_Class=Low < Log_Solubility_Class=High
[B.2] 228/229 predictors = All remaining variables (208/228 factor + 20/228 numeric)
##################################
# Loading R libraries
##################################
library(AppliedPredictiveModeling)
library(caret)
library(rpart)
library(lattice)
library(dplyr)
library(tidyr)
library(moments)
library(skimr)
library(RANN)
library(pls)
library(corrplot)
library(tidyverse)
library(lares)
library(DMwR)
library(gridExtra)
library(rattle)
library(rpart.plot)
library(RColorBrewer)
library(stats)
library(nnet)
library(elasticnet)
library(earth)
library(party)
library(kernlab)
library(randomForest)
library(Cubist)
library(pROC)
library(mda)
library(klaR)
library(pamr)
##################################
# Loading source and
# formulating the train set
##################################
data(solubility)
Solubility_Train <- as.data.frame(cbind(solTrainY,solTrainX))
Solubility_Test <- as.data.frame(cbind(solTestY,solTestX))
##################################
# Applying dichotomization and
# defining the response variable
##################################
Solubility_Train$Log_Solubility_Class <- ifelse(Solubility_Train$solTrainY<mean(Solubility_Train$solTrainY),
"Low","High")
Solubility_Train$Log_Solubility_Class <- factor(Solubility_Train$Log_Solubility_Class,
levels = c("Low","High"))
Solubility_Test$Log_Solubility_Class <- ifelse(Solubility_Test$solTestY<mean(Solubility_Train$solTrainY),
"Low","High")
Solubility_Test$Log_Solubility_Class <- factor(Solubility_Test$Log_Solubility_Class,
levels = c("Low","High"))
Solubility_Train$solTrainY <- NULL
Solubility_Test$solTestY <- NULL
##################################
# Performing a general exploration of the train set
##################################
dim(Solubility_Train)## [1] 951 229str(Solubility_Train)## 'data.frame': 951 obs. of 229 variables:
## $ FP001 : int 0 0 1 0 0 1 0 1 1 1 ...
## $ FP002 : int 1 1 1 0 0 0 1 0 0 1 ...
## $ FP003 : int 0 0 1 1 1 1 0 1 1 1 ...
## $ FP004 : int 0 1 1 0 1 1 1 1 1 1 ...
## $ FP005 : int 1 1 1 0 1 0 1 0 0 1 ...
## $ FP006 : int 0 1 0 0 1 0 0 0 1 1 ...
## $ FP007 : int 0 1 0 1 0 0 0 1 1 1 ...
## $ FP008 : int 1 1 1 0 0 0 1 0 0 0 ...
## $ FP009 : int 0 0 0 0 1 1 1 0 1 0 ...
## $ FP010 : int 0 0 1 0 0 0 0 0 0 0 ...
## $ FP011 : int 0 1 0 0 0 0 0 0 1 0 ...
## $ FP012 : int 0 0 0 0 0 1 0 1 0 0 ...
## $ FP013 : int 0 0 0 0 1 0 1 0 0 0 ...
## $ FP014 : int 0 0 0 0 0 0 1 0 0 0 ...
## $ FP015 : int 1 1 1 1 1 1 1 1 1 1 ...
## $ FP016 : int 0 1 0 0 1 1 0 1 0 0 ...
## $ FP017 : int 0 0 1 1 0 0 0 0 1 1 ...
## $ FP018 : int 0 1 0 0 0 0 0 0 0 0 ...
## $ FP019 : int 1 0 0 0 1 0 1 0 0 0 ...
## $ FP020 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP021 : int 0 0 0 0 0 1 0 0 1 0 ...
## $ FP022 : int 0 0 0 0 0 0 0 0 0 1 ...
## $ FP023 : int 0 0 0 1 0 0 0 0 1 0 ...
## $ FP024 : int 1 0 0 0 1 0 0 0 0 0 ...
## $ FP025 : int 0 0 1 0 0 0 0 0 0 0 ...
## $ FP026 : int 1 0 0 0 0 0 1 0 0 0 ...
## $ FP027 : int 0 0 0 0 0 0 0 0 0 1 ...
## $ FP028 : int 0 1 0 0 0 0 0 0 1 1 ...
## $ FP029 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP030 : int 0 0 0 0 1 0 0 0 0 0 ...
## $ FP031 : int 0 0 0 0 0 0 0 1 0 0 ...
## $ FP032 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP033 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP034 : int 0 0 0 0 1 0 0 0 0 1 ...
## $ FP035 : int 0 0 0 0 0 0 0 0 1 0 ...
## $ FP036 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP037 : int 0 0 0 0 0 0 0 0 1 0 ...
## $ FP038 : int 0 0 1 0 0 0 0 0 0 0 ...
## $ FP039 : int 1 0 0 0 0 0 0 0 0 0 ...
## $ FP040 : int 1 0 0 0 0 0 0 0 0 0 ...
## $ FP041 : int 0 0 0 1 0 0 0 0 1 0 ...
## $ FP042 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP043 : int 0 1 0 0 0 0 0 0 0 0 ...
## $ FP044 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP045 : int 0 0 1 0 0 0 0 0 0 0 ...
## $ FP046 : int 0 1 0 0 0 0 1 0 0 1 ...
## $ FP047 : int 0 1 1 0 0 0 1 0 0 0 ...
## $ FP048 : int 0 0 0 0 0 0 0 1 0 0 ...
## $ FP049 : int 0 0 0 0 0 0 1 0 0 0 ...
## $ FP050 : int 0 0 0 0 0 0 0 1 0 1 ...
## $ FP051 : int 0 1 0 0 0 0 0 0 0 0 ...
## $ FP052 : int 0 0 0 0 0 0 0 0 0 1 ...
## $ FP053 : int 0 0 0 0 0 0 1 0 0 0 ...
## $ FP054 : int 0 0 0 1 0 0 0 0 1 1 ...
## $ FP055 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP056 : int 1 0 0 0 0 0 0 0 0 0 ...
## $ FP057 : int 0 0 0 0 0 0 1 0 0 0 ...
## $ FP058 : int 0 0 0 0 0 0 0 0 0 1 ...
## $ FP059 : int 0 0 0 0 0 0 0 1 0 0 ...
## $ FP060 : int 0 1 1 0 0 0 0 1 1 0 ...
## $ FP061 : int 0 0 1 0 0 0 0 1 1 0 ...
## $ FP062 : int 0 0 1 0 0 1 0 1 1 1 ...
## $ FP063 : int 1 1 0 0 1 1 1 0 0 1 ...
## $ FP064 : int 0 1 1 0 1 1 0 1 0 0 ...
## $ FP065 : int 1 1 0 0 1 0 1 0 1 1 ...
## $ FP066 : int 1 0 1 1 1 1 1 1 1 1 ...
## $ FP067 : int 1 1 0 0 1 1 1 0 0 1 ...
## $ FP068 : int 0 1 0 0 1 1 1 0 0 1 ...
## $ FP069 : int 1 0 1 1 1 1 0 1 1 0 ...
## $ FP070 : int 1 1 0 1 0 0 1 0 1 0 ...
## $ FP071 : int 0 0 0 0 0 0 1 0 1 1 ...
## $ FP072 : int 0 1 1 0 0 1 0 1 1 1 ...
## $ FP073 : int 0 1 1 0 0 0 0 0 1 0 ...
## $ FP074 : int 0 1 0 0 0 0 0 0 1 0 ...
## $ FP075 : int 0 1 0 0 1 1 1 0 0 1 ...
## $ FP076 : int 1 1 0 0 0 0 1 0 1 1 ...
## $ FP077 : int 0 1 0 1 0 0 0 1 1 1 ...
## $ FP078 : int 0 1 0 0 0 0 0 0 1 0 ...
## $ FP079 : int 1 1 1 1 1 0 1 0 1 1 ...
## $ FP080 : int 0 1 0 0 1 1 1 1 0 0 ...
## $ FP081 : int 0 0 1 1 0 0 0 1 1 1 ...
## $ FP082 : int 1 1 1 0 1 1 1 0 1 1 ...
## $ FP083 : int 0 0 0 0 1 0 0 0 0 1 ...
## $ FP084 : int 1 1 0 0 1 0 1 0 0 0 ...
## $ FP085 : int 0 1 0 0 0 0 1 0 0 0 ...
## $ FP086 : int 0 0 0 1 1 0 0 1 1 1 ...
## $ FP087 : int 1 1 1 1 1 0 1 0 1 1 ...
## $ FP088 : int 0 1 0 0 0 0 0 1 1 0 ...
## $ FP089 : int 1 1 0 0 0 0 1 0 0 0 ...
## $ FP090 : int 0 1 0 1 0 0 0 1 1 1 ...
## $ FP091 : int 1 1 0 0 1 0 1 0 0 1 ...
## $ FP092 : int 0 0 0 0 1 1 1 0 1 0 ...
## $ FP093 : int 0 1 0 1 0 0 0 1 1 1 ...
## $ FP094 : int 0 0 0 0 1 0 0 1 0 0 ...
## $ FP095 : int 0 0 0 0 0 0 0 0 1 1 ...
## $ FP096 : int 0 0 0 0 0 0 0 0 1 0 ...
## $ FP097 : int 1 1 0 0 0 0 1 0 1 0 ...
## $ FP098 : int 0 0 1 0 0 0 0 1 0 0 ...
## $ FP099 : int 0 0 0 0 0 0 0 0 1 0 ...
## [list output truncated]summary(Solubility_Train)## FP001 FP002 FP003 FP004
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :1.0000 Median :0.0000 Median :1.0000
## Mean :0.4932 Mean :0.5394 Mean :0.4364 Mean :0.5846
## 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP005 FP006 FP007 FP008
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.000
## Median :1.0000 Median :0.0000 Median :0.0000 Median :0.000
## Mean :0.5794 Mean :0.4006 Mean :0.3638 Mean :0.326
## 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.000
## FP009 FP010 FP011 FP012
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.2797 Mean :0.1788 Mean :0.2145 Mean :0.1767
## 3rd Qu.:1.0000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP013 FP014 FP015 FP016
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:1.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :1.0000 Median :0.0000
## Mean :0.1661 Mean :0.1609 Mean :0.8601 Mean :0.1462
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:1.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP017 FP018 FP019 FP020
## Min. :0.0000 Min. :0.0000 Min. :0.000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.000 Median :0.0000
## Mean :0.1441 Mean :0.1314 Mean :0.122 Mean :0.1199
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.000 Max. :1.0000
## FP021 FP022 FP023 FP024
## Min. :0.0000 Min. :0.0000 Min. :0.000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.000 Median :0.0000
## Mean :0.1209 Mean :0.1041 Mean :0.123 Mean :0.1125
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.000 Max. :1.0000
## FP025 FP026 FP027 FP028
## Min. :0.0000 Min. :0.00000 Min. :0.00000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.0000
## Median :0.0000 Median :0.00000 Median :0.00000 Median :0.0000
## Mean :0.1157 Mean :0.08412 Mean :0.09779 Mean :0.1062
## 3rd Qu.:0.0000 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.00000 Max. :1.00000 Max. :1.0000
## FP029 FP030 FP031 FP032
## Min. :0.000 Min. :0.00000 Min. :0.00000 Min. :0.00000
## 1st Qu.:0.000 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000
## Median :0.000 Median :0.00000 Median :0.00000 Median :0.00000
## Mean :0.102 Mean :0.09359 Mean :0.08938 Mean :0.07361
## 3rd Qu.:0.000 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000
## Max. :1.000 Max. :1.00000 Max. :1.00000 Max. :1.00000
## FP033 FP034 FP035 FP036
## Min. :0.0000 Min. :0.00000 Min. :0.00000 Min. :0.00000
## 1st Qu.:0.0000 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000
## Median :0.0000 Median :0.00000 Median :0.00000 Median :0.00000
## Mean :0.0694 Mean :0.07992 Mean :0.07256 Mean :0.07571
## 3rd Qu.:0.0000 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000
## Max. :1.0000 Max. :1.00000 Max. :1.00000 Max. :1.00000
## FP037 FP038 FP039 FP040
## Min. :0.00000 Min. :0.00000 Min. :0.00000 Min. :0.00000
## 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000
## Median :0.00000 Median :0.00000 Median :0.00000 Median :0.00000
## Mean :0.07045 Mean :0.08622 Mean :0.07466 Mean :0.06835
## 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000
## Max. :1.00000 Max. :1.00000 Max. :1.00000 Max. :1.00000
## FP041 FP042 FP043 FP044
## Min. :0.00000 Min. :0.00000 Min. :0.00000 Min. :0.00000
## 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000
## Median :0.00000 Median :0.00000 Median :0.00000 Median :0.00000
## Mean :0.06309 Mean :0.05678 Mean :0.06625 Mean :0.05994
## 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000
## Max. :1.00000 Max. :1.00000 Max. :1.00000 Max. :1.00000
## FP045 FP046 FP047 FP048
## Min. :0.00000 Min. :0.0000 Min. :0.000 Min. :0.0000
## 1st Qu.:0.00000 1st Qu.:0.0000 1st Qu.:0.000 1st Qu.:0.0000
## Median :0.00000 Median :0.0000 Median :0.000 Median :0.0000
## Mean :0.05573 Mean :0.3155 Mean :0.266 Mean :0.1241
## 3rd Qu.:0.00000 3rd Qu.:1.0000 3rd Qu.:1.000 3rd Qu.:0.0000
## Max. :1.00000 Max. :1.0000 Max. :1.000 Max. :1.0000
## FP049 FP050 FP051 FP052
## Min. :0.000 Min. :0.0000 Min. :0.0000 Min. :0.00000
## 1st Qu.:0.000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.00000
## Median :0.000 Median :0.0000 Median :0.0000 Median :0.00000
## Mean :0.122 Mean :0.1125 Mean :0.1094 Mean :0.09148
## 3rd Qu.:0.000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.00000
## Max. :1.000 Max. :1.0000 Max. :1.0000 Max. :1.00000
## FP053 FP054 FP055 FP056
## Min. :0.00000 Min. :0.00000 Min. :0.00000 Min. :0.00000
## 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000
## Median :0.00000 Median :0.00000 Median :0.00000 Median :0.00000
## Mean :0.09359 Mean :0.07571 Mean :0.05363 Mean :0.06519
## 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000
## Max. :1.00000 Max. :1.00000 Max. :1.00000 Max. :1.00000
## FP057 FP058 FP059 FP060
## Min. :0.0000 Min. :0.0000 Min. :0.00000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.00000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.00000 Median :0.0000
## Mean :0.1199 Mean :0.1136 Mean :0.05468 Mean :0.4816
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.00000 3rd Qu.:1.0000
## Max. :1.0000 Max. :1.0000 Max. :1.00000 Max. :1.0000
## FP061 FP062 FP063 FP064
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.4469 Mean :0.4374 Mean :0.4259 Mean :0.4164
## 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP065 FP066 FP067 FP068
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :1.0000 Median :1.0000 Median :0.0000 Median :0.0000
## Mean :0.5931 Mean :0.6099 Mean :0.3796 Mean :0.3617
## 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP069 FP070 FP071 FP072
## Min. :0.0000 Min. :0.0000 Min. :0.000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.000 Median :1.0000
## Mean :0.3617 Mean :0.3554 Mean :0.327 Mean :0.6583
## 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.000 3rd Qu.:1.0000
## Max. :1.0000 Max. :1.0000 Max. :1.000 Max. :1.0000
## FP073 FP074 FP075 FP076
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.3102 Mean :0.3249 Mean :0.3386 Mean :0.3281
## 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP077 FP078 FP079 FP080
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :1.0000 Median :0.0000
## Mean :0.3207 Mean :0.3039 Mean :0.6898 Mean :0.3028
## 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP081 FP082 FP083 FP084
## Min. :0.0000 Min. :0.000 Min. :0.0000 Min. :0.000
## 1st Qu.:0.0000 1st Qu.:0.000 1st Qu.:0.0000 1st Qu.:0.000
## Median :0.0000 Median :1.000 Median :0.0000 Median :0.000
## Mean :0.2787 Mean :0.714 Mean :0.2734 Mean :0.286
## 3rd Qu.:1.0000 3rd Qu.:1.000 3rd Qu.:1.0000 3rd Qu.:1.000
## Max. :1.0000 Max. :1.000 Max. :1.0000 Max. :1.000
## FP085 FP086 FP087 FP088
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :1.0000 Median :0.0000
## Mean :0.2555 Mean :0.2692 Mean :0.7266 Mean :0.2629
## 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP089 FP090 FP091 FP092
## Min. :0.0000 Min. :0.0000 Min. :0.000 Min. :0.000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.000 1st Qu.:0.000
## Median :0.0000 Median :0.0000 Median :0.000 Median :0.000
## Mean :0.2471 Mean :0.2492 Mean :0.225 Mean :0.244
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.000 3rd Qu.:0.000
## Max. :1.0000 Max. :1.0000 Max. :1.000 Max. :1.000
## FP093 FP094 FP095 FP096
## Min. :0.000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.244 Mean :0.2313 Mean :0.2198 Mean :0.2177
## 3rd Qu.:0.000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000
## Max. :1.000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP097 FP098 FP099 FP100
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.2355 Mean :0.2376 Mean :0.2271 Mean :0.2313
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP101 FP102 FP103 FP104
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.2366 Mean :0.2019 Mean :0.2187 Mean :0.2229
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP105 FP106 FP107 FP108
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.000
## Mean :0.2156 Mean :0.1914 Mean :0.2114 Mean :0.205
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.000
## FP109 FP110 FP111 FP112
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.1767 Mean :0.2061 Mean :0.1966 Mean :0.1945
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP113 FP114 FP115 FP116
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.1956 Mean :0.1556 Mean :0.1788 Mean :0.1924
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP117 FP118 FP119 FP120
## Min. :0.0000 Min. :0.0000 Min. :0.000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.000 Median :0.0000
## Mean :0.1788 Mean :0.1924 Mean :0.163 Mean :0.1661
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.000 Max. :1.0000
## FP121 FP122 FP123 FP124
## Min. :0.0000 Min. :0.000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.000 Median :0.0000 Median :0.0000
## Mean :0.1399 Mean :0.164 Mean :0.1672 Mean :0.1619
## 3rd Qu.:0.0000 3rd Qu.:0.000 3rd Qu.:0.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.000 Max. :1.0000 Max. :1.0000
## FP125 FP126 FP127 FP128
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.1556 Mean :0.1483 Mean :0.1399 Mean :0.1483
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP129 FP130 FP131 FP132
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.1388 Mean :0.1052 Mean :0.1262 Mean :0.1251
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP133 FP134 FP135 FP136
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.1262 Mean :0.1272 Mean :0.1262 Mean :0.1209
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP137 FP138 FP139 FP140
## Min. :0.0000 Min. :0.0000 Min. :0.00000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.00000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.00000 Median :0.0000
## Mean :0.1157 Mean :0.1115 Mean :0.08202 Mean :0.1115
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.00000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.00000 Max. :1.0000
## FP141 FP142 FP143 FP144
## Min. :0.0000 Min. :0.0000 Min. :0.00000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.00000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.00000 Median :0.0000
## Mean :0.1167 Mean :0.1094 Mean :0.08097 Mean :0.1041
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.00000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.00000 Max. :1.0000
## FP145 FP146 FP147 FP148
## Min. :0.0000 Min. :0.000 Min. :0.0000 Min. :0.00000
## 1st Qu.:0.0000 1st Qu.:0.000 1st Qu.:0.0000 1st Qu.:0.00000
## Median :0.0000 Median :0.000 Median :0.0000 Median :0.00000
## Mean :0.1041 Mean :0.103 Mean :0.1052 Mean :0.08728
## 3rd Qu.:0.0000 3rd Qu.:0.000 3rd Qu.:0.0000 3rd Qu.:0.00000
## Max. :1.0000 Max. :1.000 Max. :1.0000 Max. :1.00000
## FP149 FP150 FP151 FP152
## Min. :0.00000 Min. :0.00000 Min. :0.00000 Min. :0.00000
## 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000
## Median :0.00000 Median :0.00000 Median :0.00000 Median :0.00000
## Mean :0.09043 Mean :0.07886 Mean :0.05573 Mean :0.08202
## 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000
## Max. :1.00000 Max. :1.00000 Max. :1.00000 Max. :1.00000
## FP153 FP154 FP155 FP156
## Min. :0.00000 Min. :0.00000 Min. :0.0000 Min. :0.00000
## 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.0000 1st Qu.:0.00000
## Median :0.00000 Median :0.00000 Median :0.0000 Median :0.00000
## Mean :0.07781 Mean :0.03785 Mean :0.0694 Mean :0.07045
## 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.0000 3rd Qu.:0.00000
## Max. :1.00000 Max. :1.00000 Max. :1.0000 Max. :1.00000
## FP157 FP158 FP159 FP160
## Min. :0.00000 Min. :0.00000 Min. :0.00000 Min. :0.00000
## 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000
## Median :0.00000 Median :0.00000 Median :0.00000 Median :0.00000
## Mean :0.06204 Mean :0.05363 Mean :0.07045 Mean :0.06835
## 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000
## Max. :1.00000 Max. :1.00000 Max. :1.00000 Max. :1.00000
## FP161 FP162 FP163 FP164
## Min. :0.00000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.00000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.00000 Median :0.0000 Median :0.0000 Median :1.0000
## Mean :0.06625 Mean :0.4953 Mean :0.4763 Mean :0.6278
## 3rd Qu.:0.00000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000
## Max. :1.00000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP165 FP166 FP167 FP168
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :1.0000
## Mean :0.3491 Mean :0.3312 Mean :0.3281 Mean :0.6656
## 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP169 FP170 FP171 FP172
## Min. :0.0000 Min. :0.000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.000 Median :0.0000 Median :0.0000
## Mean :0.1861 Mean :0.184 Mean :0.1693 Mean :0.1514
## 3rd Qu.:0.0000 3rd Qu.:0.000 3rd Qu.:0.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.000 Max. :1.0000 Max. :1.0000
## FP173 FP174 FP175 FP176
## Min. :0.000 Min. :0.0000 Min. :0.0000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.000
## Median :0.000 Median :0.0000 Median :0.0000 Median :0.000
## Mean :0.142 Mean :0.1304 Mean :0.1346 Mean :0.122
## 3rd Qu.:0.000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.000
## Max. :1.000 Max. :1.0000 Max. :1.0000 Max. :1.000
## FP177 FP178 FP179 FP180
## Min. :0.0000 Min. :0.0000 Min. :0.00000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.00000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.00000 Median :0.0000
## Mean :0.1209 Mean :0.1209 Mean :0.09779 Mean :0.1073
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.00000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.00000 Max. :1.0000
## FP181 FP182 FP183 FP184
## Min. :0.00000 Min. :0.00000 Min. :0.00000 Min. :0.00000
## 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000
## Median :0.00000 Median :0.00000 Median :0.00000 Median :0.00000
## Mean :0.09359 Mean :0.09884 Mean :0.07571 Mean :0.08412
## 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000
## Max. :1.00000 Max. :1.00000 Max. :1.00000 Max. :1.00000
## FP185 FP186 FP187 FP188
## Min. :0.00000 Min. :0.00000 Min. :0.00000 Min. :0.00000
## 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000
## Median :0.00000 Median :0.00000 Median :0.00000 Median :0.00000
## Mean :0.08517 Mean :0.07676 Mean :0.07256 Mean :0.06835
## 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000
## Max. :1.00000 Max. :1.00000 Max. :1.00000 Max. :1.00000
## FP189 FP190 FP191 FP192
## Min. :0.00000 Min. :0.00000 Min. :0.00000 Min. :0.00000
## 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000
## Median :0.00000 Median :0.00000 Median :0.00000 Median :0.00000
## Mean :0.07676 Mean :0.07256 Mean :0.07045 Mean :0.06099
## 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000
## Max. :1.00000 Max. :1.00000 Max. :1.00000 Max. :1.00000
## FP193 FP194 FP195 FP196
## Min. :0.00000 Min. :0.00000 Min. :0.00000 Min. :0.00000
## 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000
## Median :0.00000 Median :0.00000 Median :0.00000 Median :0.00000
## Mean :0.06204 Mean :0.05889 Mean :0.06099 Mean :0.05678
## 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000
## Max. :1.00000 Max. :1.00000 Max. :1.00000 Max. :1.00000
## FP197 FP198 FP199 FP200
## Min. :0.00000 Min. :0.00000 Min. :0.00000 Min. :0.00000
## 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000
## Median :0.00000 Median :0.00000 Median :0.00000 Median :0.00000
## Mean :0.05258 Mean :0.05678 Mean :0.04732 Mean :0.04942
## 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000
## Max. :1.00000 Max. :1.00000 Max. :1.00000 Max. :1.00000
## FP201 FP202 FP203 FP204
## Min. :0.00000 Min. :0.0000 Min. :0.0000 Min. :0.00000
## 1st Qu.:0.00000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.00000
## Median :0.00000 Median :0.0000 Median :0.0000 Median :0.00000
## Mean :0.05258 Mean :0.2576 Mean :0.1146 Mean :0.09884
## 3rd Qu.:0.00000 3rd Qu.:1.0000 3rd Qu.:0.0000 3rd Qu.:0.00000
## Max. :1.00000 Max. :1.0000 Max. :1.0000 Max. :1.00000
## FP205 FP206 FP207 FP208
## Min. :0.00000 Min. :0.00000 Min. :0.00000 Min. :0.0000
## 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.0000
## Median :0.00000 Median :0.00000 Median :0.00000 Median :0.0000
## Mean :0.07781 Mean :0.05994 Mean :0.05678 Mean :0.1125
## 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.0000
## Max. :1.00000 Max. :1.00000 Max. :1.00000 Max. :1.0000
## MolWeight NumAtoms NumNonHAtoms NumBonds
## Min. : 46.09 Min. : 5.00 Min. : 2.00 Min. : 4.00
## 1st Qu.:122.61 1st Qu.:17.00 1st Qu.: 8.00 1st Qu.:17.00
## Median :179.23 Median :22.00 Median :12.00 Median :23.00
## Mean :201.65 Mean :25.51 Mean :13.16 Mean :25.91
## 3rd Qu.:264.34 3rd Qu.:31.00 3rd Qu.:17.00 3rd Qu.:31.50
## Max. :665.81 Max. :94.00 Max. :47.00 Max. :97.00
## NumNonHBonds NumMultBonds NumRotBonds NumDblBonds
## Min. : 1.00 Min. : 0.000 Min. : 0.000 Min. :0.000
## 1st Qu.: 8.00 1st Qu.: 1.000 1st Qu.: 0.000 1st Qu.:0.000
## Median :12.00 Median : 6.000 Median : 2.000 Median :1.000
## Mean :13.56 Mean : 6.148 Mean : 2.251 Mean :1.006
## 3rd Qu.:18.00 3rd Qu.:10.000 3rd Qu.: 3.500 3rd Qu.:2.000
## Max. :50.00 Max. :25.000 Max. :16.000 Max. :7.000
## NumAromaticBonds NumHydrogen NumCarbon NumNitrogen
## Min. : 0.000 Min. : 0.00 Min. : 1.000 Min. :0.0000
## 1st Qu.: 0.000 1st Qu.: 7.00 1st Qu.: 6.000 1st Qu.:0.0000
## Median : 6.000 Median :11.00 Median : 9.000 Median :0.0000
## Mean : 5.121 Mean :12.35 Mean : 9.893 Mean :0.8128
## 3rd Qu.: 6.000 3rd Qu.:16.00 3rd Qu.:12.000 3rd Qu.:1.0000
## Max. :25.000 Max. :47.00 Max. :33.000 Max. :6.0000
## NumOxygen NumSulfer NumChlorine NumHalogen
## Min. : 0.000 Min. :0.000 Min. : 0.0000 Min. : 0.0000
## 1st Qu.: 0.000 1st Qu.:0.000 1st Qu.: 0.0000 1st Qu.: 0.0000
## Median : 1.000 Median :0.000 Median : 0.0000 Median : 0.0000
## Mean : 1.574 Mean :0.164 Mean : 0.5563 Mean : 0.6982
## 3rd Qu.: 2.000 3rd Qu.:0.000 3rd Qu.: 0.0000 3rd Qu.: 1.0000
## Max. :13.000 Max. :4.000 Max. :10.0000 Max. :10.0000
## NumRings HydrophilicFactor SurfaceArea1 SurfaceArea2
## Min. :0.000 Min. :-0.98500 Min. : 0.00 Min. : 0.00
## 1st Qu.:0.000 1st Qu.:-0.76300 1st Qu.: 9.23 1st Qu.: 10.63
## Median :1.000 Median :-0.31400 Median : 29.10 Median : 33.12
## Mean :1.402 Mean :-0.02059 Mean : 36.46 Mean : 40.23
## 3rd Qu.:2.000 3rd Qu.: 0.31300 3rd Qu.: 53.28 3rd Qu.: 60.66
## Max. :7.000 Max. :13.48300 Max. :331.94 Max. :331.94
## Log_Solubility_Class
## Low :427
## High:524
##
##
##
## ##################################
# Performing a general exploration of the test set
##################################
dim(Solubility_Test)## [1] 316 229str(Solubility_Test)## 'data.frame': 316 obs. of 229 variables:
## $ FP001 : int 1 1 0 0 1 1 1 0 1 0 ...
## $ FP002 : int 0 0 1 0 1 0 0 0 0 1 ...
## $ FP003 : int 0 1 0 1 0 0 0 0 1 0 ...
## $ FP004 : int 1 1 0 0 1 1 1 1 1 0 ...
## $ FP005 : int 0 0 1 0 1 0 0 0 0 1 ...
## $ FP006 : int 0 1 0 1 1 0 0 0 0 0 ...
## $ FP007 : int 0 0 0 0 0 0 0 1 1 0 ...
## $ FP008 : int 0 0 0 0 1 0 0 0 0 0 ...
## $ FP009 : int 1 0 0 0 0 0 0 0 0 0 ...
## $ FP010 : int 1 0 1 0 0 0 0 0 0 0 ...
## $ FP011 : int 0 1 0 0 1 0 0 0 0 0 ...
## $ FP012 : int 0 1 0 0 0 1 0 1 0 0 ...
## $ FP013 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP014 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP015 : int 1 1 0 1 1 1 1 1 1 1 ...
## $ FP016 : int 0 1 0 0 0 0 0 1 0 0 ...
## $ FP017 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP018 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP019 : int 0 0 0 0 1 0 0 0 0 1 ...
## $ FP020 : int 0 0 0 0 0 1 0 0 0 0 ...
## $ FP021 : int 1 0 0 0 0 0 0 0 0 0 ...
## $ FP022 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP023 : int 0 0 0 0 0 0 1 0 0 0 ...
## $ FP024 : int 0 0 0 0 1 0 0 0 0 1 ...
## $ FP025 : int 1 0 0 0 0 0 0 0 0 0 ...
## $ FP026 : int 0 0 0 0 0 0 0 0 0 1 ...
## $ FP027 : int 0 0 0 1 0 0 0 0 0 0 ...
## $ FP028 : int 0 0 0 1 0 0 0 0 0 0 ...
## $ FP029 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP030 : int 0 0 0 1 0 0 0 0 0 0 ...
## $ FP031 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP032 : int 0 0 1 0 0 0 0 0 0 0 ...
## $ FP033 : int 0 0 1 0 0 0 0 0 0 0 ...
## $ FP034 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP035 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP036 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP037 : int 0 0 0 0 0 0 0 0 1 0 ...
## $ FP038 : int 1 0 0 0 0 0 0 0 0 0 ...
## $ FP039 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP040 : int 0 0 0 0 1 0 0 0 0 0 ...
## $ FP041 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP042 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP043 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP044 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP045 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP046 : int 0 0 1 0 0 0 0 0 0 1 ...
## $ FP047 : int 0 0 0 0 1 0 0 0 0 0 ...
## $ FP048 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP049 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP050 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP051 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP052 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP053 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP054 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP055 : int 0 0 1 0 0 0 0 0 0 0 ...
## $ FP056 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP057 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP058 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP059 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP060 : int 1 1 1 0 0 1 0 1 0 0 ...
## $ FP061 : int 1 1 1 0 0 1 0 0 0 0 ...
## $ FP062 : int 1 1 0 0 1 1 1 0 1 0 ...
## $ FP063 : int 0 1 0 1 1 0 0 0 0 1 ...
## $ FP064 : int 1 1 0 0 0 0 0 0 1 0 ...
## $ FP065 : int 0 0 1 0 0 0 0 0 0 0 ...
## $ FP066 : int 0 1 0 1 0 1 0 0 1 1 ...
## $ FP067 : int 0 1 0 1 1 0 0 0 0 1 ...
## $ FP068 : int 0 1 0 1 1 0 0 0 0 0 ...
## $ FP069 : int 0 0 0 0 0 0 0 0 1 1 ...
## $ FP070 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP071 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP072 : int 1 1 1 0 1 1 1 1 1 0 ...
## $ FP073 : int 1 0 1 0 0 0 0 0 0 0 ...
## $ FP074 : int 0 0 1 0 0 0 0 0 1 0 ...
## $ FP075 : int 0 1 0 1 0 0 0 1 0 0 ...
## $ FP076 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP077 : int 0 0 0 1 0 0 0 1 0 0 ...
## $ FP078 : int 0 0 1 0 0 0 0 0 0 0 ...
## $ FP079 : int 0 0 1 1 1 0 0 0 0 1 ...
## $ FP080 : int 1 1 0 1 0 0 0 1 0 0 ...
## $ FP081 : int 0 0 0 1 0 0 0 0 1 0 ...
## $ FP082 : int 0 0 1 0 1 0 0 0 0 1 ...
## $ FP083 : int 0 1 0 1 1 0 0 0 0 0 ...
## $ FP084 : int 0 0 0 1 1 0 0 1 0 1 ...
## $ FP085 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP086 : int 0 0 0 1 0 0 0 0 0 0 ...
## $ FP087 : int 0 0 1 1 1 0 0 1 0 1 ...
## $ FP088 : int 1 0 0 0 0 0 0 1 1 0 ...
## $ FP089 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP090 : int 0 0 0 1 0 0 0 1 0 0 ...
## $ FP091 : int 0 0 0 1 1 0 0 0 0 0 ...
## $ FP092 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP093 : int 0 0 0 1 0 0 0 1 0 0 ...
## $ FP094 : int 0 1 0 0 0 0 0 0 1 0 ...
## $ FP095 : int 0 0 1 1 0 0 0 0 0 0 ...
## $ FP096 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP097 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ FP098 : int 1 1 0 0 0 1 0 0 0 0 ...
## $ FP099 : int 0 0 0 0 0 0 0 0 0 0 ...
## [list output truncated]summary(Solubility_Test)## FP001 FP002 FP003 FP004
## Min. :0.0000 Min. :0.0000 Min. :0.000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.000 1st Qu.:0.0000
## Median :0.0000 Median :1.0000 Median :0.000 Median :1.0000
## Mean :0.4684 Mean :0.5854 Mean :0.443 Mean :0.5316
## 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.000 3rd Qu.:1.0000
## Max. :1.0000 Max. :1.0000 Max. :1.000 Max. :1.0000
## FP005 FP006 FP007 FP008
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :1.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.6171 Mean :0.3513 Mean :0.3544 Mean :0.3608
## 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP009 FP010 FP011 FP012
## Min. :0.0000 Min. :0.000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.000 Median :0.0000 Median :0.0000
## Mean :0.2627 Mean :0.193 Mean :0.1741 Mean :0.1677
## 3rd Qu.:1.0000 3rd Qu.:0.000 3rd Qu.:0.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.000 Max. :1.0000 Max. :1.0000
## FP013 FP014 FP015 FP016
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:1.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :1.0000 Median :0.0000
## Mean :0.1646 Mean :0.1582 Mean :0.8291 Mean :0.1424
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:1.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP017 FP018 FP019 FP020
## Min. :0.0000 Min. :0.00000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.00000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.00000 Median :0.0000 Median :0.0000
## Mean :0.1487 Mean :0.08544 Mean :0.1139 Mean :0.1076
## 3rd Qu.:0.0000 3rd Qu.:0.00000 3rd Qu.:0.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.00000 Max. :1.0000 Max. :1.0000
## FP021 FP022 FP023 FP024
## Min. :0.0000 Min. :0.0000 Min. :0.00000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.00000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.00000 Median :0.0000
## Mean :0.1076 Mean :0.1171 Mean :0.08544 Mean :0.0981
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.00000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.00000 Max. :1.0000
## FP025 FP026 FP027 FP028
## Min. :0.00000 Min. :0.0000 Min. :0.00000 Min. :0.00000
## 1st Qu.:0.00000 1st Qu.:0.0000 1st Qu.:0.00000 1st Qu.:0.00000
## Median :0.00000 Median :0.0000 Median :0.00000 Median :0.00000
## Mean :0.07911 Mean :0.1171 Mean :0.07911 Mean :0.05696
## 3rd Qu.:0.00000 3rd Qu.:0.0000 3rd Qu.:0.00000 3rd Qu.:0.00000
## Max. :1.00000 Max. :1.0000 Max. :1.00000 Max. :1.00000
## FP029 FP030 FP031 FP032
## Min. :0.00000 Min. :0.00000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.00000 Median :0.00000 Median :0.0000 Median :0.0000
## Mean :0.05063 Mean :0.08228 Mean :0.0981 Mean :0.1297
## 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.0000 3rd Qu.:0.0000
## Max. :1.00000 Max. :1.00000 Max. :1.0000 Max. :1.0000
## FP033 FP034 FP035 FP036
## Min. :0.0000 Min. :0.00000 Min. :0.0000 Min. :0.00000
## 1st Qu.:0.0000 1st Qu.:0.00000 1st Qu.:0.0000 1st Qu.:0.00000
## Median :0.0000 Median :0.00000 Median :0.0000 Median :0.00000
## Mean :0.1203 Mean :0.06646 Mean :0.0981 Mean :0.06013
## 3rd Qu.:0.0000 3rd Qu.:0.00000 3rd Qu.:0.0000 3rd Qu.:0.00000
## Max. :1.0000 Max. :1.00000 Max. :1.0000 Max. :1.00000
## FP037 FP038 FP039 FP040
## Min. :0.00000 Min. :0.00000 Min. :0.00000 Min. :0.00000
## 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000
## Median :0.00000 Median :0.00000 Median :0.00000 Median :0.00000
## Mean :0.09494 Mean :0.03165 Mean :0.06329 Mean :0.05696
## 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000
## Max. :1.00000 Max. :1.00000 Max. :1.00000 Max. :1.00000
## FP041 FP042 FP043 FP044
## Min. :0.00000 Min. :0.00000 Min. :0.0000 Min. :0.00000
## 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.0000 1st Qu.:0.00000
## Median :0.00000 Median :0.00000 Median :0.0000 Median :0.00000
## Mean :0.06013 Mean :0.06013 Mean :0.0443 Mean :0.06013
## 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.0000 3rd Qu.:0.00000
## Max. :1.00000 Max. :1.00000 Max. :1.0000 Max. :1.00000
## FP045 FP046 FP047 FP048
## Min. :0.00000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.00000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.00000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.06329 Mean :0.3259 Mean :0.2975 Mean :0.1139
## 3rd Qu.:0.00000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:0.0000
## Max. :1.00000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP049 FP050 FP051 FP052
## Min. :0.0000 Min. :0.0000 Min. :0.00000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.00000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.00000 Median :0.0000
## Mean :0.1076 Mean :0.1139 Mean :0.05696 Mean :0.1044
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.00000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.00000 Max. :1.0000
## FP053 FP054 FP055 FP056
## Min. :0.00000 Min. :0.0000 Min. :0.00000 Min. :0.00000
## 1st Qu.:0.00000 1st Qu.:0.0000 1st Qu.:0.00000 1st Qu.:0.00000
## Median :0.00000 Median :0.0000 Median :0.00000 Median :0.00000
## Mean :0.06013 Mean :0.0981 Mean :0.09177 Mean :0.06329
## 3rd Qu.:0.00000 3rd Qu.:0.0000 3rd Qu.:0.00000 3rd Qu.:0.00000
## Max. :1.00000 Max. :1.0000 Max. :1.00000 Max. :1.00000
## FP057 FP058 FP059 FP060
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.1234 Mean :0.1361 Mean :0.0443 Mean :0.4525
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:1.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP061 FP062 FP063 FP064
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.3924 Mean :0.4272 Mean :0.3576 Mean :0.3892
## 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP065 FP066 FP067 FP068
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :1.0000 Median :1.0000 Median :0.0000 Median :0.0000
## Mean :0.5981 Mean :0.6171 Mean :0.3259 Mean :0.2911
## 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP069 FP070 FP071 FP072
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :1.0000
## Mean :0.3734 Mean :0.3323 Mean :0.3449 Mean :0.6456
## 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP073 FP074 FP075 FP076
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.2911 Mean :0.3259 Mean :0.2563 Mean :0.3165
## 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP077 FP078 FP079 FP080
## Min. :0.000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.000 Median :0.0000 Median :1.0000 Median :0.0000
## Mean :0.307 Mean :0.3101 Mean :0.7278 Mean :0.2627
## 3rd Qu.:1.000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000
## Max. :1.000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP081 FP082 FP083 FP084
## Min. :0.000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.000 Median :1.0000 Median :0.0000 Median :0.0000
## Mean :0.288 Mean :0.7437 Mean :0.2532 Mean :0.2247
## 3rd Qu.:1.000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:0.0000
## Max. :1.000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP085 FP086 FP087 FP088
## Min. :0.000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.000 1st Qu.:0.0000 1st Qu.:1.0000 1st Qu.:0.0000
## Median :0.000 Median :0.0000 Median :1.0000 Median :0.0000
## Mean :0.269 Mean :0.2722 Mean :0.7627 Mean :0.2437
## 3rd Qu.:1.000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:0.0000
## Max. :1.000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP089 FP090 FP091 FP092
## Min. :0.0000 Min. :0.0000 Min. :0.000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.000 Median :0.0000
## Mean :0.2532 Mean :0.2278 Mean :0.231 Mean :0.2184
## 3rd Qu.:1.0000 3rd Qu.:0.0000 3rd Qu.:0.000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.000 Max. :1.0000
## FP093 FP094 FP095 FP096
## Min. :0.0000 Min. :0.00 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.00 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.00 Median :0.0000 Median :0.0000
## Mean :0.2152 Mean :0.25 Mean :0.2057 Mean :0.1867
## 3rd Qu.:0.0000 3rd Qu.:0.25 3rd Qu.:0.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.00 Max. :1.0000 Max. :1.0000
## FP097 FP098 FP099 FP100
## Min. :0.0000 Min. :0.0000 Min. :0.000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.000 Median :0.0000
## Mean :0.2089 Mean :0.2025 Mean :0.212 Mean :0.1804
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.000 Max. :1.0000
## FP101 FP102 FP103 FP104
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.1772 Mean :0.1456 Mean :0.2184 Mean :0.1835
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP105 FP106 FP107 FP108
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.2152 Mean :0.1361 Mean :0.1962 Mean :0.1804
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP109 FP110 FP111 FP112
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.1741 Mean :0.1646 Mean :0.1804 Mean :0.1772
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP113 FP114 FP115 FP116
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.1646 Mean :0.1772 Mean :0.1582 Mean :0.1487
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP117 FP118 FP119 FP120
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.1709 Mean :0.1171 Mean :0.1677 Mean :0.1551
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP121 FP122 FP123 FP124
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.1076 Mean :0.1361 Mean :0.1456 Mean :0.1329
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP125 FP126 FP127 FP128
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.1203 Mean :0.1139 Mean :0.1487 Mean :0.1076
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP129 FP130 FP131 FP132
## Min. :0.0000 Min. :0.00000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.00000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.00000 Median :0.0000 Median :0.0000
## Mean :0.1392 Mean :0.08228 Mean :0.1076 Mean :0.1266
## 3rd Qu.:0.0000 3rd Qu.:0.00000 3rd Qu.:0.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.00000 Max. :1.0000 Max. :1.0000
## FP133 FP134 FP135 FP136
## Min. :0.0000 Min. :0.00000 Min. :0.00000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.0000
## Median :0.0000 Median :0.00000 Median :0.00000 Median :0.0000
## Mean :0.1361 Mean :0.08544 Mean :0.06329 Mean :0.1013
## 3rd Qu.:0.0000 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.00000 Max. :1.00000 Max. :1.0000
## FP137 FP138 FP139 FP140
## Min. :0.00000 Min. :0.00000 Min. :0.00000 Min. :0.00000
## 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000
## Median :0.00000 Median :0.00000 Median :0.00000 Median :0.00000
## Mean :0.08861 Mean :0.08228 Mean :0.06329 Mean :0.08861
## 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000
## Max. :1.00000 Max. :1.00000 Max. :1.00000 Max. :1.00000
## FP141 FP142 FP143 FP144
## Min. :0.00000 Min. :0.00000 Min. :0.0000 Min. :0.00000
## 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.0000 1st Qu.:0.00000
## Median :0.00000 Median :0.00000 Median :0.0000 Median :0.00000
## Mean :0.06962 Mean :0.09494 Mean :0.0538 Mean :0.09177
## 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.0000 3rd Qu.:0.00000
## Max. :1.00000 Max. :1.00000 Max. :1.0000 Max. :1.00000
## FP145 FP146 FP147 FP148
## Min. :0.00000 Min. :0.00000 Min. :0.00000 Min. :0.00000
## 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000
## Median :0.00000 Median :0.00000 Median :0.00000 Median :0.00000
## Mean :0.06329 Mean :0.09177 Mean :0.06962 Mean :0.07911
## 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000
## Max. :1.00000 Max. :1.00000 Max. :1.00000 Max. :1.00000
## FP149 FP150 FP151 FP152
## Min. :0.00000 Min. :0.00000 Min. :0.00000 Min. :0.0000
## 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.0000
## Median :0.00000 Median :0.00000 Median :0.00000 Median :0.0000
## Mean :0.08228 Mean :0.06646 Mean :0.03165 Mean :0.0538
## 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.0000
## Max. :1.00000 Max. :1.00000 Max. :1.00000 Max. :1.0000
## FP153 FP154 FP155 FP156
## Min. :0.00000 Min. :0.00000 Min. :0.00000 Min. :0.00000
## 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000
## Median :0.00000 Median :0.00000 Median :0.00000 Median :0.00000
## Mean :0.03481 Mean :0.03165 Mean :0.06646 Mean :0.04747
## 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000
## Max. :1.00000 Max. :1.00000 Max. :1.00000 Max. :1.00000
## FP157 FP158 FP159 FP160
## Min. :0.00000 Min. :0.00000 Min. :0.00000 Min. :0.00000
## 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000
## Median :0.00000 Median :0.00000 Median :0.00000 Median :0.00000
## Mean :0.05696 Mean :0.07911 Mean :0.03481 Mean :0.03481
## 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000
## Max. :1.00000 Max. :1.00000 Max. :1.00000 Max. :1.00000
## FP161 FP162 FP163 FP164
## Min. :0.00000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.00000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.00000 Median :1.0000 Median :0.0000 Median :1.0000
## Mean :0.03481 Mean :0.5316 Mean :0.4525 Mean :0.6551
## 3rd Qu.:0.00000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000
## Max. :1.00000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP165 FP166 FP167 FP168
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :1.0000
## Mean :0.3196 Mean :0.3386 Mean :0.3006 Mean :0.7152
## 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP169 FP170 FP171 FP172
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.1867 Mean :0.1551 Mean :0.1297 Mean :0.1487
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP173 FP174 FP175 FP176
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.1361 Mean :0.1551 Mean :0.1329 Mean :0.1076
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## FP177 FP178 FP179 FP180
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.00000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.00000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.00000
## Mean :0.1013 Mean :0.1076 Mean :0.1392 Mean :0.06962
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.00000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.00000
## FP181 FP182 FP183 FP184
## Min. :0.0000 Min. :0.00000 Min. :0.0000 Min. :0.00000
## 1st Qu.:0.0000 1st Qu.:0.00000 1st Qu.:0.0000 1st Qu.:0.00000
## Median :0.0000 Median :0.00000 Median :0.0000 Median :0.00000
## Mean :0.1044 Mean :0.07595 Mean :0.1329 Mean :0.09494
## 3rd Qu.:0.0000 3rd Qu.:0.00000 3rd Qu.:0.0000 3rd Qu.:0.00000
## Max. :1.0000 Max. :1.00000 Max. :1.0000 Max. :1.00000
## FP185 FP186 FP187 FP188
## Min. :0.0000 Min. :0.00000 Min. :0.00000 Min. :0.00000
## 1st Qu.:0.0000 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000
## Median :0.0000 Median :0.00000 Median :0.00000 Median :0.00000
## Mean :0.0981 Mean :0.06013 Mean :0.06646 Mean :0.06962
## 3rd Qu.:0.0000 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000
## Max. :1.0000 Max. :1.00000 Max. :1.00000 Max. :1.00000
## FP189 FP190 FP191 FP192
## Min. :0.00000 Min. :0.0000 Min. :0.00000 Min. :0.00000
## 1st Qu.:0.00000 1st Qu.:0.0000 1st Qu.:0.00000 1st Qu.:0.00000
## Median :0.00000 Median :0.0000 Median :0.00000 Median :0.00000
## Mean :0.04114 Mean :0.0538 Mean :0.05696 Mean :0.06962
## 3rd Qu.:0.00000 3rd Qu.:0.0000 3rd Qu.:0.00000 3rd Qu.:0.00000
## Max. :1.00000 Max. :1.0000 Max. :1.00000 Max. :1.00000
## FP193 FP194 FP195 FP196
## Min. :0.00000 Min. :0.00000 Min. :0.00000 Min. :0.00000
## 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000
## Median :0.00000 Median :0.00000 Median :0.00000 Median :0.00000
## Mean :0.06962 Mean :0.06646 Mean :0.05063 Mean :0.06962
## 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000
## Max. :1.00000 Max. :1.00000 Max. :1.00000 Max. :1.00000
## FP197 FP198 FP199 FP200
## Min. :0.00000 Min. :0.0000 Min. :0.00000 Min. :0.00000
## 1st Qu.:0.00000 1st Qu.:0.0000 1st Qu.:0.00000 1st Qu.:0.00000
## Median :0.00000 Median :0.0000 Median :0.00000 Median :0.00000
## Mean :0.06329 Mean :0.0443 Mean :0.07278 Mean :0.06329
## 3rd Qu.:0.00000 3rd Qu.:0.0000 3rd Qu.:0.00000 3rd Qu.:0.00000
## Max. :1.00000 Max. :1.0000 Max. :1.00000 Max. :1.00000
## FP201 FP202 FP203 FP204
## Min. :0.00000 Min. :0.0000 Min. :0.0000 Min. :0.00000
## 1st Qu.:0.00000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.00000
## Median :0.00000 Median :0.0000 Median :0.0000 Median :0.00000
## Mean :0.04114 Mean :0.2658 Mean :0.1361 Mean :0.09494
## 3rd Qu.:0.00000 3rd Qu.:1.0000 3rd Qu.:0.0000 3rd Qu.:0.00000
## Max. :1.00000 Max. :1.0000 Max. :1.0000 Max. :1.00000
## FP205 FP206 FP207 FP208
## Min. :0.00000 Min. :0.00000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.00000 Median :0.00000 Median :0.0000 Median :0.0000
## Mean :0.07911 Mean :0.05063 Mean :0.0443 Mean :0.1361
## 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.0000 3rd Qu.:0.0000
## Max. :1.00000 Max. :1.00000 Max. :1.0000 Max. :1.0000
## MolWeight NumAtoms NumNonHAtoms NumBonds NumNonHBonds
## Min. : 56.07 Min. : 5.0 Min. : 3.00 Min. : 4 Min. : 2.0
## 1st Qu.:121.91 1st Qu.:17.0 1st Qu.: 8.00 1st Qu.:16 1st Qu.: 8.0
## Median :170.11 Median :22.0 Median :11.00 Median :23 Median :12.0
## Mean :194.12 Mean :24.6 Mean :12.71 Mean :25 Mean :13.1
## 3rd Qu.:253.82 3rd Qu.:29.0 3rd Qu.:16.00 3rd Qu.:30 3rd Qu.:17.0
## Max. :478.92 Max. :68.0 Max. :33.00 Max. :71 Max. :36.0
## NumMultBonds NumRotBonds NumDblBonds NumAromaticBonds
## Min. : 0.000 Min. : 0.000 Min. :0.0000 Min. : 0.000
## 1st Qu.: 1.000 1st Qu.: 0.000 1st Qu.:0.0000 1st Qu.: 0.000
## Median : 6.000 Median : 1.000 Median :1.0000 Median : 6.000
## Mean : 6.313 Mean : 1.949 Mean :0.8892 Mean : 5.399
## 3rd Qu.:10.000 3rd Qu.: 3.000 3rd Qu.:1.0000 3rd Qu.:10.000
## Max. :27.000 Max. :16.000 Max. :6.0000 Max. :27.000
## NumHydrogen NumCarbon NumNitrogen NumOxygen
## Min. : 0.0 Min. : 1.000 Min. :0.0000 Min. :0.000
## 1st Qu.: 7.0 1st Qu.: 6.000 1st Qu.:0.0000 1st Qu.:0.000
## Median :11.0 Median : 8.000 Median :0.0000 Median :1.000
## Mean :11.9 Mean : 9.785 Mean :0.7089 Mean :1.389
## 3rd Qu.:15.0 3rd Qu.:12.000 3rd Qu.:1.0000 3rd Qu.:2.000
## Max. :40.0 Max. :24.000 Max. :6.0000 Max. :9.000
## NumSulfer NumChlorine NumHalogen NumRings
## Min. :0.0000 Min. :0.000 Min. :0.0000 Min. :0.000
## 1st Qu.:0.0000 1st Qu.:0.000 1st Qu.:0.0000 1st Qu.:1.000
## Median :0.0000 Median :0.000 Median :0.0000 Median :1.000
## Mean :0.1013 Mean :0.557 Mean :0.7089 Mean :1.399
## 3rd Qu.:0.0000 3rd Qu.:0.000 3rd Qu.:1.0000 3rd Qu.:2.000
## Max. :3.0000 Max. :9.000 Max. :9.0000 Max. :6.000
## HydrophilicFactor SurfaceArea1 SurfaceArea2 Log_Solubility_Class
## Min. :-0.9860 Min. : 0.00 Min. : 0.00 Low :143
## 1st Qu.:-0.7670 1st Qu.: 9.23 1st Qu.: 9.23 High:173
## Median :-0.3970 Median : 26.30 Median : 26.30
## Mean :-0.1022 Mean : 32.76 Mean : 35.04
## 3rd Qu.: 0.2140 3rd Qu.: 49.55 3rd Qu.: 52.32
## Max. : 5.0000 Max. :201.85 Max. :201.85##################################
# Formulating a data type assessment summary
##################################
PDA <- Solubility_Train
(PDA.Summary <- data.frame(
Column.Index=c(1:length(names(PDA))),
Column.Name= names(PDA),
Column.Type=sapply(PDA, function(x) class(x)),
row.names=NULL)
)## Column.Index Column.Name Column.Type
## 1 1 FP001 integer
## 2 2 FP002 integer
## 3 3 FP003 integer
## 4 4 FP004 integer
## 5 5 FP005 integer
## 6 6 FP006 integer
## 7 7 FP007 integer
## 8 8 FP008 integer
## 9 9 FP009 integer
## 10 10 FP010 integer
## 11 11 FP011 integer
## 12 12 FP012 integer
## 13 13 FP013 integer
## 14 14 FP014 integer
## 15 15 FP015 integer
## 16 16 FP016 integer
## 17 17 FP017 integer
## 18 18 FP018 integer
## 19 19 FP019 integer
## 20 20 FP020 integer
## 21 21 FP021 integer
## 22 22 FP022 integer
## 23 23 FP023 integer
## 24 24 FP024 integer
## 25 25 FP025 integer
## 26 26 FP026 integer
## 27 27 FP027 integer
## 28 28 FP028 integer
## 29 29 FP029 integer
## 30 30 FP030 integer
## 31 31 FP031 integer
## 32 32 FP032 integer
## 33 33 FP033 integer
## 34 34 FP034 integer
## 35 35 FP035 integer
## 36 36 FP036 integer
## 37 37 FP037 integer
## 38 38 FP038 integer
## 39 39 FP039 integer
## 40 40 FP040 integer
## 41 41 FP041 integer
## 42 42 FP042 integer
## 43 43 FP043 integer
## 44 44 FP044 integer
## 45 45 FP045 integer
## 46 46 FP046 integer
## 47 47 FP047 integer
## 48 48 FP048 integer
## 49 49 FP049 integer
## 50 50 FP050 integer
## 51 51 FP051 integer
## 52 52 FP052 integer
## 53 53 FP053 integer
## 54 54 FP054 integer
## 55 55 FP055 integer
## 56 56 FP056 integer
## 57 57 FP057 integer
## 58 58 FP058 integer
## 59 59 FP059 integer
## 60 60 FP060 integer
## 61 61 FP061 integer
## 62 62 FP062 integer
## 63 63 FP063 integer
## 64 64 FP064 integer
## 65 65 FP065 integer
## 66 66 FP066 integer
## 67 67 FP067 integer
## 68 68 FP068 integer
## 69 69 FP069 integer
## 70 70 FP070 integer
## 71 71 FP071 integer
## 72 72 FP072 integer
## 73 73 FP073 integer
## 74 74 FP074 integer
## 75 75 FP075 integer
## 76 76 FP076 integer
## 77 77 FP077 integer
## 78 78 FP078 integer
## 79 79 FP079 integer
## 80 80 FP080 integer
## 81 81 FP081 integer
## 82 82 FP082 integer
## 83 83 FP083 integer
## 84 84 FP084 integer
## 85 85 FP085 integer
## 86 86 FP086 integer
## 87 87 FP087 integer
## 88 88 FP088 integer
## 89 89 FP089 integer
## 90 90 FP090 integer
## 91 91 FP091 integer
## 92 92 FP092 integer
## 93 93 FP093 integer
## 94 94 FP094 integer
## 95 95 FP095 integer
## 96 96 FP096 integer
## 97 97 FP097 integer
## 98 98 FP098 integer
## 99 99 FP099 integer
## 100 100 FP100 integer
## 101 101 FP101 integer
## 102 102 FP102 integer
## 103 103 FP103 integer
## 104 104 FP104 integer
## 105 105 FP105 integer
## 106 106 FP106 integer
## 107 107 FP107 integer
## 108 108 FP108 integer
## 109 109 FP109 integer
## 110 110 FP110 integer
## 111 111 FP111 integer
## 112 112 FP112 integer
## 113 113 FP113 integer
## 114 114 FP114 integer
## 115 115 FP115 integer
## 116 116 FP116 integer
## 117 117 FP117 integer
## 118 118 FP118 integer
## 119 119 FP119 integer
## 120 120 FP120 integer
## 121 121 FP121 integer
## 122 122 FP122 integer
## 123 123 FP123 integer
## 124 124 FP124 integer
## 125 125 FP125 integer
## 126 126 FP126 integer
## 127 127 FP127 integer
## 128 128 FP128 integer
## 129 129 FP129 integer
## 130 130 FP130 integer
## 131 131 FP131 integer
## 132 132 FP132 integer
## 133 133 FP133 integer
## 134 134 FP134 integer
## 135 135 FP135 integer
## 136 136 FP136 integer
## 137 137 FP137 integer
## 138 138 FP138 integer
## 139 139 FP139 integer
## 140 140 FP140 integer
## 141 141 FP141 integer
## 142 142 FP142 integer
## 143 143 FP143 integer
## 144 144 FP144 integer
## 145 145 FP145 integer
## 146 146 FP146 integer
## 147 147 FP147 integer
## 148 148 FP148 integer
## 149 149 FP149 integer
## 150 150 FP150 integer
## 151 151 FP151 integer
## 152 152 FP152 integer
## 153 153 FP153 integer
## 154 154 FP154 integer
## 155 155 FP155 integer
## 156 156 FP156 integer
## 157 157 FP157 integer
## 158 158 FP158 integer
## 159 159 FP159 integer
## 160 160 FP160 integer
## 161 161 FP161 integer
## 162 162 FP162 integer
## 163 163 FP163 integer
## 164 164 FP164 integer
## 165 165 FP165 integer
## 166 166 FP166 integer
## 167 167 FP167 integer
## 168 168 FP168 integer
## 169 169 FP169 integer
## 170 170 FP170 integer
## 171 171 FP171 integer
## 172 172 FP172 integer
## 173 173 FP173 integer
## 174 174 FP174 integer
## 175 175 FP175 integer
## 176 176 FP176 integer
## 177 177 FP177 integer
## 178 178 FP178 integer
## 179 179 FP179 integer
## 180 180 FP180 integer
## 181 181 FP181 integer
## 182 182 FP182 integer
## 183 183 FP183 integer
## 184 184 FP184 integer
## 185 185 FP185 integer
## 186 186 FP186 integer
## 187 187 FP187 integer
## 188 188 FP188 integer
## 189 189 FP189 integer
## 190 190 FP190 integer
## 191 191 FP191 integer
## 192 192 FP192 integer
## 193 193 FP193 integer
## 194 194 FP194 integer
## 195 195 FP195 integer
## 196 196 FP196 integer
## 197 197 FP197 integer
## 198 198 FP198 integer
## 199 199 FP199 integer
## 200 200 FP200 integer
## 201 201 FP201 integer
## 202 202 FP202 integer
## 203 203 FP203 integer
## 204 204 FP204 integer
## 205 205 FP205 integer
## 206 206 FP206 integer
## 207 207 FP207 integer
## 208 208 FP208 integer
## 209 209 MolWeight numeric
## 210 210 NumAtoms integer
## 211 211 NumNonHAtoms integer
## 212 212 NumBonds integer
## 213 213 NumNonHBonds integer
## 214 214 NumMultBonds integer
## 215 215 NumRotBonds integer
## 216 216 NumDblBonds integer
## 217 217 NumAromaticBonds integer
## 218 218 NumHydrogen integer
## 219 219 NumCarbon integer
## 220 220 NumNitrogen integer
## 221 221 NumOxygen integer
## 222 222 NumSulfer integer
## 223 223 NumChlorine integer
## 224 224 NumHalogen integer
## 225 225 NumRings integer
## 226 226 HydrophilicFactor numeric
## 227 227 SurfaceArea1 numeric
## 228 228 SurfaceArea2 numeric
## 229 229 Log_Solubility_Class factor1.2 Data Quality Assessment
Data quality assessment:
[A] No missing observations noted for any variable.
[B] Low variance observed for 127 variables with First.Second.Mode.Ratio>5.
[B.1]-[B.33] FP013 to FP045 variables (factor)
[B.34]-[B.45] FP048 to FP059 variables (factor)
[B.46] FP114 variable (factor)
[B.47]-[B.50] FP119 to FP122 variable (factor)
[B.51]-[B.88] FP124 to FP161 variables (factor)
[B.89]-[B.118] FP172 to FP201 variables (factor)
[B.119]-[B.124] FP203 to FP208 variables (factor)
[B.125] NumSulfer variable (numeric)
[B.126] NumChlorine variable (numeric)
[B.127] NumHalogen variable (numeric)
[C] Low variance observed for 4 variables with Unique.Count.Ratio<0.01.
[C.1] NumDblBonds variable (numeric)
[C.2] NumNitrogen variable (numeric)
[C.3] NumSulfer variable (numeric)
[C.4] NumRings variable (numeric)
[D] High skewness observed for 3 variables with Skewness>3 or Skewness<(-3).
[D.1] NumSulfer variable (numeric)
[D.2] NumChlorine variable (numeric)
[D.3] HydrophilicFactor variable (numeric)
##################################
# Loading dataset
##################################
DQA <- Solubility_Train
##################################
# Formulating an overall data quality assessment summary
##################################
(DQA.Summary <- data.frame(
Column.Index=c(1:length(names(DQA))),
Column.Name= names(DQA),
Column.Type=sapply(DQA, function(x) class(x)),
Row.Count=sapply(DQA, function(x) nrow(DQA)),
NA.Count=sapply(DQA,function(x)sum(is.na(x))),
Fill.Rate=sapply(DQA,function(x)format(round((sum(!is.na(x))/nrow(DQA)),3),nsmall=3)),
row.names=NULL)
)## Column.Index Column.Name Column.Type Row.Count NA.Count Fill.Rate
## 1 1 FP001 integer 951 0 1.000
## 2 2 FP002 integer 951 0 1.000
## 3 3 FP003 integer 951 0 1.000
## 4 4 FP004 integer 951 0 1.000
## 5 5 FP005 integer 951 0 1.000
## 6 6 FP006 integer 951 0 1.000
## 7 7 FP007 integer 951 0 1.000
## 8 8 FP008 integer 951 0 1.000
## 9 9 FP009 integer 951 0 1.000
## 10 10 FP010 integer 951 0 1.000
## 11 11 FP011 integer 951 0 1.000
## 12 12 FP012 integer 951 0 1.000
## 13 13 FP013 integer 951 0 1.000
## 14 14 FP014 integer 951 0 1.000
## 15 15 FP015 integer 951 0 1.000
## 16 16 FP016 integer 951 0 1.000
## 17 17 FP017 integer 951 0 1.000
## 18 18 FP018 integer 951 0 1.000
## 19 19 FP019 integer 951 0 1.000
## 20 20 FP020 integer 951 0 1.000
## 21 21 FP021 integer 951 0 1.000
## 22 22 FP022 integer 951 0 1.000
## 23 23 FP023 integer 951 0 1.000
## 24 24 FP024 integer 951 0 1.000
## 25 25 FP025 integer 951 0 1.000
## 26 26 FP026 integer 951 0 1.000
## 27 27 FP027 integer 951 0 1.000
## 28 28 FP028 integer 951 0 1.000
## 29 29 FP029 integer 951 0 1.000
## 30 30 FP030 integer 951 0 1.000
## 31 31 FP031 integer 951 0 1.000
## 32 32 FP032 integer 951 0 1.000
## 33 33 FP033 integer 951 0 1.000
## 34 34 FP034 integer 951 0 1.000
## 35 35 FP035 integer 951 0 1.000
## 36 36 FP036 integer 951 0 1.000
## 37 37 FP037 integer 951 0 1.000
## 38 38 FP038 integer 951 0 1.000
## 39 39 FP039 integer 951 0 1.000
## 40 40 FP040 integer 951 0 1.000
## 41 41 FP041 integer 951 0 1.000
## 42 42 FP042 integer 951 0 1.000
## 43 43 FP043 integer 951 0 1.000
## 44 44 FP044 integer 951 0 1.000
## 45 45 FP045 integer 951 0 1.000
## 46 46 FP046 integer 951 0 1.000
## 47 47 FP047 integer 951 0 1.000
## 48 48 FP048 integer 951 0 1.000
## 49 49 FP049 integer 951 0 1.000
## 50 50 FP050 integer 951 0 1.000
## 51 51 FP051 integer 951 0 1.000
## 52 52 FP052 integer 951 0 1.000
## 53 53 FP053 integer 951 0 1.000
## 54 54 FP054 integer 951 0 1.000
## 55 55 FP055 integer 951 0 1.000
## 56 56 FP056 integer 951 0 1.000
## 57 57 FP057 integer 951 0 1.000
## 58 58 FP058 integer 951 0 1.000
## 59 59 FP059 integer 951 0 1.000
## 60 60 FP060 integer 951 0 1.000
## 61 61 FP061 integer 951 0 1.000
## 62 62 FP062 integer 951 0 1.000
## 63 63 FP063 integer 951 0 1.000
## 64 64 FP064 integer 951 0 1.000
## 65 65 FP065 integer 951 0 1.000
## 66 66 FP066 integer 951 0 1.000
## 67 67 FP067 integer 951 0 1.000
## 68 68 FP068 integer 951 0 1.000
## 69 69 FP069 integer 951 0 1.000
## 70 70 FP070 integer 951 0 1.000
## 71 71 FP071 integer 951 0 1.000
## 72 72 FP072 integer 951 0 1.000
## 73 73 FP073 integer 951 0 1.000
## 74 74 FP074 integer 951 0 1.000
## 75 75 FP075 integer 951 0 1.000
## 76 76 FP076 integer 951 0 1.000
## 77 77 FP077 integer 951 0 1.000
## 78 78 FP078 integer 951 0 1.000
## 79 79 FP079 integer 951 0 1.000
## 80 80 FP080 integer 951 0 1.000
## 81 81 FP081 integer 951 0 1.000
## 82 82 FP082 integer 951 0 1.000
## 83 83 FP083 integer 951 0 1.000
## 84 84 FP084 integer 951 0 1.000
## 85 85 FP085 integer 951 0 1.000
## 86 86 FP086 integer 951 0 1.000
## 87 87 FP087 integer 951 0 1.000
## 88 88 FP088 integer 951 0 1.000
## 89 89 FP089 integer 951 0 1.000
## 90 90 FP090 integer 951 0 1.000
## 91 91 FP091 integer 951 0 1.000
## 92 92 FP092 integer 951 0 1.000
## 93 93 FP093 integer 951 0 1.000
## 94 94 FP094 integer 951 0 1.000
## 95 95 FP095 integer 951 0 1.000
## 96 96 FP096 integer 951 0 1.000
## 97 97 FP097 integer 951 0 1.000
## 98 98 FP098 integer 951 0 1.000
## 99 99 FP099 integer 951 0 1.000
## 100 100 FP100 integer 951 0 1.000
## 101 101 FP101 integer 951 0 1.000
## 102 102 FP102 integer 951 0 1.000
## 103 103 FP103 integer 951 0 1.000
## 104 104 FP104 integer 951 0 1.000
## 105 105 FP105 integer 951 0 1.000
## 106 106 FP106 integer 951 0 1.000
## 107 107 FP107 integer 951 0 1.000
## 108 108 FP108 integer 951 0 1.000
## 109 109 FP109 integer 951 0 1.000
## 110 110 FP110 integer 951 0 1.000
## 111 111 FP111 integer 951 0 1.000
## 112 112 FP112 integer 951 0 1.000
## 113 113 FP113 integer 951 0 1.000
## 114 114 FP114 integer 951 0 1.000
## 115 115 FP115 integer 951 0 1.000
## 116 116 FP116 integer 951 0 1.000
## 117 117 FP117 integer 951 0 1.000
## 118 118 FP118 integer 951 0 1.000
## 119 119 FP119 integer 951 0 1.000
## 120 120 FP120 integer 951 0 1.000
## 121 121 FP121 integer 951 0 1.000
## 122 122 FP122 integer 951 0 1.000
## 123 123 FP123 integer 951 0 1.000
## 124 124 FP124 integer 951 0 1.000
## 125 125 FP125 integer 951 0 1.000
## 126 126 FP126 integer 951 0 1.000
## 127 127 FP127 integer 951 0 1.000
## 128 128 FP128 integer 951 0 1.000
## 129 129 FP129 integer 951 0 1.000
## 130 130 FP130 integer 951 0 1.000
## 131 131 FP131 integer 951 0 1.000
## 132 132 FP132 integer 951 0 1.000
## 133 133 FP133 integer 951 0 1.000
## 134 134 FP134 integer 951 0 1.000
## 135 135 FP135 integer 951 0 1.000
## 136 136 FP136 integer 951 0 1.000
## 137 137 FP137 integer 951 0 1.000
## 138 138 FP138 integer 951 0 1.000
## 139 139 FP139 integer 951 0 1.000
## 140 140 FP140 integer 951 0 1.000
## 141 141 FP141 integer 951 0 1.000
## 142 142 FP142 integer 951 0 1.000
## 143 143 FP143 integer 951 0 1.000
## 144 144 FP144 integer 951 0 1.000
## 145 145 FP145 integer 951 0 1.000
## 146 146 FP146 integer 951 0 1.000
## 147 147 FP147 integer 951 0 1.000
## 148 148 FP148 integer 951 0 1.000
## 149 149 FP149 integer 951 0 1.000
## 150 150 FP150 integer 951 0 1.000
## 151 151 FP151 integer 951 0 1.000
## 152 152 FP152 integer 951 0 1.000
## 153 153 FP153 integer 951 0 1.000
## 154 154 FP154 integer 951 0 1.000
## 155 155 FP155 integer 951 0 1.000
## 156 156 FP156 integer 951 0 1.000
## 157 157 FP157 integer 951 0 1.000
## 158 158 FP158 integer 951 0 1.000
## 159 159 FP159 integer 951 0 1.000
## 160 160 FP160 integer 951 0 1.000
## 161 161 FP161 integer 951 0 1.000
## 162 162 FP162 integer 951 0 1.000
## 163 163 FP163 integer 951 0 1.000
## 164 164 FP164 integer 951 0 1.000
## 165 165 FP165 integer 951 0 1.000
## 166 166 FP166 integer 951 0 1.000
## 167 167 FP167 integer 951 0 1.000
## 168 168 FP168 integer 951 0 1.000
## 169 169 FP169 integer 951 0 1.000
## 170 170 FP170 integer 951 0 1.000
## 171 171 FP171 integer 951 0 1.000
## 172 172 FP172 integer 951 0 1.000
## 173 173 FP173 integer 951 0 1.000
## 174 174 FP174 integer 951 0 1.000
## 175 175 FP175 integer 951 0 1.000
## 176 176 FP176 integer 951 0 1.000
## 177 177 FP177 integer 951 0 1.000
## 178 178 FP178 integer 951 0 1.000
## 179 179 FP179 integer 951 0 1.000
## 180 180 FP180 integer 951 0 1.000
## 181 181 FP181 integer 951 0 1.000
## 182 182 FP182 integer 951 0 1.000
## 183 183 FP183 integer 951 0 1.000
## 184 184 FP184 integer 951 0 1.000
## 185 185 FP185 integer 951 0 1.000
## 186 186 FP186 integer 951 0 1.000
## 187 187 FP187 integer 951 0 1.000
## 188 188 FP188 integer 951 0 1.000
## 189 189 FP189 integer 951 0 1.000
## 190 190 FP190 integer 951 0 1.000
## 191 191 FP191 integer 951 0 1.000
## 192 192 FP192 integer 951 0 1.000
## 193 193 FP193 integer 951 0 1.000
## 194 194 FP194 integer 951 0 1.000
## 195 195 FP195 integer 951 0 1.000
## 196 196 FP196 integer 951 0 1.000
## 197 197 FP197 integer 951 0 1.000
## 198 198 FP198 integer 951 0 1.000
## 199 199 FP199 integer 951 0 1.000
## 200 200 FP200 integer 951 0 1.000
## 201 201 FP201 integer 951 0 1.000
## 202 202 FP202 integer 951 0 1.000
## 203 203 FP203 integer 951 0 1.000
## 204 204 FP204 integer 951 0 1.000
## 205 205 FP205 integer 951 0 1.000
## 206 206 FP206 integer 951 0 1.000
## 207 207 FP207 integer 951 0 1.000
## 208 208 FP208 integer 951 0 1.000
## 209 209 MolWeight numeric 951 0 1.000
## 210 210 NumAtoms integer 951 0 1.000
## 211 211 NumNonHAtoms integer 951 0 1.000
## 212 212 NumBonds integer 951 0 1.000
## 213 213 NumNonHBonds integer 951 0 1.000
## 214 214 NumMultBonds integer 951 0 1.000
## 215 215 NumRotBonds integer 951 0 1.000
## 216 216 NumDblBonds integer 951 0 1.000
## 217 217 NumAromaticBonds integer 951 0 1.000
## 218 218 NumHydrogen integer 951 0 1.000
## 219 219 NumCarbon integer 951 0 1.000
## 220 220 NumNitrogen integer 951 0 1.000
## 221 221 NumOxygen integer 951 0 1.000
## 222 222 NumSulfer integer 951 0 1.000
## 223 223 NumChlorine integer 951 0 1.000
## 224 224 NumHalogen integer 951 0 1.000
## 225 225 NumRings integer 951 0 1.000
## 226 226 HydrophilicFactor numeric 951 0 1.000
## 227 227 SurfaceArea1 numeric 951 0 1.000
## 228 228 SurfaceArea2 numeric 951 0 1.000
## 229 229 Log_Solubility_Class factor 951 0 1.000##################################
# Listing all predictors
##################################
DQA.Predictors <- DQA[,!names(DQA) %in% c("Log_Solubility_Class")]
##################################
# Listing all numeric predictors
##################################
DQA.Predictors.Numeric <- DQA.Predictors[,-(grep("FP", names(DQA.Predictors)))]
if (length(names(DQA.Predictors.Numeric))>0) {
print(paste0("There are ",
(length(names(DQA.Predictors.Numeric))),
" numeric predictor variable(s)."))
} else {
print("There are no numeric predictor variables.")
}## [1] "There are 20 numeric predictor variable(s)."##################################
# Listing all factor predictors
##################################
DQA.Predictors.Factor <-as.data.frame(lapply(DQA.Predictors[(grep("FP", names(DQA.Predictors)))],factor))
if (length(names(DQA.Predictors.Factor))>0) {
print(paste0("There are ",
(length(names(DQA.Predictors.Factor))),
" factor predictor variable(s)."))
} else {
print("There are no factor predictor variables.")
}## [1] "There are 208 factor predictor variable(s)."##################################
# Formulating a data quality assessment summary for factor predictors
##################################
if (length(names(DQA.Predictors.Factor))>0) {
##################################
# Formulating a function to determine the first mode
##################################
FirstModes <- function(x) {
ux <- unique(na.omit(x))
tab <- tabulate(match(x, ux))
ux[tab == max(tab)]
}
##################################
# Formulating a function to determine the second mode
##################################
SecondModes <- function(x) {
ux <- unique(na.omit(x))
tab <- tabulate(match(x, ux))
fm = ux[tab == max(tab)]
sm = x[!(x %in% fm)]
usm <- unique(sm)
tabsm <- tabulate(match(sm, usm))
ifelse(is.na(usm[tabsm == max(tabsm)])==TRUE,
return("x"),
return(usm[tabsm == max(tabsm)]))
}
(DQA.Predictors.Factor.Summary <- data.frame(
Column.Name= names(DQA.Predictors.Factor),
Column.Type=sapply(DQA.Predictors.Factor, function(x) class(x)),
Unique.Count=sapply(DQA.Predictors.Factor, function(x) length(unique(x))),
First.Mode.Value=sapply(DQA.Predictors.Factor, function(x) as.character(FirstModes(x)[1])),
Second.Mode.Value=sapply(DQA.Predictors.Factor, function(x) as.character(SecondModes(x)[1])),
First.Mode.Count=sapply(DQA.Predictors.Factor, function(x) sum(na.omit(x) == FirstModes(x)[1])),
Second.Mode.Count=sapply(DQA.Predictors.Factor, function(x) sum(na.omit(x) == SecondModes(x)[1])),
Unique.Count.Ratio=sapply(DQA.Predictors.Factor, function(x) format(round((length(unique(x))/nrow(DQA.Predictors.Factor)),3), nsmall=3)),
First.Second.Mode.Ratio=sapply(DQA.Predictors.Factor, function(x) format(round((sum(na.omit(x) == FirstModes(x)[1])/sum(na.omit(x) == SecondModes(x)[1])),3), nsmall=3)),
row.names=NULL)
)
} ## Column.Name Column.Type Unique.Count First.Mode.Value Second.Mode.Value
## 1 FP001 factor 2 0 1
## 2 FP002 factor 2 1 0
## 3 FP003 factor 2 0 1
## 4 FP004 factor 2 1 0
## 5 FP005 factor 2 1 0
## 6 FP006 factor 2 0 1
## 7 FP007 factor 2 0 1
## 8 FP008 factor 2 0 1
## 9 FP009 factor 2 0 1
## 10 FP010 factor 2 0 1
## 11 FP011 factor 2 0 1
## 12 FP012 factor 2 0 1
## 13 FP013 factor 2 0 1
## 14 FP014 factor 2 0 1
## 15 FP015 factor 2 1 0
## 16 FP016 factor 2 0 1
## 17 FP017 factor 2 0 1
## 18 FP018 factor 2 0 1
## 19 FP019 factor 2 0 1
## 20 FP020 factor 2 0 1
## 21 FP021 factor 2 0 1
## 22 FP022 factor 2 0 1
## 23 FP023 factor 2 0 1
## 24 FP024 factor 2 0 1
## 25 FP025 factor 2 0 1
## 26 FP026 factor 2 0 1
## 27 FP027 factor 2 0 1
## 28 FP028 factor 2 0 1
## 29 FP029 factor 2 0 1
## 30 FP030 factor 2 0 1
## 31 FP031 factor 2 0 1
## 32 FP032 factor 2 0 1
## 33 FP033 factor 2 0 1
## 34 FP034 factor 2 0 1
## 35 FP035 factor 2 0 1
## 36 FP036 factor 2 0 1
## 37 FP037 factor 2 0 1
## 38 FP038 factor 2 0 1
## 39 FP039 factor 2 0 1
## 40 FP040 factor 2 0 1
## 41 FP041 factor 2 0 1
## 42 FP042 factor 2 0 1
## 43 FP043 factor 2 0 1
## 44 FP044 factor 2 0 1
## 45 FP045 factor 2 0 1
## 46 FP046 factor 2 0 1
## 47 FP047 factor 2 0 1
## 48 FP048 factor 2 0 1
## 49 FP049 factor 2 0 1
## 50 FP050 factor 2 0 1
## 51 FP051 factor 2 0 1
## 52 FP052 factor 2 0 1
## 53 FP053 factor 2 0 1
## 54 FP054 factor 2 0 1
## 55 FP055 factor 2 0 1
## 56 FP056 factor 2 0 1
## 57 FP057 factor 2 0 1
## 58 FP058 factor 2 0 1
## 59 FP059 factor 2 0 1
## 60 FP060 factor 2 0 1
## 61 FP061 factor 2 0 1
## 62 FP062 factor 2 0 1
## 63 FP063 factor 2 0 1
## 64 FP064 factor 2 0 1
## 65 FP065 factor 2 1 0
## 66 FP066 factor 2 1 0
## 67 FP067 factor 2 0 1
## 68 FP068 factor 2 0 1
## 69 FP069 factor 2 0 1
## 70 FP070 factor 2 0 1
## 71 FP071 factor 2 0 1
## 72 FP072 factor 2 1 0
## 73 FP073 factor 2 0 1
## 74 FP074 factor 2 0 1
## 75 FP075 factor 2 0 1
## 76 FP076 factor 2 0 1
## 77 FP077 factor 2 0 1
## 78 FP078 factor 2 0 1
## 79 FP079 factor 2 1 0
## 80 FP080 factor 2 0 1
## 81 FP081 factor 2 0 1
## 82 FP082 factor 2 1 0
## 83 FP083 factor 2 0 1
## 84 FP084 factor 2 0 1
## 85 FP085 factor 2 0 1
## 86 FP086 factor 2 0 1
## 87 FP087 factor 2 1 0
## 88 FP088 factor 2 0 1
## 89 FP089 factor 2 0 1
## 90 FP090 factor 2 0 1
## 91 FP091 factor 2 0 1
## 92 FP092 factor 2 0 1
## 93 FP093 factor 2 0 1
## 94 FP094 factor 2 0 1
## 95 FP095 factor 2 0 1
## 96 FP096 factor 2 0 1
## 97 FP097 factor 2 0 1
## 98 FP098 factor 2 0 1
## 99 FP099 factor 2 0 1
## 100 FP100 factor 2 0 1
## 101 FP101 factor 2 0 1
## 102 FP102 factor 2 0 1
## 103 FP103 factor 2 0 1
## 104 FP104 factor 2 0 1
## 105 FP105 factor 2 0 1
## 106 FP106 factor 2 0 1
## 107 FP107 factor 2 0 1
## 108 FP108 factor 2 0 1
## 109 FP109 factor 2 0 1
## 110 FP110 factor 2 0 1
## 111 FP111 factor 2 0 1
## 112 FP112 factor 2 0 1
## 113 FP113 factor 2 0 1
## 114 FP114 factor 2 0 1
## 115 FP115 factor 2 0 1
## 116 FP116 factor 2 0 1
## 117 FP117 factor 2 0 1
## 118 FP118 factor 2 0 1
## 119 FP119 factor 2 0 1
## 120 FP120 factor 2 0 1
## 121 FP121 factor 2 0 1
## 122 FP122 factor 2 0 1
## 123 FP123 factor 2 0 1
## 124 FP124 factor 2 0 1
## 125 FP125 factor 2 0 1
## 126 FP126 factor 2 0 1
## 127 FP127 factor 2 0 1
## 128 FP128 factor 2 0 1
## 129 FP129 factor 2 0 1
## 130 FP130 factor 2 0 1
## 131 FP131 factor 2 0 1
## 132 FP132 factor 2 0 1
## 133 FP133 factor 2 0 1
## 134 FP134 factor 2 0 1
## 135 FP135 factor 2 0 1
## 136 FP136 factor 2 0 1
## 137 FP137 factor 2 0 1
## 138 FP138 factor 2 0 1
## 139 FP139 factor 2 0 1
## 140 FP140 factor 2 0 1
## 141 FP141 factor 2 0 1
## 142 FP142 factor 2 0 1
## 143 FP143 factor 2 0 1
## 144 FP144 factor 2 0 1
## 145 FP145 factor 2 0 1
## 146 FP146 factor 2 0 1
## 147 FP147 factor 2 0 1
## 148 FP148 factor 2 0 1
## 149 FP149 factor 2 0 1
## 150 FP150 factor 2 0 1
## 151 FP151 factor 2 0 1
## 152 FP152 factor 2 0 1
## 153 FP153 factor 2 0 1
## 154 FP154 factor 2 0 1
## 155 FP155 factor 2 0 1
## 156 FP156 factor 2 0 1
## 157 FP157 factor 2 0 1
## 158 FP158 factor 2 0 1
## 159 FP159 factor 2 0 1
## 160 FP160 factor 2 0 1
## 161 FP161 factor 2 0 1
## 162 FP162 factor 2 0 1
## 163 FP163 factor 2 0 1
## 164 FP164 factor 2 1 0
## 165 FP165 factor 2 0 1
## 166 FP166 factor 2 0 1
## 167 FP167 factor 2 0 1
## 168 FP168 factor 2 1 0
## 169 FP169 factor 2 0 1
## 170 FP170 factor 2 0 1
## 171 FP171 factor 2 0 1
## 172 FP172 factor 2 0 1
## 173 FP173 factor 2 0 1
## 174 FP174 factor 2 0 1
## 175 FP175 factor 2 0 1
## 176 FP176 factor 2 0 1
## 177 FP177 factor 2 0 1
## 178 FP178 factor 2 0 1
## 179 FP179 factor 2 0 1
## 180 FP180 factor 2 0 1
## 181 FP181 factor 2 0 1
## 182 FP182 factor 2 0 1
## 183 FP183 factor 2 0 1
## 184 FP184 factor 2 0 1
## 185 FP185 factor 2 0 1
## 186 FP186 factor 2 0 1
## 187 FP187 factor 2 0 1
## 188 FP188 factor 2 0 1
## 189 FP189 factor 2 0 1
## 190 FP190 factor 2 0 1
## 191 FP191 factor 2 0 1
## 192 FP192 factor 2 0 1
## 193 FP193 factor 2 0 1
## 194 FP194 factor 2 0 1
## 195 FP195 factor 2 0 1
## 196 FP196 factor 2 0 1
## 197 FP197 factor 2 0 1
## 198 FP198 factor 2 0 1
## 199 FP199 factor 2 0 1
## 200 FP200 factor 2 0 1
## 201 FP201 factor 2 0 1
## 202 FP202 factor 2 0 1
## 203 FP203 factor 2 0 1
## 204 FP204 factor 2 0 1
## 205 FP205 factor 2 0 1
## 206 FP206 factor 2 0 1
## 207 FP207 factor 2 0 1
## 208 FP208 factor 2 0 1
## First.Mode.Count Second.Mode.Count Unique.Count.Ratio
## 1 482 469 0.002
## 2 513 438 0.002
## 3 536 415 0.002
## 4 556 395 0.002
## 5 551 400 0.002
## 6 570 381 0.002
## 7 605 346 0.002
## 8 641 310 0.002
## 9 685 266 0.002
## 10 781 170 0.002
## 11 747 204 0.002
## 12 783 168 0.002
## 13 793 158 0.002
## 14 798 153 0.002
## 15 818 133 0.002
## 16 812 139 0.002
## 17 814 137 0.002
## 18 826 125 0.002
## 19 835 116 0.002
## 20 837 114 0.002
## 21 836 115 0.002
## 22 852 99 0.002
## 23 834 117 0.002
## 24 844 107 0.002
## 25 841 110 0.002
## 26 871 80 0.002
## 27 858 93 0.002
## 28 850 101 0.002
## 29 854 97 0.002
## 30 862 89 0.002
## 31 866 85 0.002
## 32 881 70 0.002
## 33 885 66 0.002
## 34 875 76 0.002
## 35 882 69 0.002
## 36 879 72 0.002
## 37 884 67 0.002
## 38 869 82 0.002
## 39 880 71 0.002
## 40 886 65 0.002
## 41 891 60 0.002
## 42 897 54 0.002
## 43 888 63 0.002
## 44 894 57 0.002
## 45 898 53 0.002
## 46 651 300 0.002
## 47 698 253 0.002
## 48 833 118 0.002
## 49 835 116 0.002
## 50 844 107 0.002
## 51 847 104 0.002
## 52 864 87 0.002
## 53 862 89 0.002
## 54 879 72 0.002
## 55 900 51 0.002
## 56 889 62 0.002
## 57 837 114 0.002
## 58 843 108 0.002
## 59 899 52 0.002
## 60 493 458 0.002
## 61 526 425 0.002
## 62 535 416 0.002
## 63 546 405 0.002
## 64 555 396 0.002
## 65 564 387 0.002
## 66 580 371 0.002
## 67 590 361 0.002
## 68 607 344 0.002
## 69 607 344 0.002
## 70 613 338 0.002
## 71 640 311 0.002
## 72 626 325 0.002
## 73 656 295 0.002
## 74 642 309 0.002
## 75 629 322 0.002
## 76 639 312 0.002
## 77 646 305 0.002
## 78 662 289 0.002
## 79 656 295 0.002
## 80 663 288 0.002
## 81 686 265 0.002
## 82 679 272 0.002
## 83 691 260 0.002
## 84 679 272 0.002
## 85 708 243 0.002
## 86 695 256 0.002
## 87 691 260 0.002
## 88 701 250 0.002
## 89 716 235 0.002
## 90 714 237 0.002
## 91 737 214 0.002
## 92 719 232 0.002
## 93 719 232 0.002
## 94 731 220 0.002
## 95 742 209 0.002
## 96 744 207 0.002
## 97 727 224 0.002
## 98 725 226 0.002
## 99 735 216 0.002
## 100 731 220 0.002
## 101 726 225 0.002
## 102 759 192 0.002
## 103 743 208 0.002
## 104 739 212 0.002
## 105 746 205 0.002
## 106 769 182 0.002
## 107 750 201 0.002
## 108 756 195 0.002
## 109 783 168 0.002
## 110 755 196 0.002
## 111 764 187 0.002
## 112 766 185 0.002
## 113 765 186 0.002
## 114 803 148 0.002
## 115 781 170 0.002
## 116 768 183 0.002
## 117 781 170 0.002
## 118 768 183 0.002
## 119 796 155 0.002
## 120 793 158 0.002
## 121 818 133 0.002
## 122 795 156 0.002
## 123 792 159 0.002
## 124 797 154 0.002
## 125 803 148 0.002
## 126 810 141 0.002
## 127 818 133 0.002
## 128 810 141 0.002
## 129 819 132 0.002
## 130 851 100 0.002
## 131 831 120 0.002
## 132 832 119 0.002
## 133 831 120 0.002
## 134 830 121 0.002
## 135 831 120 0.002
## 136 836 115 0.002
## 137 841 110 0.002
## 138 845 106 0.002
## 139 873 78 0.002
## 140 845 106 0.002
## 141 840 111 0.002
## 142 847 104 0.002
## 143 874 77 0.002
## 144 852 99 0.002
## 145 852 99 0.002
## 146 853 98 0.002
## 147 851 100 0.002
## 148 868 83 0.002
## 149 865 86 0.002
## 150 876 75 0.002
## 151 898 53 0.002
## 152 873 78 0.002
## 153 877 74 0.002
## 154 915 36 0.002
## 155 885 66 0.002
## 156 884 67 0.002
## 157 892 59 0.002
## 158 900 51 0.002
## 159 884 67 0.002
## 160 886 65 0.002
## 161 888 63 0.002
## 162 480 471 0.002
## 163 498 453 0.002
## 164 597 354 0.002
## 165 619 332 0.002
## 166 636 315 0.002
## 167 639 312 0.002
## 168 633 318 0.002
## 169 774 177 0.002
## 170 776 175 0.002
## 171 790 161 0.002
## 172 807 144 0.002
## 173 816 135 0.002
## 174 827 124 0.002
## 175 823 128 0.002
## 176 835 116 0.002
## 177 836 115 0.002
## 178 836 115 0.002
## 179 858 93 0.002
## 180 849 102 0.002
## 181 862 89 0.002
## 182 857 94 0.002
## 183 879 72 0.002
## 184 871 80 0.002
## 185 870 81 0.002
## 186 878 73 0.002
## 187 882 69 0.002
## 188 886 65 0.002
## 189 878 73 0.002
## 190 882 69 0.002
## 191 884 67 0.002
## 192 893 58 0.002
## 193 892 59 0.002
## 194 895 56 0.002
## 195 893 58 0.002
## 196 897 54 0.002
## 197 901 50 0.002
## 198 897 54 0.002
## 199 906 45 0.002
## 200 904 47 0.002
## 201 901 50 0.002
## 202 706 245 0.002
## 203 842 109 0.002
## 204 857 94 0.002
## 205 877 74 0.002
## 206 894 57 0.002
## 207 897 54 0.002
## 208 844 107 0.002
## First.Second.Mode.Ratio
## 1 1.028
## 2 1.171
## 3 1.292
## 4 1.408
## 5 1.377
## 6 1.496
## 7 1.749
## 8 2.068
## 9 2.575
## 10 4.594
## 11 3.662
## 12 4.661
## 13 5.019
## 14 5.216
## 15 6.150
## 16 5.842
## 17 5.942
## 18 6.608
## 19 7.198
## 20 7.342
## 21 7.270
## 22 8.606
## 23 7.128
## 24 7.888
## 25 7.645
## 26 10.887
## 27 9.226
## 28 8.416
## 29 8.804
## 30 9.685
## 31 10.188
## 32 12.586
## 33 13.409
## 34 11.513
## 35 12.783
## 36 12.208
## 37 13.194
## 38 10.598
## 39 12.394
## 40 13.631
## 41 14.850
## 42 16.611
## 43 14.095
## 44 15.684
## 45 16.943
## 46 2.170
## 47 2.759
## 48 7.059
## 49 7.198
## 50 7.888
## 51 8.144
## 52 9.931
## 53 9.685
## 54 12.208
## 55 17.647
## 56 14.339
## 57 7.342
## 58 7.806
## 59 17.288
## 60 1.076
## 61 1.238
## 62 1.286
## 63 1.348
## 64 1.402
## 65 1.457
## 66 1.563
## 67 1.634
## 68 1.765
## 69 1.765
## 70 1.814
## 71 2.058
## 72 1.926
## 73 2.224
## 74 2.078
## 75 1.953
## 76 2.048
## 77 2.118
## 78 2.291
## 79 2.224
## 80 2.302
## 81 2.589
## 82 2.496
## 83 2.658
## 84 2.496
## 85 2.914
## 86 2.715
## 87 2.658
## 88 2.804
## 89 3.047
## 90 3.013
## 91 3.444
## 92 3.099
## 93 3.099
## 94 3.323
## 95 3.550
## 96 3.594
## 97 3.246
## 98 3.208
## 99 3.403
## 100 3.323
## 101 3.227
## 102 3.953
## 103 3.572
## 104 3.486
## 105 3.639
## 106 4.225
## 107 3.731
## 108 3.877
## 109 4.661
## 110 3.852
## 111 4.086
## 112 4.141
## 113 4.113
## 114 5.426
## 115 4.594
## 116 4.197
## 117 4.594
## 118 4.197
## 119 5.135
## 120 5.019
## 121 6.150
## 122 5.096
## 123 4.981
## 124 5.175
## 125 5.426
## 126 5.745
## 127 6.150
## 128 5.745
## 129 6.205
## 130 8.510
## 131 6.925
## 132 6.992
## 133 6.925
## 134 6.860
## 135 6.925
## 136 7.270
## 137 7.645
## 138 7.972
## 139 11.192
## 140 7.972
## 141 7.568
## 142 8.144
## 143 11.351
## 144 8.606
## 145 8.606
## 146 8.704
## 147 8.510
## 148 10.458
## 149 10.058
## 150 11.680
## 151 16.943
## 152 11.192
## 153 11.851
## 154 25.417
## 155 13.409
## 156 13.194
## 157 15.119
## 158 17.647
## 159 13.194
## 160 13.631
## 161 14.095
## 162 1.019
## 163 1.099
## 164 1.686
## 165 1.864
## 166 2.019
## 167 2.048
## 168 1.991
## 169 4.373
## 170 4.434
## 171 4.907
## 172 5.604
## 173 6.044
## 174 6.669
## 175 6.430
## 176 7.198
## 177 7.270
## 178 7.270
## 179 9.226
## 180 8.324
## 181 9.685
## 182 9.117
## 183 12.208
## 184 10.887
## 185 10.741
## 186 12.027
## 187 12.783
## 188 13.631
## 189 12.027
## 190 12.783
## 191 13.194
## 192 15.397
## 193 15.119
## 194 15.982
## 195 15.397
## 196 16.611
## 197 18.020
## 198 16.611
## 199 20.133
## 200 19.234
## 201 18.020
## 202 2.882
## 203 7.725
## 204 9.117
## 205 11.851
## 206 15.684
## 207 16.611
## 208 7.888##################################
# Formulating a data quality assessment summary for numeric predictors
##################################
if (length(names(DQA.Predictors.Numeric))>0) {
##################################
# Formulating a function to determine the first mode
##################################
FirstModes <- function(x) {
ux <- unique(na.omit(x))
tab <- tabulate(match(x, ux))
ux[tab == max(tab)]
}
##################################
# Formulating a function to determine the second mode
##################################
SecondModes <- function(x) {
ux <- unique(na.omit(x))
tab <- tabulate(match(x, ux))
fm = ux[tab == max(tab)]
sm = na.omit(x)[!(na.omit(x) %in% fm)]
usm <- unique(sm)
tabsm <- tabulate(match(sm, usm))
ifelse(is.na(usm[tabsm == max(tabsm)])==TRUE,
return(0.00001),
return(usm[tabsm == max(tabsm)]))
}
(DQA.Predictors.Numeric.Summary <- data.frame(
Column.Name= names(DQA.Predictors.Numeric),
Column.Type=sapply(DQA.Predictors.Numeric, function(x) class(x)),
Unique.Count=sapply(DQA.Predictors.Numeric, function(x) length(unique(x))),
Unique.Count.Ratio=sapply(DQA.Predictors.Numeric, function(x) format(round((length(unique(x))/nrow(DQA.Predictors.Numeric)),3), nsmall=3)),
First.Mode.Value=sapply(DQA.Predictors.Numeric, function(x) format(round((FirstModes(x)[1]),3),nsmall=3)),
Second.Mode.Value=sapply(DQA.Predictors.Numeric, function(x) format(round((SecondModes(x)[1]),3),nsmall=3)),
First.Mode.Count=sapply(DQA.Predictors.Numeric, function(x) sum(na.omit(x) == FirstModes(x)[1])),
Second.Mode.Count=sapply(DQA.Predictors.Numeric, function(x) sum(na.omit(x) == SecondModes(x)[1])),
First.Second.Mode.Ratio=sapply(DQA.Predictors.Numeric, function(x) format(round((sum(na.omit(x) == FirstModes(x)[1])/sum(na.omit(x) == SecondModes(x)[1])),3), nsmall=3)),
Minimum=sapply(DQA.Predictors.Numeric, function(x) format(round(min(x,na.rm = TRUE),3), nsmall=3)),
Mean=sapply(DQA.Predictors.Numeric, function(x) format(round(mean(x,na.rm = TRUE),3), nsmall=3)),
Median=sapply(DQA.Predictors.Numeric, function(x) format(round(median(x,na.rm = TRUE),3), nsmall=3)),
Maximum=sapply(DQA.Predictors.Numeric, function(x) format(round(max(x,na.rm = TRUE),3), nsmall=3)),
Skewness=sapply(DQA.Predictors.Numeric, function(x) format(round(skewness(x,na.rm = TRUE),3), nsmall=3)),
Kurtosis=sapply(DQA.Predictors.Numeric, function(x) format(round(kurtosis(x,na.rm = TRUE),3), nsmall=3)),
Percentile25th=sapply(DQA.Predictors.Numeric, function(x) format(round(quantile(x,probs=0.25,na.rm = TRUE),3), nsmall=3)),
Percentile75th=sapply(DQA.Predictors.Numeric, function(x) format(round(quantile(x,probs=0.75,na.rm = TRUE),3), nsmall=3)),
row.names=NULL)
)
}## Column.Name Column.Type Unique.Count Unique.Count.Ratio
## 1 MolWeight numeric 646 0.679
## 2 NumAtoms integer 66 0.069
## 3 NumNonHAtoms integer 36 0.038
## 4 NumBonds integer 72 0.076
## 5 NumNonHBonds integer 39 0.041
## 6 NumMultBonds integer 25 0.026
## 7 NumRotBonds integer 15 0.016
## 8 NumDblBonds integer 8 0.008
## 9 NumAromaticBonds integer 16 0.017
## 10 NumHydrogen integer 41 0.043
## 11 NumCarbon integer 28 0.029
## 12 NumNitrogen integer 7 0.007
## 13 NumOxygen integer 11 0.012
## 14 NumSulfer integer 5 0.005
## 15 NumChlorine integer 11 0.012
## 16 NumHalogen integer 11 0.012
## 17 NumRings integer 8 0.008
## 18 HydrophilicFactor numeric 369 0.388
## 19 SurfaceArea1 numeric 252 0.265
## 20 SurfaceArea2 numeric 287 0.302
## First.Mode.Value Second.Mode.Value First.Mode.Count Second.Mode.Count
## 1 102.200 116.230 16 14
## 2 22.000 24.000 73 51
## 3 8.000 11.000 104 73
## 4 23.000 19.000 69 56
## 5 8.000 7.000 82 66
## 6 0.000 7.000 158 122
## 7 0.000 1.000 272 186
## 8 0.000 1.000 427 268
## 9 0.000 6.000 400 302
## 10 12.000 8.000 83 79
## 11 6.000 7.000 105 97
## 12 0.000 1.000 546 191
## 13 0.000 2.000 325 218
## 14 0.000 1.000 830 96
## 15 0.000 1.000 750 81
## 16 0.000 1.000 685 107
## 17 1.000 0.000 323 260
## 18 -0.828 -0.158 21 20
## 19 0.000 20.230 218 76
## 20 0.000 20.230 211 75
## First.Second.Mode.Ratio Minimum Mean Median Maximum Skewness Kurtosis
## 1 1.143 46.090 201.654 179.230 665.810 0.988 3.945
## 2 1.431 5.000 25.507 22.000 94.000 1.364 5.523
## 3 1.425 2.000 13.161 12.000 47.000 0.993 4.129
## 4 1.232 4.000 25.909 23.000 97.000 1.360 5.408
## 5 1.242 1.000 13.563 12.000 50.000 0.969 3.842
## 6 1.295 0.000 6.148 6.000 25.000 0.670 3.053
## 7 1.462 0.000 2.251 2.000 16.000 1.577 6.437
## 8 1.593 0.000 1.006 1.000 7.000 1.360 4.760
## 9 1.325 0.000 5.121 6.000 25.000 0.796 3.241
## 10 1.051 0.000 12.346 11.000 47.000 1.262 5.261
## 11 1.082 1.000 9.893 9.000 33.000 0.927 3.616
## 12 2.859 0.000 0.813 0.000 6.000 1.554 4.831
## 13 1.491 0.000 1.574 1.000 13.000 1.772 8.494
## 14 8.646 0.000 0.164 0.000 4.000 3.842 21.526
## 15 9.259 0.000 0.556 0.000 10.000 3.178 13.780
## 16 6.402 0.000 0.698 0.000 10.000 2.691 10.808
## 17 1.242 0.000 1.402 1.000 7.000 1.034 3.875
## 18 1.050 -0.985 -0.021 -0.314 13.483 3.404 27.504
## 19 2.868 0.000 36.459 29.100 331.940 1.714 9.714
## 20 2.813 0.000 40.234 33.120 331.940 1.475 7.485
## Percentile25th Percentile75th
## 1 122.605 264.340
## 2 17.000 31.000
## 3 8.000 17.000
## 4 17.000 31.500
## 5 8.000 18.000
## 6 1.000 10.000
## 7 0.000 3.500
## 8 0.000 2.000
## 9 0.000 6.000
## 10 7.000 16.000
## 11 6.000 12.000
## 12 0.000 1.000
## 13 0.000 2.000
## 14 0.000 0.000
## 15 0.000 0.000
## 16 0.000 1.000
## 17 0.000 2.000
## 18 -0.763 0.313
## 19 9.230 53.280
## 20 10.630 60.660##################################
# Identifying potential data quality issues
##################################
##################################
# Checking for missing observations
##################################
if ((nrow(DQA.Summary[DQA.Summary$NA.Count>0,]))>0){
print(paste0("Missing observations noted for ",
(nrow(DQA.Summary[DQA.Summary$NA.Count>0,])),
" variable(s) with NA.Count>0 and Fill.Rate<1.0."))
DQA.Summary[DQA.Summary$NA.Count>0,]
} else {
print("No missing observations noted.")
}## [1] "No missing observations noted."##################################
# Checking for zero or near-zero variance predictors
##################################
if (length(names(DQA.Predictors.Factor))==0) {
print("No factor predictors noted.")
} else if (nrow(DQA.Predictors.Factor.Summary[as.numeric(as.character(DQA.Predictors.Factor.Summary$First.Second.Mode.Ratio))>5,])>0){
print(paste0("Low variance observed for ",
(nrow(DQA.Predictors.Factor.Summary[as.numeric(as.character(DQA.Predictors.Factor.Summary$First.Second.Mode.Ratio))>5,])),
" factor variable(s) with First.Second.Mode.Ratio>5."))
DQA.Predictors.Factor.Summary[as.numeric(as.character(DQA.Predictors.Factor.Summary$First.Second.Mode.Ratio))>5,]
} else {
print("No low variance factor predictors due to high first-second mode ratio noted.")
}## [1] "Low variance observed for 124 factor variable(s) with First.Second.Mode.Ratio>5."## Column.Name Column.Type Unique.Count First.Mode.Value Second.Mode.Value
## 13 FP013 factor 2 0 1
## 14 FP014 factor 2 0 1
## 15 FP015 factor 2 1 0
## 16 FP016 factor 2 0 1
## 17 FP017 factor 2 0 1
## 18 FP018 factor 2 0 1
## 19 FP019 factor 2 0 1
## 20 FP020 factor 2 0 1
## 21 FP021 factor 2 0 1
## 22 FP022 factor 2 0 1
## 23 FP023 factor 2 0 1
## 24 FP024 factor 2 0 1
## 25 FP025 factor 2 0 1
## 26 FP026 factor 2 0 1
## 27 FP027 factor 2 0 1
## 28 FP028 factor 2 0 1
## 29 FP029 factor 2 0 1
## 30 FP030 factor 2 0 1
## 31 FP031 factor 2 0 1
## 32 FP032 factor 2 0 1
## 33 FP033 factor 2 0 1
## 34 FP034 factor 2 0 1
## 35 FP035 factor 2 0 1
## 36 FP036 factor 2 0 1
## 37 FP037 factor 2 0 1
## 38 FP038 factor 2 0 1
## 39 FP039 factor 2 0 1
## 40 FP040 factor 2 0 1
## 41 FP041 factor 2 0 1
## 42 FP042 factor 2 0 1
## 43 FP043 factor 2 0 1
## 44 FP044 factor 2 0 1
## 45 FP045 factor 2 0 1
## 48 FP048 factor 2 0 1
## 49 FP049 factor 2 0 1
## 50 FP050 factor 2 0 1
## 51 FP051 factor 2 0 1
## 52 FP052 factor 2 0 1
## 53 FP053 factor 2 0 1
## 54 FP054 factor 2 0 1
## 55 FP055 factor 2 0 1
## 56 FP056 factor 2 0 1
## 57 FP057 factor 2 0 1
## 58 FP058 factor 2 0 1
## 59 FP059 factor 2 0 1
## 114 FP114 factor 2 0 1
## 119 FP119 factor 2 0 1
## 120 FP120 factor 2 0 1
## 121 FP121 factor 2 0 1
## 122 FP122 factor 2 0 1
## 124 FP124 factor 2 0 1
## 125 FP125 factor 2 0 1
## 126 FP126 factor 2 0 1
## 127 FP127 factor 2 0 1
## 128 FP128 factor 2 0 1
## 129 FP129 factor 2 0 1
## 130 FP130 factor 2 0 1
## 131 FP131 factor 2 0 1
## 132 FP132 factor 2 0 1
## 133 FP133 factor 2 0 1
## 134 FP134 factor 2 0 1
## 135 FP135 factor 2 0 1
## 136 FP136 factor 2 0 1
## 137 FP137 factor 2 0 1
## 138 FP138 factor 2 0 1
## 139 FP139 factor 2 0 1
## 140 FP140 factor 2 0 1
## 141 FP141 factor 2 0 1
## 142 FP142 factor 2 0 1
## 143 FP143 factor 2 0 1
## 144 FP144 factor 2 0 1
## 145 FP145 factor 2 0 1
## 146 FP146 factor 2 0 1
## 147 FP147 factor 2 0 1
## 148 FP148 factor 2 0 1
## 149 FP149 factor 2 0 1
## 150 FP150 factor 2 0 1
## 151 FP151 factor 2 0 1
## 152 FP152 factor 2 0 1
## 153 FP153 factor 2 0 1
## 154 FP154 factor 2 0 1
## 155 FP155 factor 2 0 1
## 156 FP156 factor 2 0 1
## 157 FP157 factor 2 0 1
## 158 FP158 factor 2 0 1
## 159 FP159 factor 2 0 1
## 160 FP160 factor 2 0 1
## 161 FP161 factor 2 0 1
## 172 FP172 factor 2 0 1
## 173 FP173 factor 2 0 1
## 174 FP174 factor 2 0 1
## 175 FP175 factor 2 0 1
## 176 FP176 factor 2 0 1
## 177 FP177 factor 2 0 1
## 178 FP178 factor 2 0 1
## 179 FP179 factor 2 0 1
## 180 FP180 factor 2 0 1
## 181 FP181 factor 2 0 1
## 182 FP182 factor 2 0 1
## 183 FP183 factor 2 0 1
## 184 FP184 factor 2 0 1
## 185 FP185 factor 2 0 1
## 186 FP186 factor 2 0 1
## 187 FP187 factor 2 0 1
## 188 FP188 factor 2 0 1
## 189 FP189 factor 2 0 1
## 190 FP190 factor 2 0 1
## 191 FP191 factor 2 0 1
## 192 FP192 factor 2 0 1
## 193 FP193 factor 2 0 1
## 194 FP194 factor 2 0 1
## 195 FP195 factor 2 0 1
## 196 FP196 factor 2 0 1
## 197 FP197 factor 2 0 1
## 198 FP198 factor 2 0 1
## 199 FP199 factor 2 0 1
## 200 FP200 factor 2 0 1
## 201 FP201 factor 2 0 1
## 203 FP203 factor 2 0 1
## 204 FP204 factor 2 0 1
## 205 FP205 factor 2 0 1
## 206 FP206 factor 2 0 1
## 207 FP207 factor 2 0 1
## 208 FP208 factor 2 0 1
## First.Mode.Count Second.Mode.Count Unique.Count.Ratio
## 13 793 158 0.002
## 14 798 153 0.002
## 15 818 133 0.002
## 16 812 139 0.002
## 17 814 137 0.002
## 18 826 125 0.002
## 19 835 116 0.002
## 20 837 114 0.002
## 21 836 115 0.002
## 22 852 99 0.002
## 23 834 117 0.002
## 24 844 107 0.002
## 25 841 110 0.002
## 26 871 80 0.002
## 27 858 93 0.002
## 28 850 101 0.002
## 29 854 97 0.002
## 30 862 89 0.002
## 31 866 85 0.002
## 32 881 70 0.002
## 33 885 66 0.002
## 34 875 76 0.002
## 35 882 69 0.002
## 36 879 72 0.002
## 37 884 67 0.002
## 38 869 82 0.002
## 39 880 71 0.002
## 40 886 65 0.002
## 41 891 60 0.002
## 42 897 54 0.002
## 43 888 63 0.002
## 44 894 57 0.002
## 45 898 53 0.002
## 48 833 118 0.002
## 49 835 116 0.002
## 50 844 107 0.002
## 51 847 104 0.002
## 52 864 87 0.002
## 53 862 89 0.002
## 54 879 72 0.002
## 55 900 51 0.002
## 56 889 62 0.002
## 57 837 114 0.002
## 58 843 108 0.002
## 59 899 52 0.002
## 114 803 148 0.002
## 119 796 155 0.002
## 120 793 158 0.002
## 121 818 133 0.002
## 122 795 156 0.002
## 124 797 154 0.002
## 125 803 148 0.002
## 126 810 141 0.002
## 127 818 133 0.002
## 128 810 141 0.002
## 129 819 132 0.002
## 130 851 100 0.002
## 131 831 120 0.002
## 132 832 119 0.002
## 133 831 120 0.002
## 134 830 121 0.002
## 135 831 120 0.002
## 136 836 115 0.002
## 137 841 110 0.002
## 138 845 106 0.002
## 139 873 78 0.002
## 140 845 106 0.002
## 141 840 111 0.002
## 142 847 104 0.002
## 143 874 77 0.002
## 144 852 99 0.002
## 145 852 99 0.002
## 146 853 98 0.002
## 147 851 100 0.002
## 148 868 83 0.002
## 149 865 86 0.002
## 150 876 75 0.002
## 151 898 53 0.002
## 152 873 78 0.002
## 153 877 74 0.002
## 154 915 36 0.002
## 155 885 66 0.002
## 156 884 67 0.002
## 157 892 59 0.002
## 158 900 51 0.002
## 159 884 67 0.002
## 160 886 65 0.002
## 161 888 63 0.002
## 172 807 144 0.002
## 173 816 135 0.002
## 174 827 124 0.002
## 175 823 128 0.002
## 176 835 116 0.002
## 177 836 115 0.002
## 178 836 115 0.002
## 179 858 93 0.002
## 180 849 102 0.002
## 181 862 89 0.002
## 182 857 94 0.002
## 183 879 72 0.002
## 184 871 80 0.002
## 185 870 81 0.002
## 186 878 73 0.002
## 187 882 69 0.002
## 188 886 65 0.002
## 189 878 73 0.002
## 190 882 69 0.002
## 191 884 67 0.002
## 192 893 58 0.002
## 193 892 59 0.002
## 194 895 56 0.002
## 195 893 58 0.002
## 196 897 54 0.002
## 197 901 50 0.002
## 198 897 54 0.002
## 199 906 45 0.002
## 200 904 47 0.002
## 201 901 50 0.002
## 203 842 109 0.002
## 204 857 94 0.002
## 205 877 74 0.002
## 206 894 57 0.002
## 207 897 54 0.002
## 208 844 107 0.002
## First.Second.Mode.Ratio
## 13 5.019
## 14 5.216
## 15 6.150
## 16 5.842
## 17 5.942
## 18 6.608
## 19 7.198
## 20 7.342
## 21 7.270
## 22 8.606
## 23 7.128
## 24 7.888
## 25 7.645
## 26 10.887
## 27 9.226
## 28 8.416
## 29 8.804
## 30 9.685
## 31 10.188
## 32 12.586
## 33 13.409
## 34 11.513
## 35 12.783
## 36 12.208
## 37 13.194
## 38 10.598
## 39 12.394
## 40 13.631
## 41 14.850
## 42 16.611
## 43 14.095
## 44 15.684
## 45 16.943
## 48 7.059
## 49 7.198
## 50 7.888
## 51 8.144
## 52 9.931
## 53 9.685
## 54 12.208
## 55 17.647
## 56 14.339
## 57 7.342
## 58 7.806
## 59 17.288
## 114 5.426
## 119 5.135
## 120 5.019
## 121 6.150
## 122 5.096
## 124 5.175
## 125 5.426
## 126 5.745
## 127 6.150
## 128 5.745
## 129 6.205
## 130 8.510
## 131 6.925
## 132 6.992
## 133 6.925
## 134 6.860
## 135 6.925
## 136 7.270
## 137 7.645
## 138 7.972
## 139 11.192
## 140 7.972
## 141 7.568
## 142 8.144
## 143 11.351
## 144 8.606
## 145 8.606
## 146 8.704
## 147 8.510
## 148 10.458
## 149 10.058
## 150 11.680
## 151 16.943
## 152 11.192
## 153 11.851
## 154 25.417
## 155 13.409
## 156 13.194
## 157 15.119
## 158 17.647
## 159 13.194
## 160 13.631
## 161 14.095
## 172 5.604
## 173 6.044
## 174 6.669
## 175 6.430
## 176 7.198
## 177 7.270
## 178 7.270
## 179 9.226
## 180 8.324
## 181 9.685
## 182 9.117
## 183 12.208
## 184 10.887
## 185 10.741
## 186 12.027
## 187 12.783
## 188 13.631
## 189 12.027
## 190 12.783
## 191 13.194
## 192 15.397
## 193 15.119
## 194 15.982
## 195 15.397
## 196 16.611
## 197 18.020
## 198 16.611
## 199 20.133
## 200 19.234
## 201 18.020
## 203 7.725
## 204 9.117
## 205 11.851
## 206 15.684
## 207 16.611
## 208 7.888if (length(names(DQA.Predictors.Numeric))==0) {
print("No numeric predictors noted.")
} else if (nrow(DQA.Predictors.Numeric.Summary[as.numeric(as.character(DQA.Predictors.Numeric.Summary$First.Second.Mode.Ratio))>5,])>0){
print(paste0("Low variance observed for ",
(nrow(DQA.Predictors.Numeric.Summary[as.numeric(as.character(DQA.Predictors.Numeric.Summary$First.Second.Mode.Ratio))>5,])),
" numeric variable(s) with First.Second.Mode.Ratio>5."))
DQA.Predictors.Numeric.Summary[as.numeric(as.character(DQA.Predictors.Numeric.Summary$First.Second.Mode.Ratio))>5,]
} else {
print("No low variance numeric predictors due to high first-second mode ratio noted.")
}## [1] "Low variance observed for 3 numeric variable(s) with First.Second.Mode.Ratio>5."## Column.Name Column.Type Unique.Count Unique.Count.Ratio First.Mode.Value
## 14 NumSulfer integer 5 0.005 0.000
## 15 NumChlorine integer 11 0.012 0.000
## 16 NumHalogen integer 11 0.012 0.000
## Second.Mode.Value First.Mode.Count Second.Mode.Count First.Second.Mode.Ratio
## 14 1.000 830 96 8.646
## 15 1.000 750 81 9.259
## 16 1.000 685 107 6.402
## Minimum Mean Median Maximum Skewness Kurtosis Percentile25th Percentile75th
## 14 0.000 0.164 0.000 4.000 3.842 21.526 0.000 0.000
## 15 0.000 0.556 0.000 10.000 3.178 13.780 0.000 0.000
## 16 0.000 0.698 0.000 10.000 2.691 10.808 0.000 1.000if (length(names(DQA.Predictors.Numeric))==0) {
print("No numeric predictors noted.")
} else if (nrow(DQA.Predictors.Numeric.Summary[as.numeric(as.character(DQA.Predictors.Numeric.Summary$Unique.Count.Ratio))<0.01,])>0){
print(paste0("Low variance observed for ",
(nrow(DQA.Predictors.Numeric.Summary[as.numeric(as.character(DQA.Predictors.Numeric.Summary$Unique.Count.Ratio))<0.01,])),
" numeric variable(s) with Unique.Count.Ratio<0.01."))
DQA.Predictors.Numeric.Summary[as.numeric(as.character(DQA.Predictors.Numeric.Summary$Unique.Count.Ratio))<0.01,]
} else {
print("No low variance numeric predictors due to low unique count ratio noted.")
}## [1] "Low variance observed for 4 numeric variable(s) with Unique.Count.Ratio<0.01."## Column.Name Column.Type Unique.Count Unique.Count.Ratio First.Mode.Value
## 8 NumDblBonds integer 8 0.008 0.000
## 12 NumNitrogen integer 7 0.007 0.000
## 14 NumSulfer integer 5 0.005 0.000
## 17 NumRings integer 8 0.008 1.000
## Second.Mode.Value First.Mode.Count Second.Mode.Count First.Second.Mode.Ratio
## 8 1.000 427 268 1.593
## 12 1.000 546 191 2.859
## 14 1.000 830 96 8.646
## 17 0.000 323 260 1.242
## Minimum Mean Median Maximum Skewness Kurtosis Percentile25th Percentile75th
## 8 0.000 1.006 1.000 7.000 1.360 4.760 0.000 2.000
## 12 0.000 0.813 0.000 6.000 1.554 4.831 0.000 1.000
## 14 0.000 0.164 0.000 4.000 3.842 21.526 0.000 0.000
## 17 0.000 1.402 1.000 7.000 1.034 3.875 0.000 2.000##################################
# Checking for skewed predictors
##################################
if (length(names(DQA.Predictors.Numeric))==0) {
print("No numeric predictors noted.")
} else if (nrow(DQA.Predictors.Numeric.Summary[as.numeric(as.character(DQA.Predictors.Numeric.Summary$Skewness))>3 |
as.numeric(as.character(DQA.Predictors.Numeric.Summary$Skewness))<(-3),])>0){
print(paste0("High skewness observed for ",
(nrow(DQA.Predictors.Numeric.Summary[as.numeric(as.character(DQA.Predictors.Numeric.Summary$Skewness))>3 |
as.numeric(as.character(DQA.Predictors.Numeric.Summary$Skewness))<(-3),])),
" numeric variable(s) with Skewness>3 or Skewness<(-3)."))
DQA.Predictors.Numeric.Summary[as.numeric(as.character(DQA.Predictors.Numeric.Summary$Skewness))>3 |
as.numeric(as.character(DQA.Predictors.Numeric.Summary$Skewness))<(-3),]
} else {
print("No skewed numeric predictors noted.")
}## [1] "High skewness observed for 3 numeric variable(s) with Skewness>3 or Skewness<(-3)."## Column.Name Column.Type Unique.Count Unique.Count.Ratio
## 14 NumSulfer integer 5 0.005
## 15 NumChlorine integer 11 0.012
## 18 HydrophilicFactor numeric 369 0.388
## First.Mode.Value Second.Mode.Value First.Mode.Count Second.Mode.Count
## 14 0.000 1.000 830 96
## 15 0.000 1.000 750 81
## 18 -0.828 -0.158 21 20
## First.Second.Mode.Ratio Minimum Mean Median Maximum Skewness Kurtosis
## 14 8.646 0.000 0.164 0.000 4.000 3.842 21.526
## 15 9.259 0.000 0.556 0.000 10.000 3.178 13.780
## 18 1.050 -0.985 -0.021 -0.314 13.483 3.404 27.504
## Percentile25th Percentile75th
## 14 0.000 0.000
## 15 0.000 0.000
## 18 -0.763 0.3131.3 Data Preprocessing
1.3.1 Outlier
Outlier data assessment:
[A] Outliers noted for 20 variables with the numeric data visualized through a boxplot including observations classified as suspected outliers using the IQR criterion. The IQR criterion means that all observations above the (75th percentile + 1.5 x IQR) or below the (25th percentile - 1.5 x IQR) are suspected outliers, where IQR is the difference between the third quartile (75th percentile) and first quartile (25th percentile). Outlier treatment for numerical stability remains optional depending on potential model requirements for the subsequent steps.
[A.1] MolWeight variable (8 outliers detected)
[A.2] NumAtoms variable (44 outliers detected)
[A.3] NumNonHAtoms variable (15 outliers detected)
[A.4] NumBonds variable (51 outliers detected)
[A.5] NumNonHBonds variable (18 outliers detected)
[A.6] NumMultBonds variable (6 outliers detected)
[A.7] NumRotBonds variable (23 outliers detected)
[A.8] NumDblBonds variable (3 outliers detected)
[A.9] NumAromaticBonds variable (35 outliers detected)
[A.10] NumHydrogen variable (32 outliers detected)
[A.11] NumCarbon variable (35 outliers detected)
[A.12] NumNitrogen variable (91 outliers detected)
[A.13] NumOxygen variable (36 outliers detected)
[A.14] NumSulfer variable (121 outliers detected)
[A.15] NumChlorine variable (201 outliers detected)
[A.16] NumHalogen variable (99 outliers detected)
[A.17] NumRings variable (4 outliers detected)
[A.18] HydrophilicFactor variable (53 outliers detected)
[A.19] SurfaceArea1 variable (19 outliers detected)
[A.20] SurfaceArea2 variable (12 outliers detected)
##################################
# Loading dataset
##################################
DPA <- Solubility_Train
##################################
# Listing all predictors
##################################
DPA.Predictors <- DPA[,!names(DPA) %in% c("Log_Solubility_Class")]
##################################
# Listing all numeric predictors
##################################
DPA.Predictors.Numeric <- DPA.Predictors[,-(grep("FP", names(DPA.Predictors)))]
##################################
# Identifying outliers for the numeric predictors
##################################
OutlierCountList <- c()
for (i in 1:ncol(DPA.Predictors.Numeric)) {
Outliers <- boxplot.stats(DPA.Predictors.Numeric[,i])$out
OutlierCount <- length(Outliers)
OutlierCountList <- append(OutlierCountList,OutlierCount)
OutlierIndices <- which(DPA.Predictors.Numeric[,i] %in% c(Outliers))
boxplot(DPA.Predictors.Numeric[,i],
ylab = names(DPA.Predictors.Numeric)[i],
main = names(DPA.Predictors.Numeric)[i],
horizontal=TRUE)
mtext(paste0(OutlierCount, " Outlier(s) Detected"))
}
OutlierCountSummary <- as.data.frame(cbind(names(DPA.Predictors.Numeric),(OutlierCountList)))
names(OutlierCountSummary) <- c("NumericPredictors","OutlierCount")
OutlierCountSummary$OutlierCount <- as.numeric(as.character(OutlierCountSummary$OutlierCount))
NumericPredictorWithOutlierCount <- nrow(OutlierCountSummary[OutlierCountSummary$OutlierCount>0,])
print(paste0(NumericPredictorWithOutlierCount, " numeric variable(s) were noted with outlier(s)." ))## [1] "20 numeric variable(s) were noted with outlier(s)."##################################
# Gathering descriptive statistics
##################################
(DPA_Skimmed <- skim(DPA.Predictors.Numeric))| Name | DPA.Predictors.Numeric |
| Number of rows | 951 |
| Number of columns | 20 |
| _______________________ | |
| Column type frequency: | |
| numeric | 20 |
| ________________________ | |
| Group variables | None |
Variable type: numeric
| skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
|---|---|---|---|---|---|---|---|---|---|---|
| MolWeight | 0 | 1 | 201.65 | 97.91 | 46.09 | 122.60 | 179.23 | 264.34 | 665.81 | ▇▆▂▁▁ |
| NumAtoms | 0 | 1 | 25.51 | 12.61 | 5.00 | 17.00 | 22.00 | 31.00 | 94.00 | ▇▆▂▁▁ |
| NumNonHAtoms | 0 | 1 | 13.16 | 6.50 | 2.00 | 8.00 | 12.00 | 17.00 | 47.00 | ▇▆▂▁▁ |
| NumBonds | 0 | 1 | 25.91 | 13.48 | 4.00 | 17.00 | 23.00 | 31.50 | 97.00 | ▇▇▂▁▁ |
| NumNonHBonds | 0 | 1 | 13.56 | 7.57 | 1.00 | 8.00 | 12.00 | 18.00 | 50.00 | ▇▇▂▁▁ |
| NumMultBonds | 0 | 1 | 6.15 | 5.17 | 0.00 | 1.00 | 6.00 | 10.00 | 25.00 | ▇▆▃▁▁ |
| NumRotBonds | 0 | 1 | 2.25 | 2.41 | 0.00 | 0.00 | 2.00 | 3.50 | 16.00 | ▇▂▁▁▁ |
| NumDblBonds | 0 | 1 | 1.01 | 1.21 | 0.00 | 0.00 | 1.00 | 2.00 | 7.00 | ▇▂▁▁▁ |
| NumAromaticBonds | 0 | 1 | 5.12 | 5.26 | 0.00 | 0.00 | 6.00 | 6.00 | 25.00 | ▇▆▃▁▁ |
| NumHydrogen | 0 | 1 | 12.35 | 7.32 | 0.00 | 7.00 | 11.00 | 16.00 | 47.00 | ▇▇▂▁▁ |
| NumCarbon | 0 | 1 | 9.89 | 5.29 | 1.00 | 6.00 | 9.00 | 12.00 | 33.00 | ▇▇▃▁▁ |
| NumNitrogen | 0 | 1 | 0.81 | 1.19 | 0.00 | 0.00 | 0.00 | 1.00 | 6.00 | ▇▂▁▁▁ |
| NumOxygen | 0 | 1 | 1.57 | 1.73 | 0.00 | 0.00 | 1.00 | 2.00 | 13.00 | ▇▂▁▁▁ |
| NumSulfer | 0 | 1 | 0.16 | 0.49 | 0.00 | 0.00 | 0.00 | 0.00 | 4.00 | ▇▁▁▁▁ |
| NumChlorine | 0 | 1 | 0.56 | 1.40 | 0.00 | 0.00 | 0.00 | 0.00 | 10.00 | ▇▁▁▁▁ |
| NumHalogen | 0 | 1 | 0.70 | 1.47 | 0.00 | 0.00 | 0.00 | 1.00 | 10.00 | ▇▁▁▁▁ |
| NumRings | 0 | 1 | 1.40 | 1.30 | 0.00 | 0.00 | 1.00 | 2.00 | 7.00 | ▇▃▂▁▁ |
| HydrophilicFactor | 0 | 1 | -0.02 | 1.13 | -0.98 | -0.76 | -0.31 | 0.31 | 13.48 | ▇▁▁▁▁ |
| SurfaceArea1 | 0 | 1 | 36.46 | 35.29 | 0.00 | 9.23 | 29.10 | 53.28 | 331.94 | ▇▂▁▁▁ |
| SurfaceArea2 | 0 | 1 | 40.23 | 38.12 | 0.00 | 10.63 | 33.12 | 60.66 | 331.94 | ▇▂▁▁▁ |
###################################
# Verifying the data dimensions
###################################
dim(DPA.Predictors.Numeric)## [1] 951 201.3.2 Zero and Near-Zero Variance
Zero and near-zero variance data assessment:
[A] Low variance noted for 127 variables from the previous data quality assessment using a lower threshold.
[B] Low variance noted for 3 variables using a preprocessing summary from the caret package. The nearZeroVar method using both the freqCut and uniqueCut criteria set at 95/5 and 10, respectively, were applied on the dataset.
[B.1] FP154 variable (factor)
[B.2] FP199 variable (factor)
[B.3] FP200 variable (factor)
##################################
# Loading dataset
##################################
DPA <- Solubility_Train
##################################
# Gathering descriptive statistics
##################################
(DPA_Skimmed <- skim(DPA))| Name | DPA |
| Number of rows | 951 |
| Number of columns | 229 |
| _______________________ | |
| Column type frequency: | |
| factor | 1 |
| numeric | 228 |
| ________________________ | |
| Group variables | None |
Variable type: factor
| skim_variable | n_missing | complete_rate | ordered | n_unique | top_counts |
|---|---|---|---|---|---|
| Log_Solubility_Class | 0 | 1 | FALSE | 2 | Hig: 524, Low: 427 |
Variable type: numeric
| skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
|---|---|---|---|---|---|---|---|---|---|---|
| FP001 | 0 | 1 | 0.49 | 0.50 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▇ |
| FP002 | 0 | 1 | 0.54 | 0.50 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▇▁▁▁▇ |
| FP003 | 0 | 1 | 0.44 | 0.50 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▆ |
| FP004 | 0 | 1 | 0.58 | 0.49 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▆▁▁▁▇ |
| FP005 | 0 | 1 | 0.58 | 0.49 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▆▁▁▁▇ |
| FP006 | 0 | 1 | 0.40 | 0.49 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▆ |
| FP007 | 0 | 1 | 0.36 | 0.48 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▅ |
| FP008 | 0 | 1 | 0.33 | 0.47 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP009 | 0 | 1 | 0.28 | 0.45 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP010 | 0 | 1 | 0.18 | 0.38 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP011 | 0 | 1 | 0.21 | 0.41 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP012 | 0 | 1 | 0.18 | 0.38 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP013 | 0 | 1 | 0.17 | 0.37 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP014 | 0 | 1 | 0.16 | 0.37 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP015 | 0 | 1 | 0.86 | 0.35 | 0.00 | 1.00 | 1.00 | 1.00 | 1.00 | ▁▁▁▁▇ |
| FP016 | 0 | 1 | 0.15 | 0.35 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP017 | 0 | 1 | 0.14 | 0.35 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP018 | 0 | 1 | 0.13 | 0.34 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP019 | 0 | 1 | 0.12 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP020 | 0 | 1 | 0.12 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP021 | 0 | 1 | 0.12 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP022 | 0 | 1 | 0.10 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP023 | 0 | 1 | 0.12 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP024 | 0 | 1 | 0.11 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP025 | 0 | 1 | 0.12 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP026 | 0 | 1 | 0.08 | 0.28 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP027 | 0 | 1 | 0.10 | 0.30 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP028 | 0 | 1 | 0.11 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP029 | 0 | 1 | 0.10 | 0.30 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP030 | 0 | 1 | 0.09 | 0.29 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP031 | 0 | 1 | 0.09 | 0.29 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP032 | 0 | 1 | 0.07 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP033 | 0 | 1 | 0.07 | 0.25 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP034 | 0 | 1 | 0.08 | 0.27 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP035 | 0 | 1 | 0.07 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP036 | 0 | 1 | 0.08 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP037 | 0 | 1 | 0.07 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP038 | 0 | 1 | 0.09 | 0.28 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP039 | 0 | 1 | 0.07 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP040 | 0 | 1 | 0.07 | 0.25 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP041 | 0 | 1 | 0.06 | 0.24 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP042 | 0 | 1 | 0.06 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP043 | 0 | 1 | 0.07 | 0.25 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP044 | 0 | 1 | 0.06 | 0.24 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP045 | 0 | 1 | 0.06 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP046 | 0 | 1 | 0.32 | 0.46 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP047 | 0 | 1 | 0.27 | 0.44 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP048 | 0 | 1 | 0.12 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP049 | 0 | 1 | 0.12 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP050 | 0 | 1 | 0.11 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP051 | 0 | 1 | 0.11 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP052 | 0 | 1 | 0.09 | 0.29 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP053 | 0 | 1 | 0.09 | 0.29 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP054 | 0 | 1 | 0.08 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP055 | 0 | 1 | 0.05 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP056 | 0 | 1 | 0.07 | 0.25 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP057 | 0 | 1 | 0.12 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP058 | 0 | 1 | 0.11 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP059 | 0 | 1 | 0.05 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP060 | 0 | 1 | 0.48 | 0.50 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▇ |
| FP061 | 0 | 1 | 0.45 | 0.50 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▆ |
| FP062 | 0 | 1 | 0.44 | 0.50 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▆ |
| FP063 | 0 | 1 | 0.43 | 0.49 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▆ |
| FP064 | 0 | 1 | 0.42 | 0.49 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▆ |
| FP065 | 0 | 1 | 0.59 | 0.49 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▆▁▁▁▇ |
| FP066 | 0 | 1 | 0.61 | 0.49 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▅▁▁▁▇ |
| FP067 | 0 | 1 | 0.38 | 0.49 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▅ |
| FP068 | 0 | 1 | 0.36 | 0.48 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▅ |
| FP069 | 0 | 1 | 0.36 | 0.48 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▅ |
| FP070 | 0 | 1 | 0.36 | 0.48 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▅ |
| FP071 | 0 | 1 | 0.33 | 0.47 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP072 | 0 | 1 | 0.66 | 0.47 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▅▁▁▁▇ |
| FP073 | 0 | 1 | 0.31 | 0.46 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP074 | 0 | 1 | 0.32 | 0.47 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP075 | 0 | 1 | 0.34 | 0.47 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▅ |
| FP076 | 0 | 1 | 0.33 | 0.47 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP077 | 0 | 1 | 0.32 | 0.47 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP078 | 0 | 1 | 0.30 | 0.46 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP079 | 0 | 1 | 0.69 | 0.46 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▃▁▁▁▇ |
| FP080 | 0 | 1 | 0.30 | 0.46 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP081 | 0 | 1 | 0.28 | 0.45 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP082 | 0 | 1 | 0.71 | 0.45 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▃▁▁▁▇ |
| FP083 | 0 | 1 | 0.27 | 0.45 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP084 | 0 | 1 | 0.29 | 0.45 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP085 | 0 | 1 | 0.26 | 0.44 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP086 | 0 | 1 | 0.27 | 0.44 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP087 | 0 | 1 | 0.73 | 0.45 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▃▁▁▁▇ |
| FP088 | 0 | 1 | 0.26 | 0.44 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP089 | 0 | 1 | 0.25 | 0.43 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP090 | 0 | 1 | 0.25 | 0.43 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP091 | 0 | 1 | 0.23 | 0.42 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP092 | 0 | 1 | 0.24 | 0.43 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP093 | 0 | 1 | 0.24 | 0.43 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP094 | 0 | 1 | 0.23 | 0.42 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP095 | 0 | 1 | 0.22 | 0.41 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP096 | 0 | 1 | 0.22 | 0.41 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP097 | 0 | 1 | 0.24 | 0.42 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP098 | 0 | 1 | 0.24 | 0.43 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP099 | 0 | 1 | 0.23 | 0.42 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP100 | 0 | 1 | 0.23 | 0.42 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP101 | 0 | 1 | 0.24 | 0.43 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP102 | 0 | 1 | 0.20 | 0.40 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP103 | 0 | 1 | 0.22 | 0.41 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP104 | 0 | 1 | 0.22 | 0.42 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP105 | 0 | 1 | 0.22 | 0.41 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP106 | 0 | 1 | 0.19 | 0.39 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP107 | 0 | 1 | 0.21 | 0.41 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP108 | 0 | 1 | 0.21 | 0.40 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP109 | 0 | 1 | 0.18 | 0.38 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP110 | 0 | 1 | 0.21 | 0.40 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP111 | 0 | 1 | 0.20 | 0.40 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP112 | 0 | 1 | 0.19 | 0.40 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP113 | 0 | 1 | 0.20 | 0.40 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP114 | 0 | 1 | 0.16 | 0.36 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP115 | 0 | 1 | 0.18 | 0.38 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP116 | 0 | 1 | 0.19 | 0.39 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP117 | 0 | 1 | 0.18 | 0.38 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP118 | 0 | 1 | 0.19 | 0.39 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP119 | 0 | 1 | 0.16 | 0.37 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP120 | 0 | 1 | 0.17 | 0.37 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP121 | 0 | 1 | 0.14 | 0.35 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP122 | 0 | 1 | 0.16 | 0.37 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP123 | 0 | 1 | 0.17 | 0.37 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP124 | 0 | 1 | 0.16 | 0.37 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP125 | 0 | 1 | 0.16 | 0.36 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP126 | 0 | 1 | 0.15 | 0.36 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP127 | 0 | 1 | 0.14 | 0.35 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP128 | 0 | 1 | 0.15 | 0.36 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP129 | 0 | 1 | 0.14 | 0.35 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP130 | 0 | 1 | 0.11 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP131 | 0 | 1 | 0.13 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP132 | 0 | 1 | 0.13 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP133 | 0 | 1 | 0.13 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP134 | 0 | 1 | 0.13 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP135 | 0 | 1 | 0.13 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP136 | 0 | 1 | 0.12 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP137 | 0 | 1 | 0.12 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP138 | 0 | 1 | 0.11 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP139 | 0 | 1 | 0.08 | 0.27 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP140 | 0 | 1 | 0.11 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP141 | 0 | 1 | 0.12 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP142 | 0 | 1 | 0.11 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP143 | 0 | 1 | 0.08 | 0.27 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP144 | 0 | 1 | 0.10 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP145 | 0 | 1 | 0.10 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP146 | 0 | 1 | 0.10 | 0.30 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP147 | 0 | 1 | 0.11 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP148 | 0 | 1 | 0.09 | 0.28 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP149 | 0 | 1 | 0.09 | 0.29 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP150 | 0 | 1 | 0.08 | 0.27 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP151 | 0 | 1 | 0.06 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP152 | 0 | 1 | 0.08 | 0.27 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP153 | 0 | 1 | 0.08 | 0.27 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP154 | 0 | 1 | 0.04 | 0.19 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP155 | 0 | 1 | 0.07 | 0.25 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP156 | 0 | 1 | 0.07 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP157 | 0 | 1 | 0.06 | 0.24 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP158 | 0 | 1 | 0.05 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP159 | 0 | 1 | 0.07 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP160 | 0 | 1 | 0.07 | 0.25 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP161 | 0 | 1 | 0.07 | 0.25 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP162 | 0 | 1 | 0.50 | 0.50 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▇ |
| FP163 | 0 | 1 | 0.48 | 0.50 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▇ |
| FP164 | 0 | 1 | 0.63 | 0.48 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▅▁▁▁▇ |
| FP165 | 0 | 1 | 0.35 | 0.48 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▅ |
| FP166 | 0 | 1 | 0.33 | 0.47 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP167 | 0 | 1 | 0.33 | 0.47 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP168 | 0 | 1 | 0.67 | 0.47 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▅▁▁▁▇ |
| FP169 | 0 | 1 | 0.19 | 0.39 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP170 | 0 | 1 | 0.18 | 0.39 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP171 | 0 | 1 | 0.17 | 0.38 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP172 | 0 | 1 | 0.15 | 0.36 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP173 | 0 | 1 | 0.14 | 0.35 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP174 | 0 | 1 | 0.13 | 0.34 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP175 | 0 | 1 | 0.13 | 0.34 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP176 | 0 | 1 | 0.12 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP177 | 0 | 1 | 0.12 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP178 | 0 | 1 | 0.12 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP179 | 0 | 1 | 0.10 | 0.30 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP180 | 0 | 1 | 0.11 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP181 | 0 | 1 | 0.09 | 0.29 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP182 | 0 | 1 | 0.10 | 0.30 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP183 | 0 | 1 | 0.08 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP184 | 0 | 1 | 0.08 | 0.28 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP185 | 0 | 1 | 0.09 | 0.28 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP186 | 0 | 1 | 0.08 | 0.27 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP187 | 0 | 1 | 0.07 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP188 | 0 | 1 | 0.07 | 0.25 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP189 | 0 | 1 | 0.08 | 0.27 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP190 | 0 | 1 | 0.07 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP191 | 0 | 1 | 0.07 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP192 | 0 | 1 | 0.06 | 0.24 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP193 | 0 | 1 | 0.06 | 0.24 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP194 | 0 | 1 | 0.06 | 0.24 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP195 | 0 | 1 | 0.06 | 0.24 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP196 | 0 | 1 | 0.06 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP197 | 0 | 1 | 0.05 | 0.22 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP198 | 0 | 1 | 0.06 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP199 | 0 | 1 | 0.05 | 0.21 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP200 | 0 | 1 | 0.05 | 0.22 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP201 | 0 | 1 | 0.05 | 0.22 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP202 | 0 | 1 | 0.26 | 0.44 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP203 | 0 | 1 | 0.11 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP204 | 0 | 1 | 0.10 | 0.30 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP205 | 0 | 1 | 0.08 | 0.27 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP206 | 0 | 1 | 0.06 | 0.24 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP207 | 0 | 1 | 0.06 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP208 | 0 | 1 | 0.11 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| MolWeight | 0 | 1 | 201.65 | 97.91 | 46.09 | 122.60 | 179.23 | 264.34 | 665.81 | ▇▆▂▁▁ |
| NumAtoms | 0 | 1 | 25.51 | 12.61 | 5.00 | 17.00 | 22.00 | 31.00 | 94.00 | ▇▆▂▁▁ |
| NumNonHAtoms | 0 | 1 | 13.16 | 6.50 | 2.00 | 8.00 | 12.00 | 17.00 | 47.00 | ▇▆▂▁▁ |
| NumBonds | 0 | 1 | 25.91 | 13.48 | 4.00 | 17.00 | 23.00 | 31.50 | 97.00 | ▇▇▂▁▁ |
| NumNonHBonds | 0 | 1 | 13.56 | 7.57 | 1.00 | 8.00 | 12.00 | 18.00 | 50.00 | ▇▇▂▁▁ |
| NumMultBonds | 0 | 1 | 6.15 | 5.17 | 0.00 | 1.00 | 6.00 | 10.00 | 25.00 | ▇▆▃▁▁ |
| NumRotBonds | 0 | 1 | 2.25 | 2.41 | 0.00 | 0.00 | 2.00 | 3.50 | 16.00 | ▇▂▁▁▁ |
| NumDblBonds | 0 | 1 | 1.01 | 1.21 | 0.00 | 0.00 | 1.00 | 2.00 | 7.00 | ▇▂▁▁▁ |
| NumAromaticBonds | 0 | 1 | 5.12 | 5.26 | 0.00 | 0.00 | 6.00 | 6.00 | 25.00 | ▇▆▃▁▁ |
| NumHydrogen | 0 | 1 | 12.35 | 7.32 | 0.00 | 7.00 | 11.00 | 16.00 | 47.00 | ▇▇▂▁▁ |
| NumCarbon | 0 | 1 | 9.89 | 5.29 | 1.00 | 6.00 | 9.00 | 12.00 | 33.00 | ▇▇▃▁▁ |
| NumNitrogen | 0 | 1 | 0.81 | 1.19 | 0.00 | 0.00 | 0.00 | 1.00 | 6.00 | ▇▂▁▁▁ |
| NumOxygen | 0 | 1 | 1.57 | 1.73 | 0.00 | 0.00 | 1.00 | 2.00 | 13.00 | ▇▂▁▁▁ |
| NumSulfer | 0 | 1 | 0.16 | 0.49 | 0.00 | 0.00 | 0.00 | 0.00 | 4.00 | ▇▁▁▁▁ |
| NumChlorine | 0 | 1 | 0.56 | 1.40 | 0.00 | 0.00 | 0.00 | 0.00 | 10.00 | ▇▁▁▁▁ |
| NumHalogen | 0 | 1 | 0.70 | 1.47 | 0.00 | 0.00 | 0.00 | 1.00 | 10.00 | ▇▁▁▁▁ |
| NumRings | 0 | 1 | 1.40 | 1.30 | 0.00 | 0.00 | 1.00 | 2.00 | 7.00 | ▇▃▂▁▁ |
| HydrophilicFactor | 0 | 1 | -0.02 | 1.13 | -0.98 | -0.76 | -0.31 | 0.31 | 13.48 | ▇▁▁▁▁ |
| SurfaceArea1 | 0 | 1 | 36.46 | 35.29 | 0.00 | 9.23 | 29.10 | 53.28 | 331.94 | ▇▂▁▁▁ |
| SurfaceArea2 | 0 | 1 | 40.23 | 38.12 | 0.00 | 10.63 | 33.12 | 60.66 | 331.94 | ▇▂▁▁▁ |
##################################
# Identifying columns with low variance
###################################
DPA_LowVariance <- nearZeroVar(DPA,
freqCut = 95/5,
uniqueCut = 10,
saveMetrics= TRUE)
(DPA_LowVariance[DPA_LowVariance$nzv,])## freqRatio percentUnique zeroVar nzv
## FP154 25.41667 0.2103049 FALSE TRUE
## FP199 20.13333 0.2103049 FALSE TRUE
## FP200 19.23404 0.2103049 FALSE TRUEif ((nrow(DPA_LowVariance[DPA_LowVariance$nzv,]))==0){
print("No low variance predictors noted.")
} else {
print(paste0("Low variance observed for ",
(nrow(DPA_LowVariance[DPA_LowVariance$nzv,])),
" numeric variable(s) with First.Second.Mode.Ratio>4 and Unique.Count.Ratio<0.10."))
DPA_LowVarianceForRemoval <- (nrow(DPA_LowVariance[DPA_LowVariance$nzv,]))
print(paste0("Low variance can be resolved by removing ",
(nrow(DPA_LowVariance[DPA_LowVariance$nzv,])),
" numeric variable(s)."))
for (j in 1:DPA_LowVarianceForRemoval) {
DPA_LowVarianceRemovedVariable <- rownames(DPA_LowVariance[DPA_LowVariance$nzv,])[j]
print(paste0("Variable ",
j,
" for removal: ",
DPA_LowVarianceRemovedVariable))
}
DPA %>%
skim() %>%
dplyr::filter(skim_variable %in% rownames(DPA_LowVariance[DPA_LowVariance$nzv,]))
##################################
# Filtering out columns with low variance
#################################
DPA_ExcludedLowVariance <- DPA[,!names(DPA) %in% rownames(DPA_LowVariance[DPA_LowVariance$nzv,])]
##################################
# Gathering descriptive statistics
##################################
(DPA_ExcludedLowVariance_Skimmed <- skim(DPA_ExcludedLowVariance))
}## [1] "Low variance observed for 3 numeric variable(s) with First.Second.Mode.Ratio>4 and Unique.Count.Ratio<0.10."
## [1] "Low variance can be resolved by removing 3 numeric variable(s)."
## [1] "Variable 1 for removal: FP154"
## [1] "Variable 2 for removal: FP199"
## [1] "Variable 3 for removal: FP200"| Name | DPA_ExcludedLowVariance |
| Number of rows | 951 |
| Number of columns | 226 |
| _______________________ | |
| Column type frequency: | |
| factor | 1 |
| numeric | 225 |
| ________________________ | |
| Group variables | None |
Variable type: factor
| skim_variable | n_missing | complete_rate | ordered | n_unique | top_counts |
|---|---|---|---|---|---|
| Log_Solubility_Class | 0 | 1 | FALSE | 2 | Hig: 524, Low: 427 |
Variable type: numeric
| skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
|---|---|---|---|---|---|---|---|---|---|---|
| FP001 | 0 | 1 | 0.49 | 0.50 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▇ |
| FP002 | 0 | 1 | 0.54 | 0.50 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▇▁▁▁▇ |
| FP003 | 0 | 1 | 0.44 | 0.50 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▆ |
| FP004 | 0 | 1 | 0.58 | 0.49 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▆▁▁▁▇ |
| FP005 | 0 | 1 | 0.58 | 0.49 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▆▁▁▁▇ |
| FP006 | 0 | 1 | 0.40 | 0.49 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▆ |
| FP007 | 0 | 1 | 0.36 | 0.48 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▅ |
| FP008 | 0 | 1 | 0.33 | 0.47 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP009 | 0 | 1 | 0.28 | 0.45 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP010 | 0 | 1 | 0.18 | 0.38 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP011 | 0 | 1 | 0.21 | 0.41 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP012 | 0 | 1 | 0.18 | 0.38 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP013 | 0 | 1 | 0.17 | 0.37 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP014 | 0 | 1 | 0.16 | 0.37 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP015 | 0 | 1 | 0.86 | 0.35 | 0.00 | 1.00 | 1.00 | 1.00 | 1.00 | ▁▁▁▁▇ |
| FP016 | 0 | 1 | 0.15 | 0.35 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP017 | 0 | 1 | 0.14 | 0.35 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP018 | 0 | 1 | 0.13 | 0.34 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP019 | 0 | 1 | 0.12 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP020 | 0 | 1 | 0.12 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP021 | 0 | 1 | 0.12 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP022 | 0 | 1 | 0.10 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP023 | 0 | 1 | 0.12 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP024 | 0 | 1 | 0.11 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP025 | 0 | 1 | 0.12 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP026 | 0 | 1 | 0.08 | 0.28 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP027 | 0 | 1 | 0.10 | 0.30 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP028 | 0 | 1 | 0.11 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP029 | 0 | 1 | 0.10 | 0.30 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP030 | 0 | 1 | 0.09 | 0.29 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP031 | 0 | 1 | 0.09 | 0.29 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP032 | 0 | 1 | 0.07 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP033 | 0 | 1 | 0.07 | 0.25 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP034 | 0 | 1 | 0.08 | 0.27 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP035 | 0 | 1 | 0.07 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP036 | 0 | 1 | 0.08 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP037 | 0 | 1 | 0.07 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP038 | 0 | 1 | 0.09 | 0.28 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP039 | 0 | 1 | 0.07 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP040 | 0 | 1 | 0.07 | 0.25 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP041 | 0 | 1 | 0.06 | 0.24 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP042 | 0 | 1 | 0.06 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP043 | 0 | 1 | 0.07 | 0.25 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP044 | 0 | 1 | 0.06 | 0.24 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP045 | 0 | 1 | 0.06 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP046 | 0 | 1 | 0.32 | 0.46 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP047 | 0 | 1 | 0.27 | 0.44 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP048 | 0 | 1 | 0.12 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP049 | 0 | 1 | 0.12 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP050 | 0 | 1 | 0.11 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP051 | 0 | 1 | 0.11 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP052 | 0 | 1 | 0.09 | 0.29 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP053 | 0 | 1 | 0.09 | 0.29 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP054 | 0 | 1 | 0.08 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP055 | 0 | 1 | 0.05 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP056 | 0 | 1 | 0.07 | 0.25 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP057 | 0 | 1 | 0.12 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP058 | 0 | 1 | 0.11 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP059 | 0 | 1 | 0.05 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP060 | 0 | 1 | 0.48 | 0.50 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▇ |
| FP061 | 0 | 1 | 0.45 | 0.50 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▆ |
| FP062 | 0 | 1 | 0.44 | 0.50 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▆ |
| FP063 | 0 | 1 | 0.43 | 0.49 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▆ |
| FP064 | 0 | 1 | 0.42 | 0.49 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▆ |
| FP065 | 0 | 1 | 0.59 | 0.49 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▆▁▁▁▇ |
| FP066 | 0 | 1 | 0.61 | 0.49 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▅▁▁▁▇ |
| FP067 | 0 | 1 | 0.38 | 0.49 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▅ |
| FP068 | 0 | 1 | 0.36 | 0.48 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▅ |
| FP069 | 0 | 1 | 0.36 | 0.48 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▅ |
| FP070 | 0 | 1 | 0.36 | 0.48 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▅ |
| FP071 | 0 | 1 | 0.33 | 0.47 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP072 | 0 | 1 | 0.66 | 0.47 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▅▁▁▁▇ |
| FP073 | 0 | 1 | 0.31 | 0.46 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP074 | 0 | 1 | 0.32 | 0.47 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP075 | 0 | 1 | 0.34 | 0.47 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▅ |
| FP076 | 0 | 1 | 0.33 | 0.47 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP077 | 0 | 1 | 0.32 | 0.47 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP078 | 0 | 1 | 0.30 | 0.46 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP079 | 0 | 1 | 0.69 | 0.46 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▃▁▁▁▇ |
| FP080 | 0 | 1 | 0.30 | 0.46 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP081 | 0 | 1 | 0.28 | 0.45 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP082 | 0 | 1 | 0.71 | 0.45 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▃▁▁▁▇ |
| FP083 | 0 | 1 | 0.27 | 0.45 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP084 | 0 | 1 | 0.29 | 0.45 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP085 | 0 | 1 | 0.26 | 0.44 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP086 | 0 | 1 | 0.27 | 0.44 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP087 | 0 | 1 | 0.73 | 0.45 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▃▁▁▁▇ |
| FP088 | 0 | 1 | 0.26 | 0.44 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP089 | 0 | 1 | 0.25 | 0.43 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP090 | 0 | 1 | 0.25 | 0.43 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP091 | 0 | 1 | 0.23 | 0.42 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP092 | 0 | 1 | 0.24 | 0.43 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP093 | 0 | 1 | 0.24 | 0.43 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP094 | 0 | 1 | 0.23 | 0.42 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP095 | 0 | 1 | 0.22 | 0.41 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP096 | 0 | 1 | 0.22 | 0.41 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP097 | 0 | 1 | 0.24 | 0.42 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP098 | 0 | 1 | 0.24 | 0.43 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP099 | 0 | 1 | 0.23 | 0.42 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP100 | 0 | 1 | 0.23 | 0.42 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP101 | 0 | 1 | 0.24 | 0.43 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP102 | 0 | 1 | 0.20 | 0.40 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP103 | 0 | 1 | 0.22 | 0.41 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP104 | 0 | 1 | 0.22 | 0.42 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP105 | 0 | 1 | 0.22 | 0.41 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP106 | 0 | 1 | 0.19 | 0.39 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP107 | 0 | 1 | 0.21 | 0.41 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP108 | 0 | 1 | 0.21 | 0.40 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP109 | 0 | 1 | 0.18 | 0.38 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP110 | 0 | 1 | 0.21 | 0.40 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP111 | 0 | 1 | 0.20 | 0.40 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP112 | 0 | 1 | 0.19 | 0.40 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP113 | 0 | 1 | 0.20 | 0.40 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP114 | 0 | 1 | 0.16 | 0.36 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP115 | 0 | 1 | 0.18 | 0.38 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP116 | 0 | 1 | 0.19 | 0.39 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP117 | 0 | 1 | 0.18 | 0.38 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP118 | 0 | 1 | 0.19 | 0.39 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP119 | 0 | 1 | 0.16 | 0.37 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP120 | 0 | 1 | 0.17 | 0.37 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP121 | 0 | 1 | 0.14 | 0.35 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP122 | 0 | 1 | 0.16 | 0.37 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP123 | 0 | 1 | 0.17 | 0.37 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP124 | 0 | 1 | 0.16 | 0.37 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP125 | 0 | 1 | 0.16 | 0.36 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP126 | 0 | 1 | 0.15 | 0.36 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP127 | 0 | 1 | 0.14 | 0.35 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP128 | 0 | 1 | 0.15 | 0.36 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP129 | 0 | 1 | 0.14 | 0.35 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP130 | 0 | 1 | 0.11 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP131 | 0 | 1 | 0.13 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP132 | 0 | 1 | 0.13 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP133 | 0 | 1 | 0.13 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP134 | 0 | 1 | 0.13 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP135 | 0 | 1 | 0.13 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP136 | 0 | 1 | 0.12 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP137 | 0 | 1 | 0.12 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP138 | 0 | 1 | 0.11 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP139 | 0 | 1 | 0.08 | 0.27 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP140 | 0 | 1 | 0.11 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP141 | 0 | 1 | 0.12 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP142 | 0 | 1 | 0.11 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP143 | 0 | 1 | 0.08 | 0.27 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP144 | 0 | 1 | 0.10 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP145 | 0 | 1 | 0.10 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP146 | 0 | 1 | 0.10 | 0.30 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP147 | 0 | 1 | 0.11 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP148 | 0 | 1 | 0.09 | 0.28 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP149 | 0 | 1 | 0.09 | 0.29 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP150 | 0 | 1 | 0.08 | 0.27 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP151 | 0 | 1 | 0.06 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP152 | 0 | 1 | 0.08 | 0.27 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP153 | 0 | 1 | 0.08 | 0.27 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP155 | 0 | 1 | 0.07 | 0.25 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP156 | 0 | 1 | 0.07 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP157 | 0 | 1 | 0.06 | 0.24 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP158 | 0 | 1 | 0.05 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP159 | 0 | 1 | 0.07 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP160 | 0 | 1 | 0.07 | 0.25 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP161 | 0 | 1 | 0.07 | 0.25 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP162 | 0 | 1 | 0.50 | 0.50 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▇ |
| FP163 | 0 | 1 | 0.48 | 0.50 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▇ |
| FP164 | 0 | 1 | 0.63 | 0.48 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▅▁▁▁▇ |
| FP165 | 0 | 1 | 0.35 | 0.48 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▅ |
| FP166 | 0 | 1 | 0.33 | 0.47 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP167 | 0 | 1 | 0.33 | 0.47 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP168 | 0 | 1 | 0.67 | 0.47 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▅▁▁▁▇ |
| FP169 | 0 | 1 | 0.19 | 0.39 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP170 | 0 | 1 | 0.18 | 0.39 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP171 | 0 | 1 | 0.17 | 0.38 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP172 | 0 | 1 | 0.15 | 0.36 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP173 | 0 | 1 | 0.14 | 0.35 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP174 | 0 | 1 | 0.13 | 0.34 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP175 | 0 | 1 | 0.13 | 0.34 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP176 | 0 | 1 | 0.12 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP177 | 0 | 1 | 0.12 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP178 | 0 | 1 | 0.12 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP179 | 0 | 1 | 0.10 | 0.30 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP180 | 0 | 1 | 0.11 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP181 | 0 | 1 | 0.09 | 0.29 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP182 | 0 | 1 | 0.10 | 0.30 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP183 | 0 | 1 | 0.08 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP184 | 0 | 1 | 0.08 | 0.28 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP185 | 0 | 1 | 0.09 | 0.28 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP186 | 0 | 1 | 0.08 | 0.27 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP187 | 0 | 1 | 0.07 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP188 | 0 | 1 | 0.07 | 0.25 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP189 | 0 | 1 | 0.08 | 0.27 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP190 | 0 | 1 | 0.07 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP191 | 0 | 1 | 0.07 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP192 | 0 | 1 | 0.06 | 0.24 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP193 | 0 | 1 | 0.06 | 0.24 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP194 | 0 | 1 | 0.06 | 0.24 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP195 | 0 | 1 | 0.06 | 0.24 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP196 | 0 | 1 | 0.06 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP197 | 0 | 1 | 0.05 | 0.22 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP198 | 0 | 1 | 0.06 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP201 | 0 | 1 | 0.05 | 0.22 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP202 | 0 | 1 | 0.26 | 0.44 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP203 | 0 | 1 | 0.11 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP204 | 0 | 1 | 0.10 | 0.30 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP205 | 0 | 1 | 0.08 | 0.27 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP206 | 0 | 1 | 0.06 | 0.24 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP207 | 0 | 1 | 0.06 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP208 | 0 | 1 | 0.11 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| MolWeight | 0 | 1 | 201.65 | 97.91 | 46.09 | 122.60 | 179.23 | 264.34 | 665.81 | ▇▆▂▁▁ |
| NumAtoms | 0 | 1 | 25.51 | 12.61 | 5.00 | 17.00 | 22.00 | 31.00 | 94.00 | ▇▆▂▁▁ |
| NumNonHAtoms | 0 | 1 | 13.16 | 6.50 | 2.00 | 8.00 | 12.00 | 17.00 | 47.00 | ▇▆▂▁▁ |
| NumBonds | 0 | 1 | 25.91 | 13.48 | 4.00 | 17.00 | 23.00 | 31.50 | 97.00 | ▇▇▂▁▁ |
| NumNonHBonds | 0 | 1 | 13.56 | 7.57 | 1.00 | 8.00 | 12.00 | 18.00 | 50.00 | ▇▇▂▁▁ |
| NumMultBonds | 0 | 1 | 6.15 | 5.17 | 0.00 | 1.00 | 6.00 | 10.00 | 25.00 | ▇▆▃▁▁ |
| NumRotBonds | 0 | 1 | 2.25 | 2.41 | 0.00 | 0.00 | 2.00 | 3.50 | 16.00 | ▇▂▁▁▁ |
| NumDblBonds | 0 | 1 | 1.01 | 1.21 | 0.00 | 0.00 | 1.00 | 2.00 | 7.00 | ▇▂▁▁▁ |
| NumAromaticBonds | 0 | 1 | 5.12 | 5.26 | 0.00 | 0.00 | 6.00 | 6.00 | 25.00 | ▇▆▃▁▁ |
| NumHydrogen | 0 | 1 | 12.35 | 7.32 | 0.00 | 7.00 | 11.00 | 16.00 | 47.00 | ▇▇▂▁▁ |
| NumCarbon | 0 | 1 | 9.89 | 5.29 | 1.00 | 6.00 | 9.00 | 12.00 | 33.00 | ▇▇▃▁▁ |
| NumNitrogen | 0 | 1 | 0.81 | 1.19 | 0.00 | 0.00 | 0.00 | 1.00 | 6.00 | ▇▂▁▁▁ |
| NumOxygen | 0 | 1 | 1.57 | 1.73 | 0.00 | 0.00 | 1.00 | 2.00 | 13.00 | ▇▂▁▁▁ |
| NumSulfer | 0 | 1 | 0.16 | 0.49 | 0.00 | 0.00 | 0.00 | 0.00 | 4.00 | ▇▁▁▁▁ |
| NumChlorine | 0 | 1 | 0.56 | 1.40 | 0.00 | 0.00 | 0.00 | 0.00 | 10.00 | ▇▁▁▁▁ |
| NumHalogen | 0 | 1 | 0.70 | 1.47 | 0.00 | 0.00 | 0.00 | 1.00 | 10.00 | ▇▁▁▁▁ |
| NumRings | 0 | 1 | 1.40 | 1.30 | 0.00 | 0.00 | 1.00 | 2.00 | 7.00 | ▇▃▂▁▁ |
| HydrophilicFactor | 0 | 1 | -0.02 | 1.13 | -0.98 | -0.76 | -0.31 | 0.31 | 13.48 | ▇▁▁▁▁ |
| SurfaceArea1 | 0 | 1 | 36.46 | 35.29 | 0.00 | 9.23 | 29.10 | 53.28 | 331.94 | ▇▂▁▁▁ |
| SurfaceArea2 | 0 | 1 | 40.23 | 38.12 | 0.00 | 10.63 | 33.12 | 60.66 | 331.94 | ▇▂▁▁▁ |
###################################
# Verifying the data dimensions
###################################
dim(DPA_ExcludedLowVariance)## [1] 951 2261.3.3 Collinearity
High collinearity data assessment:
[A] High correlation > 95% were noted for 2 variable pairs as confirmed using the preprocessing summaries from the caret and lares packages.
[A.1] NumNonHAtoms and NumNonHBonds variables (numeric)
[A.2] NumMultBonds and NumAromaticBonds variables (numeric)
[A.3] NumAtoms and NumBonds variables (numeric)
##################################
# Loading dataset
##################################
DPA <- Solubility_Train
##################################
# Listing all predictors
##################################
DPA.Predictors <- DPA[,!names(DPA) %in% c("Log_Solubility_Class")]
##################################
# Listing all numeric predictors
##################################
DPA.Predictors.Numeric <- DPA.Predictors[,-(grep("FP", names(DPA.Predictors)))]
##################################
# Visualizing pairwise correlation between predictors
##################################
DPA_CorrelationTest <- cor.mtest(DPA.Predictors.Numeric,
method = "pearson",
conf.level = .95)
corrplot(cor(DPA.Predictors.Numeric,
method = "pearson",
use="pairwise.complete.obs"),
method = "circle",
type = "upper",
order = "original",
tl.col = "black",
tl.cex = 0.75,
tl.srt = 90,
sig.level = 0.05,
p.mat = DPA_CorrelationTest$p,
insig = "blank")
##################################
# Identifying the highly correlated variables
##################################
DPA_Correlation <- cor(DPA.Predictors.Numeric,
method = "pearson",
use="pairwise.complete.obs")
(DPA_HighlyCorrelatedCount <- sum(abs(DPA_Correlation[upper.tri(DPA_Correlation)]) > 0.95))## [1] 3if (DPA_HighlyCorrelatedCount == 0) {
print("No highly correlated predictors noted.")
} else {
print(paste0("High correlation observed for ",
(DPA_HighlyCorrelatedCount),
" pairs of numeric variable(s) with Correlation.Coefficient>0.95."))
(DPA_HighlyCorrelatedPairs <- corr_cross(DPA.Predictors.Numeric,
max_pvalue = 0.05,
top = DPA_HighlyCorrelatedCount,
rm.na = TRUE,
grid = FALSE
))
}## [1] "High correlation observed for 3 pairs of numeric variable(s) with Correlation.Coefficient>0.95."
if (DPA_HighlyCorrelatedCount > 0) {
DPA_HighlyCorrelated <- findCorrelation(DPA_Correlation, cutoff = 0.95)
(DPA_HighlyCorrelatedForRemoval <- length(DPA_HighlyCorrelated))
print(paste0("High correlation can be resolved by removing ",
(DPA_HighlyCorrelatedForRemoval),
" numeric variable(s)."))
for (j in 1:DPA_HighlyCorrelatedForRemoval) {
DPA_HighlyCorrelatedRemovedVariable <- colnames(DPA.Predictors.Numeric)[DPA_HighlyCorrelated[j]]
print(paste0("Variable ",
j,
" for removal: ",
DPA_HighlyCorrelatedRemovedVariable))
}
##################################
# Filtering out columns with high correlation
#################################
DPA_ExcludedHighCorrelation <- DPA[,-DPA_HighlyCorrelated]
##################################
# Gathering descriptive statistics
##################################
(DPA_ExcludedHighCorrelation_Skimmed <- skim(DPA_ExcludedHighCorrelation))
}## [1] "High correlation can be resolved by removing 3 numeric variable(s)."
## [1] "Variable 1 for removal: NumNonHAtoms"
## [1] "Variable 2 for removal: NumBonds"
## [1] "Variable 3 for removal: NumAromaticBonds"| Name | DPA_ExcludedHighCorrelati… |
| Number of rows | 951 |
| Number of columns | 226 |
| _______________________ | |
| Column type frequency: | |
| factor | 1 |
| numeric | 225 |
| ________________________ | |
| Group variables | None |
Variable type: factor
| skim_variable | n_missing | complete_rate | ordered | n_unique | top_counts |
|---|---|---|---|---|---|
| Log_Solubility_Class | 0 | 1 | FALSE | 2 | Hig: 524, Low: 427 |
Variable type: numeric
| skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
|---|---|---|---|---|---|---|---|---|---|---|
| FP001 | 0 | 1 | 0.49 | 0.50 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▇ |
| FP002 | 0 | 1 | 0.54 | 0.50 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▇▁▁▁▇ |
| FP005 | 0 | 1 | 0.58 | 0.49 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▆▁▁▁▇ |
| FP006 | 0 | 1 | 0.40 | 0.49 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▆ |
| FP007 | 0 | 1 | 0.36 | 0.48 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▅ |
| FP008 | 0 | 1 | 0.33 | 0.47 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP010 | 0 | 1 | 0.18 | 0.38 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP011 | 0 | 1 | 0.21 | 0.41 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP012 | 0 | 1 | 0.18 | 0.38 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP013 | 0 | 1 | 0.17 | 0.37 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP014 | 0 | 1 | 0.16 | 0.37 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP015 | 0 | 1 | 0.86 | 0.35 | 0.00 | 1.00 | 1.00 | 1.00 | 1.00 | ▁▁▁▁▇ |
| FP016 | 0 | 1 | 0.15 | 0.35 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP017 | 0 | 1 | 0.14 | 0.35 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP018 | 0 | 1 | 0.13 | 0.34 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP019 | 0 | 1 | 0.12 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP020 | 0 | 1 | 0.12 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP021 | 0 | 1 | 0.12 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP022 | 0 | 1 | 0.10 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP023 | 0 | 1 | 0.12 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP024 | 0 | 1 | 0.11 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP025 | 0 | 1 | 0.12 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP026 | 0 | 1 | 0.08 | 0.28 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP027 | 0 | 1 | 0.10 | 0.30 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP028 | 0 | 1 | 0.11 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP029 | 0 | 1 | 0.10 | 0.30 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP030 | 0 | 1 | 0.09 | 0.29 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP031 | 0 | 1 | 0.09 | 0.29 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP032 | 0 | 1 | 0.07 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP033 | 0 | 1 | 0.07 | 0.25 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP034 | 0 | 1 | 0.08 | 0.27 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP035 | 0 | 1 | 0.07 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP036 | 0 | 1 | 0.08 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP037 | 0 | 1 | 0.07 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP038 | 0 | 1 | 0.09 | 0.28 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP039 | 0 | 1 | 0.07 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP040 | 0 | 1 | 0.07 | 0.25 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP041 | 0 | 1 | 0.06 | 0.24 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP042 | 0 | 1 | 0.06 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP043 | 0 | 1 | 0.07 | 0.25 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP044 | 0 | 1 | 0.06 | 0.24 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP045 | 0 | 1 | 0.06 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP046 | 0 | 1 | 0.32 | 0.46 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP047 | 0 | 1 | 0.27 | 0.44 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP048 | 0 | 1 | 0.12 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP049 | 0 | 1 | 0.12 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP050 | 0 | 1 | 0.11 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP051 | 0 | 1 | 0.11 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP052 | 0 | 1 | 0.09 | 0.29 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP053 | 0 | 1 | 0.09 | 0.29 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP054 | 0 | 1 | 0.08 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP055 | 0 | 1 | 0.05 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP056 | 0 | 1 | 0.07 | 0.25 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP057 | 0 | 1 | 0.12 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP058 | 0 | 1 | 0.11 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP059 | 0 | 1 | 0.05 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP060 | 0 | 1 | 0.48 | 0.50 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▇ |
| FP061 | 0 | 1 | 0.45 | 0.50 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▆ |
| FP062 | 0 | 1 | 0.44 | 0.50 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▆ |
| FP063 | 0 | 1 | 0.43 | 0.49 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▆ |
| FP064 | 0 | 1 | 0.42 | 0.49 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▆ |
| FP065 | 0 | 1 | 0.59 | 0.49 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▆▁▁▁▇ |
| FP066 | 0 | 1 | 0.61 | 0.49 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▅▁▁▁▇ |
| FP067 | 0 | 1 | 0.38 | 0.49 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▅ |
| FP068 | 0 | 1 | 0.36 | 0.48 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▅ |
| FP069 | 0 | 1 | 0.36 | 0.48 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▅ |
| FP070 | 0 | 1 | 0.36 | 0.48 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▅ |
| FP071 | 0 | 1 | 0.33 | 0.47 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP072 | 0 | 1 | 0.66 | 0.47 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▅▁▁▁▇ |
| FP073 | 0 | 1 | 0.31 | 0.46 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP074 | 0 | 1 | 0.32 | 0.47 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP075 | 0 | 1 | 0.34 | 0.47 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▅ |
| FP076 | 0 | 1 | 0.33 | 0.47 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP077 | 0 | 1 | 0.32 | 0.47 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP078 | 0 | 1 | 0.30 | 0.46 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP079 | 0 | 1 | 0.69 | 0.46 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▃▁▁▁▇ |
| FP080 | 0 | 1 | 0.30 | 0.46 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP081 | 0 | 1 | 0.28 | 0.45 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP082 | 0 | 1 | 0.71 | 0.45 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▃▁▁▁▇ |
| FP083 | 0 | 1 | 0.27 | 0.45 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP084 | 0 | 1 | 0.29 | 0.45 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP085 | 0 | 1 | 0.26 | 0.44 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP086 | 0 | 1 | 0.27 | 0.44 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP087 | 0 | 1 | 0.73 | 0.45 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▃▁▁▁▇ |
| FP088 | 0 | 1 | 0.26 | 0.44 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP089 | 0 | 1 | 0.25 | 0.43 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP090 | 0 | 1 | 0.25 | 0.43 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP091 | 0 | 1 | 0.23 | 0.42 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP092 | 0 | 1 | 0.24 | 0.43 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP093 | 0 | 1 | 0.24 | 0.43 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP094 | 0 | 1 | 0.23 | 0.42 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP095 | 0 | 1 | 0.22 | 0.41 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP096 | 0 | 1 | 0.22 | 0.41 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP097 | 0 | 1 | 0.24 | 0.42 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP098 | 0 | 1 | 0.24 | 0.43 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP099 | 0 | 1 | 0.23 | 0.42 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP100 | 0 | 1 | 0.23 | 0.42 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP101 | 0 | 1 | 0.24 | 0.43 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP102 | 0 | 1 | 0.20 | 0.40 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP103 | 0 | 1 | 0.22 | 0.41 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP104 | 0 | 1 | 0.22 | 0.42 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP105 | 0 | 1 | 0.22 | 0.41 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP106 | 0 | 1 | 0.19 | 0.39 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP107 | 0 | 1 | 0.21 | 0.41 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP108 | 0 | 1 | 0.21 | 0.40 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP109 | 0 | 1 | 0.18 | 0.38 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP110 | 0 | 1 | 0.21 | 0.40 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP111 | 0 | 1 | 0.20 | 0.40 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP112 | 0 | 1 | 0.19 | 0.40 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP113 | 0 | 1 | 0.20 | 0.40 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP114 | 0 | 1 | 0.16 | 0.36 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP115 | 0 | 1 | 0.18 | 0.38 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP116 | 0 | 1 | 0.19 | 0.39 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP117 | 0 | 1 | 0.18 | 0.38 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP118 | 0 | 1 | 0.19 | 0.39 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP119 | 0 | 1 | 0.16 | 0.37 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP120 | 0 | 1 | 0.17 | 0.37 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP121 | 0 | 1 | 0.14 | 0.35 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP122 | 0 | 1 | 0.16 | 0.37 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP123 | 0 | 1 | 0.17 | 0.37 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP124 | 0 | 1 | 0.16 | 0.37 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP125 | 0 | 1 | 0.16 | 0.36 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP126 | 0 | 1 | 0.15 | 0.36 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP127 | 0 | 1 | 0.14 | 0.35 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP128 | 0 | 1 | 0.15 | 0.36 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP129 | 0 | 1 | 0.14 | 0.35 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP130 | 0 | 1 | 0.11 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP131 | 0 | 1 | 0.13 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP132 | 0 | 1 | 0.13 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP133 | 0 | 1 | 0.13 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP134 | 0 | 1 | 0.13 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP135 | 0 | 1 | 0.13 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP136 | 0 | 1 | 0.12 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP137 | 0 | 1 | 0.12 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP138 | 0 | 1 | 0.11 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP139 | 0 | 1 | 0.08 | 0.27 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP140 | 0 | 1 | 0.11 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP141 | 0 | 1 | 0.12 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP142 | 0 | 1 | 0.11 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP143 | 0 | 1 | 0.08 | 0.27 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP144 | 0 | 1 | 0.10 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP145 | 0 | 1 | 0.10 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP146 | 0 | 1 | 0.10 | 0.30 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP147 | 0 | 1 | 0.11 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP148 | 0 | 1 | 0.09 | 0.28 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP149 | 0 | 1 | 0.09 | 0.29 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP150 | 0 | 1 | 0.08 | 0.27 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP151 | 0 | 1 | 0.06 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP152 | 0 | 1 | 0.08 | 0.27 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP153 | 0 | 1 | 0.08 | 0.27 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP154 | 0 | 1 | 0.04 | 0.19 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP155 | 0 | 1 | 0.07 | 0.25 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP156 | 0 | 1 | 0.07 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP157 | 0 | 1 | 0.06 | 0.24 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP158 | 0 | 1 | 0.05 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP159 | 0 | 1 | 0.07 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP160 | 0 | 1 | 0.07 | 0.25 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP161 | 0 | 1 | 0.07 | 0.25 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP162 | 0 | 1 | 0.50 | 0.50 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▇ |
| FP163 | 0 | 1 | 0.48 | 0.50 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▇ |
| FP164 | 0 | 1 | 0.63 | 0.48 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▅▁▁▁▇ |
| FP165 | 0 | 1 | 0.35 | 0.48 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▅ |
| FP166 | 0 | 1 | 0.33 | 0.47 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP167 | 0 | 1 | 0.33 | 0.47 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP168 | 0 | 1 | 0.67 | 0.47 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▅▁▁▁▇ |
| FP169 | 0 | 1 | 0.19 | 0.39 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP170 | 0 | 1 | 0.18 | 0.39 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP171 | 0 | 1 | 0.17 | 0.38 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP172 | 0 | 1 | 0.15 | 0.36 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP173 | 0 | 1 | 0.14 | 0.35 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP174 | 0 | 1 | 0.13 | 0.34 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP175 | 0 | 1 | 0.13 | 0.34 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP176 | 0 | 1 | 0.12 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP177 | 0 | 1 | 0.12 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP178 | 0 | 1 | 0.12 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP179 | 0 | 1 | 0.10 | 0.30 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP180 | 0 | 1 | 0.11 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP181 | 0 | 1 | 0.09 | 0.29 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP182 | 0 | 1 | 0.10 | 0.30 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP183 | 0 | 1 | 0.08 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP184 | 0 | 1 | 0.08 | 0.28 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP185 | 0 | 1 | 0.09 | 0.28 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP186 | 0 | 1 | 0.08 | 0.27 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP187 | 0 | 1 | 0.07 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP188 | 0 | 1 | 0.07 | 0.25 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP189 | 0 | 1 | 0.08 | 0.27 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP190 | 0 | 1 | 0.07 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP191 | 0 | 1 | 0.07 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP192 | 0 | 1 | 0.06 | 0.24 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP193 | 0 | 1 | 0.06 | 0.24 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP194 | 0 | 1 | 0.06 | 0.24 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP195 | 0 | 1 | 0.06 | 0.24 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP196 | 0 | 1 | 0.06 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP197 | 0 | 1 | 0.05 | 0.22 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP198 | 0 | 1 | 0.06 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP199 | 0 | 1 | 0.05 | 0.21 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP200 | 0 | 1 | 0.05 | 0.22 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP201 | 0 | 1 | 0.05 | 0.22 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP202 | 0 | 1 | 0.26 | 0.44 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP203 | 0 | 1 | 0.11 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP204 | 0 | 1 | 0.10 | 0.30 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP205 | 0 | 1 | 0.08 | 0.27 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP206 | 0 | 1 | 0.06 | 0.24 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP207 | 0 | 1 | 0.06 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP208 | 0 | 1 | 0.11 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| MolWeight | 0 | 1 | 201.65 | 97.91 | 46.09 | 122.60 | 179.23 | 264.34 | 665.81 | ▇▆▂▁▁ |
| NumAtoms | 0 | 1 | 25.51 | 12.61 | 5.00 | 17.00 | 22.00 | 31.00 | 94.00 | ▇▆▂▁▁ |
| NumNonHAtoms | 0 | 1 | 13.16 | 6.50 | 2.00 | 8.00 | 12.00 | 17.00 | 47.00 | ▇▆▂▁▁ |
| NumBonds | 0 | 1 | 25.91 | 13.48 | 4.00 | 17.00 | 23.00 | 31.50 | 97.00 | ▇▇▂▁▁ |
| NumNonHBonds | 0 | 1 | 13.56 | 7.57 | 1.00 | 8.00 | 12.00 | 18.00 | 50.00 | ▇▇▂▁▁ |
| NumMultBonds | 0 | 1 | 6.15 | 5.17 | 0.00 | 1.00 | 6.00 | 10.00 | 25.00 | ▇▆▃▁▁ |
| NumRotBonds | 0 | 1 | 2.25 | 2.41 | 0.00 | 0.00 | 2.00 | 3.50 | 16.00 | ▇▂▁▁▁ |
| NumDblBonds | 0 | 1 | 1.01 | 1.21 | 0.00 | 0.00 | 1.00 | 2.00 | 7.00 | ▇▂▁▁▁ |
| NumAromaticBonds | 0 | 1 | 5.12 | 5.26 | 0.00 | 0.00 | 6.00 | 6.00 | 25.00 | ▇▆▃▁▁ |
| NumHydrogen | 0 | 1 | 12.35 | 7.32 | 0.00 | 7.00 | 11.00 | 16.00 | 47.00 | ▇▇▂▁▁ |
| NumCarbon | 0 | 1 | 9.89 | 5.29 | 1.00 | 6.00 | 9.00 | 12.00 | 33.00 | ▇▇▃▁▁ |
| NumNitrogen | 0 | 1 | 0.81 | 1.19 | 0.00 | 0.00 | 0.00 | 1.00 | 6.00 | ▇▂▁▁▁ |
| NumOxygen | 0 | 1 | 1.57 | 1.73 | 0.00 | 0.00 | 1.00 | 2.00 | 13.00 | ▇▂▁▁▁ |
| NumSulfer | 0 | 1 | 0.16 | 0.49 | 0.00 | 0.00 | 0.00 | 0.00 | 4.00 | ▇▁▁▁▁ |
| NumChlorine | 0 | 1 | 0.56 | 1.40 | 0.00 | 0.00 | 0.00 | 0.00 | 10.00 | ▇▁▁▁▁ |
| NumHalogen | 0 | 1 | 0.70 | 1.47 | 0.00 | 0.00 | 0.00 | 1.00 | 10.00 | ▇▁▁▁▁ |
| NumRings | 0 | 1 | 1.40 | 1.30 | 0.00 | 0.00 | 1.00 | 2.00 | 7.00 | ▇▃▂▁▁ |
| HydrophilicFactor | 0 | 1 | -0.02 | 1.13 | -0.98 | -0.76 | -0.31 | 0.31 | 13.48 | ▇▁▁▁▁ |
| SurfaceArea1 | 0 | 1 | 36.46 | 35.29 | 0.00 | 9.23 | 29.10 | 53.28 | 331.94 | ▇▂▁▁▁ |
| SurfaceArea2 | 0 | 1 | 40.23 | 38.12 | 0.00 | 10.63 | 33.12 | 60.66 | 331.94 | ▇▂▁▁▁ |
###################################
# Verifying the data dimensions
###################################
dim(DPA_ExcludedHighCorrelation)## [1] 951 2261.3.4 Linear Dependencies
Linear dependency data assessment:
[A] Linear dependencies noted for 2 subsets of variables using the preprocessing summary from the caret package applying the findLinearCombos method which utilizes the QR decomposition of a matrix to enumerate sets of linear combinations (if they exist).
[B] Subset 1
[B.1] NumNonHBonds variable (numeric)
[B.2] NumAtoms variable (numeric)
[B.3] NumNonHAtoms variable (numeric)
[B.3] NumBonds variable (numeric)
[C] Subset 2
[C.1] NumHydrogen variable (numeric)
[C.2] NumAtoms variable (numeric)
[C.3] NumNonHAtoms variable (numeric)
##################################
# Loading dataset
##################################
DPA <- Solubility_Train
##################################
# Listing all predictors
##################################
DPA.Predictors <- DPA[,!names(DPA) %in% c("Log_Solubility_Class")]
##################################
# Listing all numeric predictors
##################################
DPA.Predictors.Numeric <- DPA.Predictors[,sapply(DPA.Predictors, is.numeric)]
##################################
# Identifying the linearly dependent variables
##################################
DPA_LinearlyDependent <- findLinearCombos(DPA.Predictors.Numeric)
(DPA_LinearlyDependentCount <- length(DPA_LinearlyDependent$linearCombos))## [1] 2if (DPA_LinearlyDependentCount == 0) {
print("No linearly dependent predictors noted.")
} else {
print(paste0("Linear dependency observed for ",
(DPA_LinearlyDependentCount),
" subset(s) of numeric variable(s)."))
for (i in 1:DPA_LinearlyDependentCount) {
DPA_LinearlyDependentSubset <- colnames(DPA.Predictors.Numeric)[DPA_LinearlyDependent$linearCombos[[i]]]
print(paste0("Linear dependent variable(s) for subset ",
i,
" include: ",
DPA_LinearlyDependentSubset))
}
}## [1] "Linear dependency observed for 2 subset(s) of numeric variable(s)."
## [1] "Linear dependent variable(s) for subset 1 include: NumNonHBonds"
## [2] "Linear dependent variable(s) for subset 1 include: NumAtoms"
## [3] "Linear dependent variable(s) for subset 1 include: NumNonHAtoms"
## [4] "Linear dependent variable(s) for subset 1 include: NumBonds"
## [1] "Linear dependent variable(s) for subset 2 include: NumHydrogen"
## [2] "Linear dependent variable(s) for subset 2 include: NumAtoms"
## [3] "Linear dependent variable(s) for subset 2 include: NumNonHAtoms"##################################
# Identifying the linearly dependent variables for removal
##################################
if (DPA_LinearlyDependentCount > 0) {
DPA_LinearlyDependent <- findLinearCombos(DPA.Predictors.Numeric)
DPA_LinearlyDependentForRemoval <- length(DPA_LinearlyDependent$remove)
print(paste0("Linear dependency can be resolved by removing ",
(DPA_LinearlyDependentForRemoval),
" numeric variable(s)."))
for (j in 1:DPA_LinearlyDependentForRemoval) {
DPA_LinearlyDependentRemovedVariable <- colnames(DPA.Predictors.Numeric)[DPA_LinearlyDependent$remove[j]]
print(paste0("Variable ",
j,
" for removal: ",
DPA_LinearlyDependentRemovedVariable))
}
##################################
# Filtering out columns with linear dependency
#################################
DPA_ExcludedLinearlyDependent <- DPA[,-DPA_LinearlyDependent$remove]
##################################
# Gathering descriptive statistics
##################################
(DPA_ExcludedLinearlyDependent_Skimmed <- skim(DPA_ExcludedLinearlyDependent))
}## [1] "Linear dependency can be resolved by removing 2 numeric variable(s)."
## [1] "Variable 1 for removal: NumNonHBonds"
## [1] "Variable 2 for removal: NumHydrogen"| Name | DPA_ExcludedLinearlyDepen… |
| Number of rows | 951 |
| Number of columns | 227 |
| _______________________ | |
| Column type frequency: | |
| factor | 1 |
| numeric | 226 |
| ________________________ | |
| Group variables | None |
Variable type: factor
| skim_variable | n_missing | complete_rate | ordered | n_unique | top_counts |
|---|---|---|---|---|---|
| Log_Solubility_Class | 0 | 1 | FALSE | 2 | Hig: 524, Low: 427 |
Variable type: numeric
| skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
|---|---|---|---|---|---|---|---|---|---|---|
| FP001 | 0 | 1 | 0.49 | 0.50 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▇ |
| FP002 | 0 | 1 | 0.54 | 0.50 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▇▁▁▁▇ |
| FP003 | 0 | 1 | 0.44 | 0.50 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▆ |
| FP004 | 0 | 1 | 0.58 | 0.49 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▆▁▁▁▇ |
| FP005 | 0 | 1 | 0.58 | 0.49 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▆▁▁▁▇ |
| FP006 | 0 | 1 | 0.40 | 0.49 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▆ |
| FP007 | 0 | 1 | 0.36 | 0.48 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▅ |
| FP008 | 0 | 1 | 0.33 | 0.47 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP009 | 0 | 1 | 0.28 | 0.45 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP010 | 0 | 1 | 0.18 | 0.38 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP011 | 0 | 1 | 0.21 | 0.41 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP012 | 0 | 1 | 0.18 | 0.38 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP013 | 0 | 1 | 0.17 | 0.37 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP014 | 0 | 1 | 0.16 | 0.37 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP015 | 0 | 1 | 0.86 | 0.35 | 0.00 | 1.00 | 1.00 | 1.00 | 1.00 | ▁▁▁▁▇ |
| FP016 | 0 | 1 | 0.15 | 0.35 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP017 | 0 | 1 | 0.14 | 0.35 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP018 | 0 | 1 | 0.13 | 0.34 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP019 | 0 | 1 | 0.12 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP020 | 0 | 1 | 0.12 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP021 | 0 | 1 | 0.12 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP022 | 0 | 1 | 0.10 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP023 | 0 | 1 | 0.12 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP024 | 0 | 1 | 0.11 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP025 | 0 | 1 | 0.12 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP026 | 0 | 1 | 0.08 | 0.28 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP027 | 0 | 1 | 0.10 | 0.30 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP028 | 0 | 1 | 0.11 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP029 | 0 | 1 | 0.10 | 0.30 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP030 | 0 | 1 | 0.09 | 0.29 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP031 | 0 | 1 | 0.09 | 0.29 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP032 | 0 | 1 | 0.07 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP033 | 0 | 1 | 0.07 | 0.25 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP034 | 0 | 1 | 0.08 | 0.27 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP035 | 0 | 1 | 0.07 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP036 | 0 | 1 | 0.08 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP037 | 0 | 1 | 0.07 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP038 | 0 | 1 | 0.09 | 0.28 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP039 | 0 | 1 | 0.07 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP040 | 0 | 1 | 0.07 | 0.25 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP041 | 0 | 1 | 0.06 | 0.24 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP042 | 0 | 1 | 0.06 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP043 | 0 | 1 | 0.07 | 0.25 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP044 | 0 | 1 | 0.06 | 0.24 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP045 | 0 | 1 | 0.06 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP046 | 0 | 1 | 0.32 | 0.46 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP047 | 0 | 1 | 0.27 | 0.44 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP048 | 0 | 1 | 0.12 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP049 | 0 | 1 | 0.12 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP050 | 0 | 1 | 0.11 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP051 | 0 | 1 | 0.11 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP052 | 0 | 1 | 0.09 | 0.29 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP053 | 0 | 1 | 0.09 | 0.29 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP054 | 0 | 1 | 0.08 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP055 | 0 | 1 | 0.05 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP056 | 0 | 1 | 0.07 | 0.25 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP057 | 0 | 1 | 0.12 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP058 | 0 | 1 | 0.11 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP059 | 0 | 1 | 0.05 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP060 | 0 | 1 | 0.48 | 0.50 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▇ |
| FP061 | 0 | 1 | 0.45 | 0.50 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▆ |
| FP062 | 0 | 1 | 0.44 | 0.50 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▆ |
| FP063 | 0 | 1 | 0.43 | 0.49 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▆ |
| FP064 | 0 | 1 | 0.42 | 0.49 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▆ |
| FP065 | 0 | 1 | 0.59 | 0.49 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▆▁▁▁▇ |
| FP066 | 0 | 1 | 0.61 | 0.49 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▅▁▁▁▇ |
| FP067 | 0 | 1 | 0.38 | 0.49 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▅ |
| FP068 | 0 | 1 | 0.36 | 0.48 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▅ |
| FP069 | 0 | 1 | 0.36 | 0.48 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▅ |
| FP070 | 0 | 1 | 0.36 | 0.48 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▅ |
| FP071 | 0 | 1 | 0.33 | 0.47 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP072 | 0 | 1 | 0.66 | 0.47 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▅▁▁▁▇ |
| FP073 | 0 | 1 | 0.31 | 0.46 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP074 | 0 | 1 | 0.32 | 0.47 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP075 | 0 | 1 | 0.34 | 0.47 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▅ |
| FP076 | 0 | 1 | 0.33 | 0.47 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP077 | 0 | 1 | 0.32 | 0.47 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP078 | 0 | 1 | 0.30 | 0.46 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP079 | 0 | 1 | 0.69 | 0.46 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▃▁▁▁▇ |
| FP080 | 0 | 1 | 0.30 | 0.46 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP081 | 0 | 1 | 0.28 | 0.45 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP082 | 0 | 1 | 0.71 | 0.45 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▃▁▁▁▇ |
| FP083 | 0 | 1 | 0.27 | 0.45 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP084 | 0 | 1 | 0.29 | 0.45 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP085 | 0 | 1 | 0.26 | 0.44 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP086 | 0 | 1 | 0.27 | 0.44 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP087 | 0 | 1 | 0.73 | 0.45 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▃▁▁▁▇ |
| FP088 | 0 | 1 | 0.26 | 0.44 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP089 | 0 | 1 | 0.25 | 0.43 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP090 | 0 | 1 | 0.25 | 0.43 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP091 | 0 | 1 | 0.23 | 0.42 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP092 | 0 | 1 | 0.24 | 0.43 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP093 | 0 | 1 | 0.24 | 0.43 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP094 | 0 | 1 | 0.23 | 0.42 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP095 | 0 | 1 | 0.22 | 0.41 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP096 | 0 | 1 | 0.22 | 0.41 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP097 | 0 | 1 | 0.24 | 0.42 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP098 | 0 | 1 | 0.24 | 0.43 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP099 | 0 | 1 | 0.23 | 0.42 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP100 | 0 | 1 | 0.23 | 0.42 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP101 | 0 | 1 | 0.24 | 0.43 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP102 | 0 | 1 | 0.20 | 0.40 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP103 | 0 | 1 | 0.22 | 0.41 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP104 | 0 | 1 | 0.22 | 0.42 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP105 | 0 | 1 | 0.22 | 0.41 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP106 | 0 | 1 | 0.19 | 0.39 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP107 | 0 | 1 | 0.21 | 0.41 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP108 | 0 | 1 | 0.21 | 0.40 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP109 | 0 | 1 | 0.18 | 0.38 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP110 | 0 | 1 | 0.21 | 0.40 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP111 | 0 | 1 | 0.20 | 0.40 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP112 | 0 | 1 | 0.19 | 0.40 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP113 | 0 | 1 | 0.20 | 0.40 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP114 | 0 | 1 | 0.16 | 0.36 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP115 | 0 | 1 | 0.18 | 0.38 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP116 | 0 | 1 | 0.19 | 0.39 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP117 | 0 | 1 | 0.18 | 0.38 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP118 | 0 | 1 | 0.19 | 0.39 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP119 | 0 | 1 | 0.16 | 0.37 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP120 | 0 | 1 | 0.17 | 0.37 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP121 | 0 | 1 | 0.14 | 0.35 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP122 | 0 | 1 | 0.16 | 0.37 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP123 | 0 | 1 | 0.17 | 0.37 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP124 | 0 | 1 | 0.16 | 0.37 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP125 | 0 | 1 | 0.16 | 0.36 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP126 | 0 | 1 | 0.15 | 0.36 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP127 | 0 | 1 | 0.14 | 0.35 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP128 | 0 | 1 | 0.15 | 0.36 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP129 | 0 | 1 | 0.14 | 0.35 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP130 | 0 | 1 | 0.11 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP131 | 0 | 1 | 0.13 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP132 | 0 | 1 | 0.13 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP133 | 0 | 1 | 0.13 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP134 | 0 | 1 | 0.13 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP135 | 0 | 1 | 0.13 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP136 | 0 | 1 | 0.12 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP137 | 0 | 1 | 0.12 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP138 | 0 | 1 | 0.11 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP139 | 0 | 1 | 0.08 | 0.27 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP140 | 0 | 1 | 0.11 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP141 | 0 | 1 | 0.12 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP142 | 0 | 1 | 0.11 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP143 | 0 | 1 | 0.08 | 0.27 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP144 | 0 | 1 | 0.10 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP145 | 0 | 1 | 0.10 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP146 | 0 | 1 | 0.10 | 0.30 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP147 | 0 | 1 | 0.11 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP148 | 0 | 1 | 0.09 | 0.28 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP149 | 0 | 1 | 0.09 | 0.29 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP150 | 0 | 1 | 0.08 | 0.27 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP151 | 0 | 1 | 0.06 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP152 | 0 | 1 | 0.08 | 0.27 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP153 | 0 | 1 | 0.08 | 0.27 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP154 | 0 | 1 | 0.04 | 0.19 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP155 | 0 | 1 | 0.07 | 0.25 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP156 | 0 | 1 | 0.07 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP157 | 0 | 1 | 0.06 | 0.24 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP158 | 0 | 1 | 0.05 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP159 | 0 | 1 | 0.07 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP160 | 0 | 1 | 0.07 | 0.25 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP161 | 0 | 1 | 0.07 | 0.25 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP162 | 0 | 1 | 0.50 | 0.50 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▇ |
| FP163 | 0 | 1 | 0.48 | 0.50 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▇ |
| FP164 | 0 | 1 | 0.63 | 0.48 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▅▁▁▁▇ |
| FP165 | 0 | 1 | 0.35 | 0.48 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▅ |
| FP166 | 0 | 1 | 0.33 | 0.47 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP167 | 0 | 1 | 0.33 | 0.47 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP168 | 0 | 1 | 0.67 | 0.47 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 | ▅▁▁▁▇ |
| FP169 | 0 | 1 | 0.19 | 0.39 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP170 | 0 | 1 | 0.18 | 0.39 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP171 | 0 | 1 | 0.17 | 0.38 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP172 | 0 | 1 | 0.15 | 0.36 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
| FP173 | 0 | 1 | 0.14 | 0.35 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP174 | 0 | 1 | 0.13 | 0.34 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP175 | 0 | 1 | 0.13 | 0.34 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP176 | 0 | 1 | 0.12 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP177 | 0 | 1 | 0.12 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP178 | 0 | 1 | 0.12 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP179 | 0 | 1 | 0.10 | 0.30 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP180 | 0 | 1 | 0.11 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP181 | 0 | 1 | 0.09 | 0.29 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP182 | 0 | 1 | 0.10 | 0.30 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP183 | 0 | 1 | 0.08 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP184 | 0 | 1 | 0.08 | 0.28 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP185 | 0 | 1 | 0.09 | 0.28 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP186 | 0 | 1 | 0.08 | 0.27 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP187 | 0 | 1 | 0.07 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP188 | 0 | 1 | 0.07 | 0.25 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP189 | 0 | 1 | 0.08 | 0.27 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP190 | 0 | 1 | 0.07 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP191 | 0 | 1 | 0.07 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP192 | 0 | 1 | 0.06 | 0.24 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP193 | 0 | 1 | 0.06 | 0.24 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP194 | 0 | 1 | 0.06 | 0.24 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP195 | 0 | 1 | 0.06 | 0.24 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP196 | 0 | 1 | 0.06 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP197 | 0 | 1 | 0.05 | 0.22 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP198 | 0 | 1 | 0.06 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP199 | 0 | 1 | 0.05 | 0.21 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP200 | 0 | 1 | 0.05 | 0.22 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP201 | 0 | 1 | 0.05 | 0.22 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP202 | 0 | 1 | 0.26 | 0.44 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▃ |
| FP203 | 0 | 1 | 0.11 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP204 | 0 | 1 | 0.10 | 0.30 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP205 | 0 | 1 | 0.08 | 0.27 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP206 | 0 | 1 | 0.06 | 0.24 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP207 | 0 | 1 | 0.06 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| FP208 | 0 | 1 | 0.11 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▁ |
| MolWeight | 0 | 1 | 201.65 | 97.91 | 46.09 | 122.60 | 179.23 | 264.34 | 665.81 | ▇▆▂▁▁ |
| NumAtoms | 0 | 1 | 25.51 | 12.61 | 5.00 | 17.00 | 22.00 | 31.00 | 94.00 | ▇▆▂▁▁ |
| NumNonHAtoms | 0 | 1 | 13.16 | 6.50 | 2.00 | 8.00 | 12.00 | 17.00 | 47.00 | ▇▆▂▁▁ |
| NumBonds | 0 | 1 | 25.91 | 13.48 | 4.00 | 17.00 | 23.00 | 31.50 | 97.00 | ▇▇▂▁▁ |
| NumMultBonds | 0 | 1 | 6.15 | 5.17 | 0.00 | 1.00 | 6.00 | 10.00 | 25.00 | ▇▆▃▁▁ |
| NumRotBonds | 0 | 1 | 2.25 | 2.41 | 0.00 | 0.00 | 2.00 | 3.50 | 16.00 | ▇▂▁▁▁ |
| NumDblBonds | 0 | 1 | 1.01 | 1.21 | 0.00 | 0.00 | 1.00 | 2.00 | 7.00 | ▇▂▁▁▁ |
| NumAromaticBonds | 0 | 1 | 5.12 | 5.26 | 0.00 | 0.00 | 6.00 | 6.00 | 25.00 | ▇▆▃▁▁ |
| NumCarbon | 0 | 1 | 9.89 | 5.29 | 1.00 | 6.00 | 9.00 | 12.00 | 33.00 | ▇▇▃▁▁ |
| NumNitrogen | 0 | 1 | 0.81 | 1.19 | 0.00 | 0.00 | 0.00 | 1.00 | 6.00 | ▇▂▁▁▁ |
| NumOxygen | 0 | 1 | 1.57 | 1.73 | 0.00 | 0.00 | 1.00 | 2.00 | 13.00 | ▇▂▁▁▁ |
| NumSulfer | 0 | 1 | 0.16 | 0.49 | 0.00 | 0.00 | 0.00 | 0.00 | 4.00 | ▇▁▁▁▁ |
| NumChlorine | 0 | 1 | 0.56 | 1.40 | 0.00 | 0.00 | 0.00 | 0.00 | 10.00 | ▇▁▁▁▁ |
| NumHalogen | 0 | 1 | 0.70 | 1.47 | 0.00 | 0.00 | 0.00 | 1.00 | 10.00 | ▇▁▁▁▁ |
| NumRings | 0 | 1 | 1.40 | 1.30 | 0.00 | 0.00 | 1.00 | 2.00 | 7.00 | ▇▃▂▁▁ |
| HydrophilicFactor | 0 | 1 | -0.02 | 1.13 | -0.98 | -0.76 | -0.31 | 0.31 | 13.48 | ▇▁▁▁▁ |
| SurfaceArea1 | 0 | 1 | 36.46 | 35.29 | 0.00 | 9.23 | 29.10 | 53.28 | 331.94 | ▇▂▁▁▁ |
| SurfaceArea2 | 0 | 1 | 40.23 | 38.12 | 0.00 | 10.63 | 33.12 | 60.66 | 331.94 | ▇▂▁▁▁ |
###################################
# Verifying the data dimensions
###################################
dim(DPA_ExcludedLinearlyDependent)## [1] 951 2271.3.5 Shape Transformation
Data transformation assessment:
[A] A number of numeric variables in the dataset were observed to be right-skewed which required shape transformation for data distribution stability. Considering that all numeric variables were strictly positive values, the BoxCox method from the caret package was used to transform their distributional shapes.
##################################
# Loading dataset
##################################
DPA <- Solubility_Train
##################################
# Listing all predictors
##################################
DPA.Predictors <- DPA[,!names(DPA) %in% c("Log_Solubility_Class")]
##################################
# Listing all numeric predictors
##################################
DPA.Predictors.Numeric <- DPA.Predictors[,-(grep("FP", names(DPA.Predictors)))]
##################################
# Applying a Box-Cox transformation
##################################
DPA_BoxCox <- preProcess(DPA.Predictors.Numeric, method = c("BoxCox"))
DPA_BoxCoxTransformed <- predict(DPA_BoxCox, DPA.Predictors.Numeric)
##################################
# Gathering descriptive statistics
##################################
(DPA_BoxCoxTransformedSkimmed <- skim(DPA_BoxCoxTransformed))| Name | DPA_BoxCoxTransformed |
| Number of rows | 951 |
| Number of columns | 20 |
| _______________________ | |
| Column type frequency: | |
| numeric | 20 |
| ________________________ | |
| Group variables | None |
Variable type: numeric
| skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
|---|---|---|---|---|---|---|---|---|---|---|
| MolWeight | 0 | 1 | 5.19 | 0.48 | 3.83 | 4.81 | 5.19 | 5.58 | 6.50 | ▁▆▇▆▁ |
| NumAtoms | 0 | 1 | 3.13 | 0.48 | 1.61 | 2.83 | 3.09 | 3.43 | 4.54 | ▁▃▇▃▁ |
| NumNonHAtoms | 0 | 1 | 2.46 | 0.50 | 0.69 | 2.08 | 2.48 | 2.83 | 3.85 | ▁▃▇▇▁ |
| NumBonds | 0 | 1 | 4.39 | 0.96 | 1.60 | 3.81 | 4.36 | 4.97 | 7.48 | ▁▅▇▃▁ |
| NumNonHBonds | 0 | 1 | 3.21 | 0.95 | 0.00 | 2.58 | 3.22 | 3.91 | 5.93 | ▁▃▇▆▁ |
| NumMultBonds | 0 | 1 | 6.15 | 5.17 | 0.00 | 1.00 | 6.00 | 10.00 | 25.00 | ▇▆▃▁▁ |
| NumRotBonds | 0 | 1 | 2.25 | 2.41 | 0.00 | 0.00 | 2.00 | 3.50 | 16.00 | ▇▂▁▁▁ |
| NumDblBonds | 0 | 1 | 1.01 | 1.21 | 0.00 | 0.00 | 1.00 | 2.00 | 7.00 | ▇▂▁▁▁ |
| NumAromaticBonds | 0 | 1 | 5.12 | 5.26 | 0.00 | 0.00 | 6.00 | 6.00 | 25.00 | ▇▆▃▁▁ |
| NumHydrogen | 0 | 1 | 12.35 | 7.32 | 0.00 | 7.00 | 11.00 | 16.00 | 47.00 | ▇▇▂▁▁ |
| NumCarbon | 0 | 1 | 3.54 | 1.34 | 0.00 | 2.62 | 3.52 | 4.25 | 7.62 | ▂▇▇▃▁ |
| NumNitrogen | 0 | 1 | 0.81 | 1.19 | 0.00 | 0.00 | 0.00 | 1.00 | 6.00 | ▇▂▁▁▁ |
| NumOxygen | 0 | 1 | 1.57 | 1.73 | 0.00 | 0.00 | 1.00 | 2.00 | 13.00 | ▇▂▁▁▁ |
| NumSulfer | 0 | 1 | 0.16 | 0.49 | 0.00 | 0.00 | 0.00 | 0.00 | 4.00 | ▇▁▁▁▁ |
| NumChlorine | 0 | 1 | 0.56 | 1.40 | 0.00 | 0.00 | 0.00 | 0.00 | 10.00 | ▇▁▁▁▁ |
| NumHalogen | 0 | 1 | 0.70 | 1.47 | 0.00 | 0.00 | 0.00 | 1.00 | 10.00 | ▇▁▁▁▁ |
| NumRings | 0 | 1 | 1.40 | 1.30 | 0.00 | 0.00 | 1.00 | 2.00 | 7.00 | ▇▃▂▁▁ |
| HydrophilicFactor | 0 | 1 | -0.02 | 1.13 | -0.98 | -0.76 | -0.31 | 0.31 | 13.48 | ▇▁▁▁▁ |
| SurfaceArea1 | 0 | 1 | 36.46 | 35.29 | 0.00 | 9.23 | 29.10 | 53.28 | 331.94 | ▇▂▁▁▁ |
| SurfaceArea2 | 0 | 1 | 40.23 | 38.12 | 0.00 | 10.63 | 33.12 | 60.66 | 331.94 | ▇▂▁▁▁ |
###################################
# Verifying the data dimensions
###################################
dim(DPA_BoxCoxTransformed)## [1] 951 201.3.6 Centering and Scaling
Centering and scaling data assessment:
[A] To maintain numerical stability during modelling, centering and scaling transformations were applied on the transformed numeric variables. The center method from the caret package was implemented which subtracts the average value of a numeric variable to all the values. As a result of centering, the variables had zero mean values. In addition, the scale method, also from the caret package, was applied which performs a center transformation with each value of the variable divided by its standard deviation. Scaling the data coerced the values to have a common standard deviation of one.
##################################
# Loading dataset
##################################
DPA <- Solubility_Train
##################################
# Listing all predictors
##################################
DPA.Predictors <- DPA[,!names(DPA) %in% c("Log_Solubility_Class")]
##################################
# Listing all numeric predictors
##################################
DPA.Predictors.Numeric <- DPA.Predictors[,-(grep("FP", names(DPA.Predictors)))]
##################################
# Applying a Box-Cox transformation
##################################
DPA_BoxCox <- preProcess(DPA.Predictors.Numeric, method = c("BoxCox"))
DPA_BoxCoxTransformed <- predict(DPA_BoxCox, DPA.Predictors.Numeric)
##################################
# Applying a center and scale data transformation
##################################
DPA.Predictors.Numeric_BoxCoxTransformed_CenteredScaled <- preProcess(DPA_BoxCoxTransformed, method = c("center","scale"))
DPA.Predictors.Numeric_BoxCoxTransformed_CenteredScaledTransformed <- predict(DPA.Predictors.Numeric_BoxCoxTransformed_CenteredScaled, DPA_BoxCoxTransformed)
##################################
# Gathering descriptive statistics
##################################
(DPA.Predictors.Numeric_BoxCoxTransformed_CenteredScaledTransformedSkimmed <- skim(DPA.Predictors.Numeric_BoxCoxTransformed_CenteredScaledTransformed))| Name | DPA.Predictors.Numeric_Bo… |
| Number of rows | 951 |
| Number of columns | 20 |
| _______________________ | |
| Column type frequency: | |
| numeric | 20 |
| ________________________ | |
| Group variables | None |
Variable type: numeric
| skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
|---|---|---|---|---|---|---|---|---|---|---|
| MolWeight | 0 | 1 | 0 | 1 | -2.84 | -0.80 | -0.01 | 0.80 | 2.72 | ▁▆▇▆▁ |
| NumAtoms | 0 | 1 | 0 | 1 | -3.16 | -0.61 | -0.07 | 0.64 | 2.95 | ▁▃▇▃▁ |
| NumNonHAtoms | 0 | 1 | 0 | 1 | -3.53 | -0.76 | 0.06 | 0.75 | 2.79 | ▁▃▇▇▁ |
| NumBonds | 0 | 1 | 0 | 1 | -2.92 | -0.61 | -0.04 | 0.60 | 3.23 | ▁▅▇▃▁ |
| NumNonHBonds | 0 | 1 | 0 | 1 | -3.38 | -0.67 | 0.01 | 0.74 | 2.86 | ▁▃▇▆▁ |
| NumMultBonds | 0 | 1 | 0 | 1 | -1.19 | -1.00 | -0.03 | 0.74 | 3.65 | ▇▇▃▁▁ |
| NumRotBonds | 0 | 1 | 0 | 1 | -0.93 | -0.93 | -0.10 | 0.52 | 5.71 | ▇▂▁▁▁ |
| NumDblBonds | 0 | 1 | 0 | 1 | -0.83 | -0.83 | -0.01 | 0.82 | 4.95 | ▇▂▁▁▁ |
| NumAromaticBonds | 0 | 1 | 0 | 1 | -0.97 | -0.97 | 0.17 | 0.17 | 3.78 | ▇▆▃▁▁ |
| NumHydrogen | 0 | 1 | 0 | 1 | -1.69 | -0.73 | -0.18 | 0.50 | 4.74 | ▇▇▂▁▁ |
| NumCarbon | 0 | 1 | 0 | 1 | -2.64 | -0.69 | -0.01 | 0.54 | 3.06 | ▂▇▇▃▁ |
| NumNitrogen | 0 | 1 | 0 | 1 | -0.69 | -0.69 | -0.69 | 0.16 | 4.37 | ▇▂▁▁▁ |
| NumOxygen | 0 | 1 | 0 | 1 | -0.91 | -0.91 | -0.33 | 0.25 | 6.61 | ▇▂▁▁▁ |
| NumSulfer | 0 | 1 | 0 | 1 | -0.34 | -0.34 | -0.34 | -0.34 | 7.86 | ▇▁▁▁▁ |
| NumChlorine | 0 | 1 | 0 | 1 | -0.40 | -0.40 | -0.40 | -0.40 | 6.74 | ▇▁▁▁▁ |
| NumHalogen | 0 | 1 | 0 | 1 | -0.47 | -0.47 | -0.47 | 0.20 | 6.32 | ▇▁▁▁▁ |
| NumRings | 0 | 1 | 0 | 1 | -1.08 | -1.08 | -0.31 | 0.46 | 4.31 | ▇▃▂▁▁ |
| HydrophilicFactor | 0 | 1 | 0 | 1 | -0.86 | -0.66 | -0.26 | 0.30 | 11.99 | ▇▁▁▁▁ |
| SurfaceArea1 | 0 | 1 | 0 | 1 | -1.03 | -0.77 | -0.21 | 0.48 | 8.37 | ▇▂▁▁▁ |
| SurfaceArea2 | 0 | 1 | 0 | 1 | -1.06 | -0.78 | -0.19 | 0.54 | 7.65 | ▇▂▁▁▁ |
###################################
# Verifying the data dimensions
###################################
dim(DPA.Predictors.Numeric_BoxCoxTransformed_CenteredScaledTransformed)## [1] 951 201.3.7 Pre-Processed Dataset
Preliminary dataset assessment:
[A] 1267 rows (observations)
[A.1] Train Set = 951 observations
[A.2] Test Set = 316 observations
[B] 221 columns (variables)
[B.1] 1/221 response = Class variable (factor)
[B.1.1] Levels = Log_Solubility_Class=Low < Log_Solubility_Class=High
[B.2] 220/221 predictors = All remaining variables (205/220 factor + 15/220 numeric)
[C] Pre-processing actions applied:
[C.1] Centering, scaling and shape transformation applied to improve data quality
[C.2] No outlier treatment applied since the high values noted were contextually valid and sensible
[C.3] 3 predictors removed due to zero or near-zero variance
[C.4] 3 predictors removed due to high correlation
[C.5] 2 predictors removed due to linear dependencies
##################################
# Creating the pre-modelling
# train set
##################################
Log_Solubility_Class <- DPA$Log_Solubility_Class
PMA.Predictors.Factor <- DPA.Predictors[,(grep("FP", names(DPA.Predictors)))]
PMA.Predictors.Factor <- as.data.frame(lapply(PMA.Predictors.Factor,factor))
PMA.Predictors.Numeric <- DPA.Predictors.Numeric_BoxCoxTransformed_CenteredScaledTransformed
PMA_BoxCoxTransformed_CenteredScaledTransformed <- cbind(Log_Solubility_Class,PMA.Predictors.Factor,PMA.Predictors.Numeric)
##################################
# Filtering out columns noted with data quality issues including
# zero and near-zero variance,
# high correlation and linear dependencies
# to create the pre-modelling dataset
##################################
PMA_BoxCoxTransformed_CenteredScaledTransformed_ExcludedLowVariance_ExcludedLinearlyDependent_ExcludedHighCorrelation <- PMA_BoxCoxTransformed_CenteredScaledTransformed[,!names(PMA_BoxCoxTransformed_CenteredScaledTransformed) %in% c("FP154","FP199","FP200","NumNonHBonds","NumHydrogen","NumNonHAtoms","NumAromaticBonds","NumAtoms")]
PMA_PreModelling_Train <- PMA_BoxCoxTransformed_CenteredScaledTransformed_ExcludedLowVariance_ExcludedLinearlyDependent_ExcludedHighCorrelation
##################################
# Gathering descriptive statistics
##################################
(PMA_PreModelling_Train_Skimmed <- skim(PMA_PreModelling_Train))| Name | PMA_PreModelling_Train |
| Number of rows | 951 |
| Number of columns | 221 |
| _______________________ | |
| Column type frequency: | |
| factor | 206 |
| numeric | 15 |
| ________________________ | |
| Group variables | None |
Variable type: factor
| skim_variable | n_missing | complete_rate | ordered | n_unique | top_counts |
|---|---|---|---|---|---|
| Log_Solubility_Class | 0 | 1 | FALSE | 2 | Hig: 524, Low: 427 |
| FP001 | 0 | 1 | FALSE | 2 | 0: 482, 1: 469 |
| FP002 | 0 | 1 | FALSE | 2 | 1: 513, 0: 438 |
| FP003 | 0 | 1 | FALSE | 2 | 0: 536, 1: 415 |
| FP004 | 0 | 1 | FALSE | 2 | 1: 556, 0: 395 |
| FP005 | 0 | 1 | FALSE | 2 | 1: 551, 0: 400 |
| FP006 | 0 | 1 | FALSE | 2 | 0: 570, 1: 381 |
| FP007 | 0 | 1 | FALSE | 2 | 0: 605, 1: 346 |
| FP008 | 0 | 1 | FALSE | 2 | 0: 641, 1: 310 |
| FP009 | 0 | 1 | FALSE | 2 | 0: 685, 1: 266 |
| FP010 | 0 | 1 | FALSE | 2 | 0: 781, 1: 170 |
| FP011 | 0 | 1 | FALSE | 2 | 0: 747, 1: 204 |
| FP012 | 0 | 1 | FALSE | 2 | 0: 783, 1: 168 |
| FP013 | 0 | 1 | FALSE | 2 | 0: 793, 1: 158 |
| FP014 | 0 | 1 | FALSE | 2 | 0: 798, 1: 153 |
| FP015 | 0 | 1 | FALSE | 2 | 1: 818, 0: 133 |
| FP016 | 0 | 1 | FALSE | 2 | 0: 812, 1: 139 |
| FP017 | 0 | 1 | FALSE | 2 | 0: 814, 1: 137 |
| FP018 | 0 | 1 | FALSE | 2 | 0: 826, 1: 125 |
| FP019 | 0 | 1 | FALSE | 2 | 0: 835, 1: 116 |
| FP020 | 0 | 1 | FALSE | 2 | 0: 837, 1: 114 |
| FP021 | 0 | 1 | FALSE | 2 | 0: 836, 1: 115 |
| FP022 | 0 | 1 | FALSE | 2 | 0: 852, 1: 99 |
| FP023 | 0 | 1 | FALSE | 2 | 0: 834, 1: 117 |
| FP024 | 0 | 1 | FALSE | 2 | 0: 844, 1: 107 |
| FP025 | 0 | 1 | FALSE | 2 | 0: 841, 1: 110 |
| FP026 | 0 | 1 | FALSE | 2 | 0: 871, 1: 80 |
| FP027 | 0 | 1 | FALSE | 2 | 0: 858, 1: 93 |
| FP028 | 0 | 1 | FALSE | 2 | 0: 850, 1: 101 |
| FP029 | 0 | 1 | FALSE | 2 | 0: 854, 1: 97 |
| FP030 | 0 | 1 | FALSE | 2 | 0: 862, 1: 89 |
| FP031 | 0 | 1 | FALSE | 2 | 0: 866, 1: 85 |
| FP032 | 0 | 1 | FALSE | 2 | 0: 881, 1: 70 |
| FP033 | 0 | 1 | FALSE | 2 | 0: 885, 1: 66 |
| FP034 | 0 | 1 | FALSE | 2 | 0: 875, 1: 76 |
| FP035 | 0 | 1 | FALSE | 2 | 0: 882, 1: 69 |
| FP036 | 0 | 1 | FALSE | 2 | 0: 879, 1: 72 |
| FP037 | 0 | 1 | FALSE | 2 | 0: 884, 1: 67 |
| FP038 | 0 | 1 | FALSE | 2 | 0: 869, 1: 82 |
| FP039 | 0 | 1 | FALSE | 2 | 0: 880, 1: 71 |
| FP040 | 0 | 1 | FALSE | 2 | 0: 886, 1: 65 |
| FP041 | 0 | 1 | FALSE | 2 | 0: 891, 1: 60 |
| FP042 | 0 | 1 | FALSE | 2 | 0: 897, 1: 54 |
| FP043 | 0 | 1 | FALSE | 2 | 0: 888, 1: 63 |
| FP044 | 0 | 1 | FALSE | 2 | 0: 894, 1: 57 |
| FP045 | 0 | 1 | FALSE | 2 | 0: 898, 1: 53 |
| FP046 | 0 | 1 | FALSE | 2 | 0: 651, 1: 300 |
| FP047 | 0 | 1 | FALSE | 2 | 0: 698, 1: 253 |
| FP048 | 0 | 1 | FALSE | 2 | 0: 833, 1: 118 |
| FP049 | 0 | 1 | FALSE | 2 | 0: 835, 1: 116 |
| FP050 | 0 | 1 | FALSE | 2 | 0: 844, 1: 107 |
| FP051 | 0 | 1 | FALSE | 2 | 0: 847, 1: 104 |
| FP052 | 0 | 1 | FALSE | 2 | 0: 864, 1: 87 |
| FP053 | 0 | 1 | FALSE | 2 | 0: 862, 1: 89 |
| FP054 | 0 | 1 | FALSE | 2 | 0: 879, 1: 72 |
| FP055 | 0 | 1 | FALSE | 2 | 0: 900, 1: 51 |
| FP056 | 0 | 1 | FALSE | 2 | 0: 889, 1: 62 |
| FP057 | 0 | 1 | FALSE | 2 | 0: 837, 1: 114 |
| FP058 | 0 | 1 | FALSE | 2 | 0: 843, 1: 108 |
| FP059 | 0 | 1 | FALSE | 2 | 0: 899, 1: 52 |
| FP060 | 0 | 1 | FALSE | 2 | 0: 493, 1: 458 |
| FP061 | 0 | 1 | FALSE | 2 | 0: 526, 1: 425 |
| FP062 | 0 | 1 | FALSE | 2 | 0: 535, 1: 416 |
| FP063 | 0 | 1 | FALSE | 2 | 0: 546, 1: 405 |
| FP064 | 0 | 1 | FALSE | 2 | 0: 555, 1: 396 |
| FP065 | 0 | 1 | FALSE | 2 | 1: 564, 0: 387 |
| FP066 | 0 | 1 | FALSE | 2 | 1: 580, 0: 371 |
| FP067 | 0 | 1 | FALSE | 2 | 0: 590, 1: 361 |
| FP068 | 0 | 1 | FALSE | 2 | 0: 607, 1: 344 |
| FP069 | 0 | 1 | FALSE | 2 | 0: 607, 1: 344 |
| FP070 | 0 | 1 | FALSE | 2 | 0: 613, 1: 338 |
| FP071 | 0 | 1 | FALSE | 2 | 0: 640, 1: 311 |
| FP072 | 0 | 1 | FALSE | 2 | 1: 626, 0: 325 |
| FP073 | 0 | 1 | FALSE | 2 | 0: 656, 1: 295 |
| FP074 | 0 | 1 | FALSE | 2 | 0: 642, 1: 309 |
| FP075 | 0 | 1 | FALSE | 2 | 0: 629, 1: 322 |
| FP076 | 0 | 1 | FALSE | 2 | 0: 639, 1: 312 |
| FP077 | 0 | 1 | FALSE | 2 | 0: 646, 1: 305 |
| FP078 | 0 | 1 | FALSE | 2 | 0: 662, 1: 289 |
| FP079 | 0 | 1 | FALSE | 2 | 1: 656, 0: 295 |
| FP080 | 0 | 1 | FALSE | 2 | 0: 663, 1: 288 |
| FP081 | 0 | 1 | FALSE | 2 | 0: 686, 1: 265 |
| FP082 | 0 | 1 | FALSE | 2 | 1: 679, 0: 272 |
| FP083 | 0 | 1 | FALSE | 2 | 0: 691, 1: 260 |
| FP084 | 0 | 1 | FALSE | 2 | 0: 679, 1: 272 |
| FP085 | 0 | 1 | FALSE | 2 | 0: 708, 1: 243 |
| FP086 | 0 | 1 | FALSE | 2 | 0: 695, 1: 256 |
| FP087 | 0 | 1 | FALSE | 2 | 1: 691, 0: 260 |
| FP088 | 0 | 1 | FALSE | 2 | 0: 701, 1: 250 |
| FP089 | 0 | 1 | FALSE | 2 | 0: 716, 1: 235 |
| FP090 | 0 | 1 | FALSE | 2 | 0: 714, 1: 237 |
| FP091 | 0 | 1 | FALSE | 2 | 0: 737, 1: 214 |
| FP092 | 0 | 1 | FALSE | 2 | 0: 719, 1: 232 |
| FP093 | 0 | 1 | FALSE | 2 | 0: 719, 1: 232 |
| FP094 | 0 | 1 | FALSE | 2 | 0: 731, 1: 220 |
| FP095 | 0 | 1 | FALSE | 2 | 0: 742, 1: 209 |
| FP096 | 0 | 1 | FALSE | 2 | 0: 744, 1: 207 |
| FP097 | 0 | 1 | FALSE | 2 | 0: 727, 1: 224 |
| FP098 | 0 | 1 | FALSE | 2 | 0: 725, 1: 226 |
| FP099 | 0 | 1 | FALSE | 2 | 0: 735, 1: 216 |
| FP100 | 0 | 1 | FALSE | 2 | 0: 731, 1: 220 |
| FP101 | 0 | 1 | FALSE | 2 | 0: 726, 1: 225 |
| FP102 | 0 | 1 | FALSE | 2 | 0: 759, 1: 192 |
| FP103 | 0 | 1 | FALSE | 2 | 0: 743, 1: 208 |
| FP104 | 0 | 1 | FALSE | 2 | 0: 739, 1: 212 |
| FP105 | 0 | 1 | FALSE | 2 | 0: 746, 1: 205 |
| FP106 | 0 | 1 | FALSE | 2 | 0: 769, 1: 182 |
| FP107 | 0 | 1 | FALSE | 2 | 0: 750, 1: 201 |
| FP108 | 0 | 1 | FALSE | 2 | 0: 756, 1: 195 |
| FP109 | 0 | 1 | FALSE | 2 | 0: 783, 1: 168 |
| FP110 | 0 | 1 | FALSE | 2 | 0: 755, 1: 196 |
| FP111 | 0 | 1 | FALSE | 2 | 0: 764, 1: 187 |
| FP112 | 0 | 1 | FALSE | 2 | 0: 766, 1: 185 |
| FP113 | 0 | 1 | FALSE | 2 | 0: 765, 1: 186 |
| FP114 | 0 | 1 | FALSE | 2 | 0: 803, 1: 148 |
| FP115 | 0 | 1 | FALSE | 2 | 0: 781, 1: 170 |
| FP116 | 0 | 1 | FALSE | 2 | 0: 768, 1: 183 |
| FP117 | 0 | 1 | FALSE | 2 | 0: 781, 1: 170 |
| FP118 | 0 | 1 | FALSE | 2 | 0: 768, 1: 183 |
| FP119 | 0 | 1 | FALSE | 2 | 0: 796, 1: 155 |
| FP120 | 0 | 1 | FALSE | 2 | 0: 793, 1: 158 |
| FP121 | 0 | 1 | FALSE | 2 | 0: 818, 1: 133 |
| FP122 | 0 | 1 | FALSE | 2 | 0: 795, 1: 156 |
| FP123 | 0 | 1 | FALSE | 2 | 0: 792, 1: 159 |
| FP124 | 0 | 1 | FALSE | 2 | 0: 797, 1: 154 |
| FP125 | 0 | 1 | FALSE | 2 | 0: 803, 1: 148 |
| FP126 | 0 | 1 | FALSE | 2 | 0: 810, 1: 141 |
| FP127 | 0 | 1 | FALSE | 2 | 0: 818, 1: 133 |
| FP128 | 0 | 1 | FALSE | 2 | 0: 810, 1: 141 |
| FP129 | 0 | 1 | FALSE | 2 | 0: 819, 1: 132 |
| FP130 | 0 | 1 | FALSE | 2 | 0: 851, 1: 100 |
| FP131 | 0 | 1 | FALSE | 2 | 0: 831, 1: 120 |
| FP132 | 0 | 1 | FALSE | 2 | 0: 832, 1: 119 |
| FP133 | 0 | 1 | FALSE | 2 | 0: 831, 1: 120 |
| FP134 | 0 | 1 | FALSE | 2 | 0: 830, 1: 121 |
| FP135 | 0 | 1 | FALSE | 2 | 0: 831, 1: 120 |
| FP136 | 0 | 1 | FALSE | 2 | 0: 836, 1: 115 |
| FP137 | 0 | 1 | FALSE | 2 | 0: 841, 1: 110 |
| FP138 | 0 | 1 | FALSE | 2 | 0: 845, 1: 106 |
| FP139 | 0 | 1 | FALSE | 2 | 0: 873, 1: 78 |
| FP140 | 0 | 1 | FALSE | 2 | 0: 845, 1: 106 |
| FP141 | 0 | 1 | FALSE | 2 | 0: 840, 1: 111 |
| FP142 | 0 | 1 | FALSE | 2 | 0: 847, 1: 104 |
| FP143 | 0 | 1 | FALSE | 2 | 0: 874, 1: 77 |
| FP144 | 0 | 1 | FALSE | 2 | 0: 852, 1: 99 |
| FP145 | 0 | 1 | FALSE | 2 | 0: 852, 1: 99 |
| FP146 | 0 | 1 | FALSE | 2 | 0: 853, 1: 98 |
| FP147 | 0 | 1 | FALSE | 2 | 0: 851, 1: 100 |
| FP148 | 0 | 1 | FALSE | 2 | 0: 868, 1: 83 |
| FP149 | 0 | 1 | FALSE | 2 | 0: 865, 1: 86 |
| FP150 | 0 | 1 | FALSE | 2 | 0: 876, 1: 75 |
| FP151 | 0 | 1 | FALSE | 2 | 0: 898, 1: 53 |
| FP152 | 0 | 1 | FALSE | 2 | 0: 873, 1: 78 |
| FP153 | 0 | 1 | FALSE | 2 | 0: 877, 1: 74 |
| FP155 | 0 | 1 | FALSE | 2 | 0: 885, 1: 66 |
| FP156 | 0 | 1 | FALSE | 2 | 0: 884, 1: 67 |
| FP157 | 0 | 1 | FALSE | 2 | 0: 892, 1: 59 |
| FP158 | 0 | 1 | FALSE | 2 | 0: 900, 1: 51 |
| FP159 | 0 | 1 | FALSE | 2 | 0: 884, 1: 67 |
| FP160 | 0 | 1 | FALSE | 2 | 0: 886, 1: 65 |
| FP161 | 0 | 1 | FALSE | 2 | 0: 888, 1: 63 |
| FP162 | 0 | 1 | FALSE | 2 | 0: 480, 1: 471 |
| FP163 | 0 | 1 | FALSE | 2 | 0: 498, 1: 453 |
| FP164 | 0 | 1 | FALSE | 2 | 1: 597, 0: 354 |
| FP165 | 0 | 1 | FALSE | 2 | 0: 619, 1: 332 |
| FP166 | 0 | 1 | FALSE | 2 | 0: 636, 1: 315 |
| FP167 | 0 | 1 | FALSE | 2 | 0: 639, 1: 312 |
| FP168 | 0 | 1 | FALSE | 2 | 1: 633, 0: 318 |
| FP169 | 0 | 1 | FALSE | 2 | 0: 774, 1: 177 |
| FP170 | 0 | 1 | FALSE | 2 | 0: 776, 1: 175 |
| FP171 | 0 | 1 | FALSE | 2 | 0: 790, 1: 161 |
| FP172 | 0 | 1 | FALSE | 2 | 0: 807, 1: 144 |
| FP173 | 0 | 1 | FALSE | 2 | 0: 816, 1: 135 |
| FP174 | 0 | 1 | FALSE | 2 | 0: 827, 1: 124 |
| FP175 | 0 | 1 | FALSE | 2 | 0: 823, 1: 128 |
| FP176 | 0 | 1 | FALSE | 2 | 0: 835, 1: 116 |
| FP177 | 0 | 1 | FALSE | 2 | 0: 836, 1: 115 |
| FP178 | 0 | 1 | FALSE | 2 | 0: 836, 1: 115 |
| FP179 | 0 | 1 | FALSE | 2 | 0: 858, 1: 93 |
| FP180 | 0 | 1 | FALSE | 2 | 0: 849, 1: 102 |
| FP181 | 0 | 1 | FALSE | 2 | 0: 862, 1: 89 |
| FP182 | 0 | 1 | FALSE | 2 | 0: 857, 1: 94 |
| FP183 | 0 | 1 | FALSE | 2 | 0: 879, 1: 72 |
| FP184 | 0 | 1 | FALSE | 2 | 0: 871, 1: 80 |
| FP185 | 0 | 1 | FALSE | 2 | 0: 870, 1: 81 |
| FP186 | 0 | 1 | FALSE | 2 | 0: 878, 1: 73 |
| FP187 | 0 | 1 | FALSE | 2 | 0: 882, 1: 69 |
| FP188 | 0 | 1 | FALSE | 2 | 0: 886, 1: 65 |
| FP189 | 0 | 1 | FALSE | 2 | 0: 878, 1: 73 |
| FP190 | 0 | 1 | FALSE | 2 | 0: 882, 1: 69 |
| FP191 | 0 | 1 | FALSE | 2 | 0: 884, 1: 67 |
| FP192 | 0 | 1 | FALSE | 2 | 0: 893, 1: 58 |
| FP193 | 0 | 1 | FALSE | 2 | 0: 892, 1: 59 |
| FP194 | 0 | 1 | FALSE | 2 | 0: 895, 1: 56 |
| FP195 | 0 | 1 | FALSE | 2 | 0: 893, 1: 58 |
| FP196 | 0 | 1 | FALSE | 2 | 0: 897, 1: 54 |
| FP197 | 0 | 1 | FALSE | 2 | 0: 901, 1: 50 |
| FP198 | 0 | 1 | FALSE | 2 | 0: 897, 1: 54 |
| FP201 | 0 | 1 | FALSE | 2 | 0: 901, 1: 50 |
| FP202 | 0 | 1 | FALSE | 2 | 0: 706, 1: 245 |
| FP203 | 0 | 1 | FALSE | 2 | 0: 842, 1: 109 |
| FP204 | 0 | 1 | FALSE | 2 | 0: 857, 1: 94 |
| FP205 | 0 | 1 | FALSE | 2 | 0: 877, 1: 74 |
| FP206 | 0 | 1 | FALSE | 2 | 0: 894, 1: 57 |
| FP207 | 0 | 1 | FALSE | 2 | 0: 897, 1: 54 |
| FP208 | 0 | 1 | FALSE | 2 | 0: 844, 1: 107 |
Variable type: numeric
| skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
|---|---|---|---|---|---|---|---|---|---|---|
| MolWeight | 0 | 1 | 0 | 1 | -2.84 | -0.80 | -0.01 | 0.80 | 2.72 | ▁▆▇▆▁ |
| NumBonds | 0 | 1 | 0 | 1 | -2.92 | -0.61 | -0.04 | 0.60 | 3.23 | ▁▅▇▃▁ |
| NumMultBonds | 0 | 1 | 0 | 1 | -1.19 | -1.00 | -0.03 | 0.74 | 3.65 | ▇▇▃▁▁ |
| NumRotBonds | 0 | 1 | 0 | 1 | -0.93 | -0.93 | -0.10 | 0.52 | 5.71 | ▇▂▁▁▁ |
| NumDblBonds | 0 | 1 | 0 | 1 | -0.83 | -0.83 | -0.01 | 0.82 | 4.95 | ▇▂▁▁▁ |
| NumCarbon | 0 | 1 | 0 | 1 | -2.64 | -0.69 | -0.01 | 0.54 | 3.06 | ▂▇▇▃▁ |
| NumNitrogen | 0 | 1 | 0 | 1 | -0.69 | -0.69 | -0.69 | 0.16 | 4.37 | ▇▂▁▁▁ |
| NumOxygen | 0 | 1 | 0 | 1 | -0.91 | -0.91 | -0.33 | 0.25 | 6.61 | ▇▂▁▁▁ |
| NumSulfer | 0 | 1 | 0 | 1 | -0.34 | -0.34 | -0.34 | -0.34 | 7.86 | ▇▁▁▁▁ |
| NumChlorine | 0 | 1 | 0 | 1 | -0.40 | -0.40 | -0.40 | -0.40 | 6.74 | ▇▁▁▁▁ |
| NumHalogen | 0 | 1 | 0 | 1 | -0.47 | -0.47 | -0.47 | 0.20 | 6.32 | ▇▁▁▁▁ |
| NumRings | 0 | 1 | 0 | 1 | -1.08 | -1.08 | -0.31 | 0.46 | 4.31 | ▇▃▂▁▁ |
| HydrophilicFactor | 0 | 1 | 0 | 1 | -0.86 | -0.66 | -0.26 | 0.30 | 11.99 | ▇▁▁▁▁ |
| SurfaceArea1 | 0 | 1 | 0 | 1 | -1.03 | -0.77 | -0.21 | 0.48 | 8.37 | ▇▂▁▁▁ |
| SurfaceArea2 | 0 | 1 | 0 | 1 | -1.06 | -0.78 | -0.19 | 0.54 | 7.65 | ▇▂▁▁▁ |
###################################
# Verifying the data dimensions
# for the train set
###################################
dim(PMA_PreModelling_Train)## [1] 951 221##################################
# Formulating the test set
##################################
DPA_Test <- Solubility_Test
DPA_Test.Predictors <- DPA_Test[,!names(DPA_Test) %in% c("Log_Solubility_Class")]
DPA_Test.Predictors.Numeric <- DPA_Test.Predictors[,-(grep("FP", names(DPA_Test.Predictors)))]
DPA_Test_BoxCox <- preProcess(DPA_Test.Predictors.Numeric, method = c("BoxCox"))
DPA_Test_BoxCoxTransformed <- predict(DPA_Test_BoxCox, DPA_Test.Predictors.Numeric)
DPA_Test.Predictors.Numeric_BoxCoxTransformed_CenteredScaled <- preProcess(DPA_Test_BoxCoxTransformed, method = c("center","scale"))
DPA_Test.Predictors.Numeric_BoxCoxTransformed_CenteredScaledTransformed <- predict(DPA_Test.Predictors.Numeric_BoxCoxTransformed_CenteredScaled, DPA_Test_BoxCoxTransformed)
##################################
# Creating the pre-modelling
# test set
##################################
Log_Solubility_Class <- DPA_Test$Log_Solubility_Class
PMA_Test.Predictors.Factor <- DPA_Test.Predictors[,(grep("FP", names(DPA_Test.Predictors)))]
PMA_Test.Predictors.Factor <- as.data.frame(lapply(PMA_Test.Predictors.Factor,factor))
PMA_Test.Predictors.Numeric <- DPA_Test.Predictors.Numeric_BoxCoxTransformed_CenteredScaledTransformed
PMA_Test_BoxCoxTransformed_CenteredScaledTransformed <- cbind(Log_Solubility_Class,PMA_Test.Predictors.Factor,PMA_Test.Predictors.Numeric)
PMA_Test_BoxCoxTransformed_CenteredScaledTransformed_ExcludedLowVariance_ExcludedLinearlyDependent_ExcludedHighCorrelation <- PMA_Test_BoxCoxTransformed_CenteredScaledTransformed[,!names(PMA_Test_BoxCoxTransformed_CenteredScaledTransformed) %in% c("FP154","FP199","FP200","NumNonHBonds","NumHydrogen","NumNonHAtoms","NumAromaticBonds","NumAtoms")]
PMA_PreModelling_Test <- PMA_Test_BoxCoxTransformed_CenteredScaledTransformed_ExcludedLowVariance_ExcludedLinearlyDependent_ExcludedHighCorrelation
##################################
# Gathering descriptive statistics
##################################
(PMA_PreModelling_Test_Skimmed <- skim(PMA_PreModelling_Test))| Name | PMA_PreModelling_Test |
| Number of rows | 316 |
| Number of columns | 221 |
| _______________________ | |
| Column type frequency: | |
| factor | 206 |
| numeric | 15 |
| ________________________ | |
| Group variables | None |
Variable type: factor
| skim_variable | n_missing | complete_rate | ordered | n_unique | top_counts |
|---|---|---|---|---|---|
| Log_Solubility_Class | 0 | 1 | FALSE | 2 | Hig: 173, Low: 143 |
| FP001 | 0 | 1 | FALSE | 2 | 0: 168, 1: 148 |
| FP002 | 0 | 1 | FALSE | 2 | 1: 185, 0: 131 |
| FP003 | 0 | 1 | FALSE | 2 | 0: 176, 1: 140 |
| FP004 | 0 | 1 | FALSE | 2 | 1: 168, 0: 148 |
| FP005 | 0 | 1 | FALSE | 2 | 1: 195, 0: 121 |
| FP006 | 0 | 1 | FALSE | 2 | 0: 205, 1: 111 |
| FP007 | 0 | 1 | FALSE | 2 | 0: 204, 1: 112 |
| FP008 | 0 | 1 | FALSE | 2 | 0: 202, 1: 114 |
| FP009 | 0 | 1 | FALSE | 2 | 0: 233, 1: 83 |
| FP010 | 0 | 1 | FALSE | 2 | 0: 255, 1: 61 |
| FP011 | 0 | 1 | FALSE | 2 | 0: 261, 1: 55 |
| FP012 | 0 | 1 | FALSE | 2 | 0: 263, 1: 53 |
| FP013 | 0 | 1 | FALSE | 2 | 0: 264, 1: 52 |
| FP014 | 0 | 1 | FALSE | 2 | 0: 266, 1: 50 |
| FP015 | 0 | 1 | FALSE | 2 | 1: 262, 0: 54 |
| FP016 | 0 | 1 | FALSE | 2 | 0: 271, 1: 45 |
| FP017 | 0 | 1 | FALSE | 2 | 0: 269, 1: 47 |
| FP018 | 0 | 1 | FALSE | 2 | 0: 289, 1: 27 |
| FP019 | 0 | 1 | FALSE | 2 | 0: 280, 1: 36 |
| FP020 | 0 | 1 | FALSE | 2 | 0: 282, 1: 34 |
| FP021 | 0 | 1 | FALSE | 2 | 0: 282, 1: 34 |
| FP022 | 0 | 1 | FALSE | 2 | 0: 279, 1: 37 |
| FP023 | 0 | 1 | FALSE | 2 | 0: 289, 1: 27 |
| FP024 | 0 | 1 | FALSE | 2 | 0: 285, 1: 31 |
| FP025 | 0 | 1 | FALSE | 2 | 0: 291, 1: 25 |
| FP026 | 0 | 1 | FALSE | 2 | 0: 279, 1: 37 |
| FP027 | 0 | 1 | FALSE | 2 | 0: 291, 1: 25 |
| FP028 | 0 | 1 | FALSE | 2 | 0: 298, 1: 18 |
| FP029 | 0 | 1 | FALSE | 2 | 0: 300, 1: 16 |
| FP030 | 0 | 1 | FALSE | 2 | 0: 290, 1: 26 |
| FP031 | 0 | 1 | FALSE | 2 | 0: 285, 1: 31 |
| FP032 | 0 | 1 | FALSE | 2 | 0: 275, 1: 41 |
| FP033 | 0 | 1 | FALSE | 2 | 0: 278, 1: 38 |
| FP034 | 0 | 1 | FALSE | 2 | 0: 295, 1: 21 |
| FP035 | 0 | 1 | FALSE | 2 | 0: 285, 1: 31 |
| FP036 | 0 | 1 | FALSE | 2 | 0: 297, 1: 19 |
| FP037 | 0 | 1 | FALSE | 2 | 0: 286, 1: 30 |
| FP038 | 0 | 1 | FALSE | 2 | 0: 306, 1: 10 |
| FP039 | 0 | 1 | FALSE | 2 | 0: 296, 1: 20 |
| FP040 | 0 | 1 | FALSE | 2 | 0: 298, 1: 18 |
| FP041 | 0 | 1 | FALSE | 2 | 0: 297, 1: 19 |
| FP042 | 0 | 1 | FALSE | 2 | 0: 297, 1: 19 |
| FP043 | 0 | 1 | FALSE | 2 | 0: 302, 1: 14 |
| FP044 | 0 | 1 | FALSE | 2 | 0: 297, 1: 19 |
| FP045 | 0 | 1 | FALSE | 2 | 0: 296, 1: 20 |
| FP046 | 0 | 1 | FALSE | 2 | 0: 213, 1: 103 |
| FP047 | 0 | 1 | FALSE | 2 | 0: 222, 1: 94 |
| FP048 | 0 | 1 | FALSE | 2 | 0: 280, 1: 36 |
| FP049 | 0 | 1 | FALSE | 2 | 0: 282, 1: 34 |
| FP050 | 0 | 1 | FALSE | 2 | 0: 280, 1: 36 |
| FP051 | 0 | 1 | FALSE | 2 | 0: 298, 1: 18 |
| FP052 | 0 | 1 | FALSE | 2 | 0: 283, 1: 33 |
| FP053 | 0 | 1 | FALSE | 2 | 0: 297, 1: 19 |
| FP054 | 0 | 1 | FALSE | 2 | 0: 285, 1: 31 |
| FP055 | 0 | 1 | FALSE | 2 | 0: 287, 1: 29 |
| FP056 | 0 | 1 | FALSE | 2 | 0: 296, 1: 20 |
| FP057 | 0 | 1 | FALSE | 2 | 0: 277, 1: 39 |
| FP058 | 0 | 1 | FALSE | 2 | 0: 273, 1: 43 |
| FP059 | 0 | 1 | FALSE | 2 | 0: 302, 1: 14 |
| FP060 | 0 | 1 | FALSE | 2 | 0: 173, 1: 143 |
| FP061 | 0 | 1 | FALSE | 2 | 0: 192, 1: 124 |
| FP062 | 0 | 1 | FALSE | 2 | 0: 181, 1: 135 |
| FP063 | 0 | 1 | FALSE | 2 | 0: 203, 1: 113 |
| FP064 | 0 | 1 | FALSE | 2 | 0: 193, 1: 123 |
| FP065 | 0 | 1 | FALSE | 2 | 1: 189, 0: 127 |
| FP066 | 0 | 1 | FALSE | 2 | 1: 195, 0: 121 |
| FP067 | 0 | 1 | FALSE | 2 | 0: 213, 1: 103 |
| FP068 | 0 | 1 | FALSE | 2 | 0: 224, 1: 92 |
| FP069 | 0 | 1 | FALSE | 2 | 0: 198, 1: 118 |
| FP070 | 0 | 1 | FALSE | 2 | 0: 211, 1: 105 |
| FP071 | 0 | 1 | FALSE | 2 | 0: 207, 1: 109 |
| FP072 | 0 | 1 | FALSE | 2 | 1: 204, 0: 112 |
| FP073 | 0 | 1 | FALSE | 2 | 0: 224, 1: 92 |
| FP074 | 0 | 1 | FALSE | 2 | 0: 213, 1: 103 |
| FP075 | 0 | 1 | FALSE | 2 | 0: 235, 1: 81 |
| FP076 | 0 | 1 | FALSE | 2 | 0: 216, 1: 100 |
| FP077 | 0 | 1 | FALSE | 2 | 0: 219, 1: 97 |
| FP078 | 0 | 1 | FALSE | 2 | 0: 218, 1: 98 |
| FP079 | 0 | 1 | FALSE | 2 | 1: 230, 0: 86 |
| FP080 | 0 | 1 | FALSE | 2 | 0: 233, 1: 83 |
| FP081 | 0 | 1 | FALSE | 2 | 0: 225, 1: 91 |
| FP082 | 0 | 1 | FALSE | 2 | 1: 235, 0: 81 |
| FP083 | 0 | 1 | FALSE | 2 | 0: 236, 1: 80 |
| FP084 | 0 | 1 | FALSE | 2 | 0: 245, 1: 71 |
| FP085 | 0 | 1 | FALSE | 2 | 0: 231, 1: 85 |
| FP086 | 0 | 1 | FALSE | 2 | 0: 230, 1: 86 |
| FP087 | 0 | 1 | FALSE | 2 | 1: 241, 0: 75 |
| FP088 | 0 | 1 | FALSE | 2 | 0: 239, 1: 77 |
| FP089 | 0 | 1 | FALSE | 2 | 0: 236, 1: 80 |
| FP090 | 0 | 1 | FALSE | 2 | 0: 244, 1: 72 |
| FP091 | 0 | 1 | FALSE | 2 | 0: 243, 1: 73 |
| FP092 | 0 | 1 | FALSE | 2 | 0: 247, 1: 69 |
| FP093 | 0 | 1 | FALSE | 2 | 0: 248, 1: 68 |
| FP094 | 0 | 1 | FALSE | 2 | 0: 237, 1: 79 |
| FP095 | 0 | 1 | FALSE | 2 | 0: 251, 1: 65 |
| FP096 | 0 | 1 | FALSE | 2 | 0: 257, 1: 59 |
| FP097 | 0 | 1 | FALSE | 2 | 0: 250, 1: 66 |
| FP098 | 0 | 1 | FALSE | 2 | 0: 252, 1: 64 |
| FP099 | 0 | 1 | FALSE | 2 | 0: 249, 1: 67 |
| FP100 | 0 | 1 | FALSE | 2 | 0: 259, 1: 57 |
| FP101 | 0 | 1 | FALSE | 2 | 0: 260, 1: 56 |
| FP102 | 0 | 1 | FALSE | 2 | 0: 270, 1: 46 |
| FP103 | 0 | 1 | FALSE | 2 | 0: 247, 1: 69 |
| FP104 | 0 | 1 | FALSE | 2 | 0: 258, 1: 58 |
| FP105 | 0 | 1 | FALSE | 2 | 0: 248, 1: 68 |
| FP106 | 0 | 1 | FALSE | 2 | 0: 273, 1: 43 |
| FP107 | 0 | 1 | FALSE | 2 | 0: 254, 1: 62 |
| FP108 | 0 | 1 | FALSE | 2 | 0: 259, 1: 57 |
| FP109 | 0 | 1 | FALSE | 2 | 0: 261, 1: 55 |
| FP110 | 0 | 1 | FALSE | 2 | 0: 264, 1: 52 |
| FP111 | 0 | 1 | FALSE | 2 | 0: 259, 1: 57 |
| FP112 | 0 | 1 | FALSE | 2 | 0: 260, 1: 56 |
| FP113 | 0 | 1 | FALSE | 2 | 0: 264, 1: 52 |
| FP114 | 0 | 1 | FALSE | 2 | 0: 260, 1: 56 |
| FP115 | 0 | 1 | FALSE | 2 | 0: 266, 1: 50 |
| FP116 | 0 | 1 | FALSE | 2 | 0: 269, 1: 47 |
| FP117 | 0 | 1 | FALSE | 2 | 0: 262, 1: 54 |
| FP118 | 0 | 1 | FALSE | 2 | 0: 279, 1: 37 |
| FP119 | 0 | 1 | FALSE | 2 | 0: 263, 1: 53 |
| FP120 | 0 | 1 | FALSE | 2 | 0: 267, 1: 49 |
| FP121 | 0 | 1 | FALSE | 2 | 0: 282, 1: 34 |
| FP122 | 0 | 1 | FALSE | 2 | 0: 273, 1: 43 |
| FP123 | 0 | 1 | FALSE | 2 | 0: 270, 1: 46 |
| FP124 | 0 | 1 | FALSE | 2 | 0: 274, 1: 42 |
| FP125 | 0 | 1 | FALSE | 2 | 0: 278, 1: 38 |
| FP126 | 0 | 1 | FALSE | 2 | 0: 280, 1: 36 |
| FP127 | 0 | 1 | FALSE | 2 | 0: 269, 1: 47 |
| FP128 | 0 | 1 | FALSE | 2 | 0: 282, 1: 34 |
| FP129 | 0 | 1 | FALSE | 2 | 0: 272, 1: 44 |
| FP130 | 0 | 1 | FALSE | 2 | 0: 290, 1: 26 |
| FP131 | 0 | 1 | FALSE | 2 | 0: 282, 1: 34 |
| FP132 | 0 | 1 | FALSE | 2 | 0: 276, 1: 40 |
| FP133 | 0 | 1 | FALSE | 2 | 0: 273, 1: 43 |
| FP134 | 0 | 1 | FALSE | 2 | 0: 289, 1: 27 |
| FP135 | 0 | 1 | FALSE | 2 | 0: 296, 1: 20 |
| FP136 | 0 | 1 | FALSE | 2 | 0: 284, 1: 32 |
| FP137 | 0 | 1 | FALSE | 2 | 0: 288, 1: 28 |
| FP138 | 0 | 1 | FALSE | 2 | 0: 290, 1: 26 |
| FP139 | 0 | 1 | FALSE | 2 | 0: 296, 1: 20 |
| FP140 | 0 | 1 | FALSE | 2 | 0: 288, 1: 28 |
| FP141 | 0 | 1 | FALSE | 2 | 0: 294, 1: 22 |
| FP142 | 0 | 1 | FALSE | 2 | 0: 286, 1: 30 |
| FP143 | 0 | 1 | FALSE | 2 | 0: 299, 1: 17 |
| FP144 | 0 | 1 | FALSE | 2 | 0: 287, 1: 29 |
| FP145 | 0 | 1 | FALSE | 2 | 0: 296, 1: 20 |
| FP146 | 0 | 1 | FALSE | 2 | 0: 287, 1: 29 |
| FP147 | 0 | 1 | FALSE | 2 | 0: 294, 1: 22 |
| FP148 | 0 | 1 | FALSE | 2 | 0: 291, 1: 25 |
| FP149 | 0 | 1 | FALSE | 2 | 0: 290, 1: 26 |
| FP150 | 0 | 1 | FALSE | 2 | 0: 295, 1: 21 |
| FP151 | 0 | 1 | FALSE | 2 | 0: 306, 1: 10 |
| FP152 | 0 | 1 | FALSE | 2 | 0: 299, 1: 17 |
| FP153 | 0 | 1 | FALSE | 2 | 0: 305, 1: 11 |
| FP155 | 0 | 1 | FALSE | 2 | 0: 295, 1: 21 |
| FP156 | 0 | 1 | FALSE | 2 | 0: 301, 1: 15 |
| FP157 | 0 | 1 | FALSE | 2 | 0: 298, 1: 18 |
| FP158 | 0 | 1 | FALSE | 2 | 0: 291, 1: 25 |
| FP159 | 0 | 1 | FALSE | 2 | 0: 305, 1: 11 |
| FP160 | 0 | 1 | FALSE | 2 | 0: 305, 1: 11 |
| FP161 | 0 | 1 | FALSE | 2 | 0: 305, 1: 11 |
| FP162 | 0 | 1 | FALSE | 2 | 1: 168, 0: 148 |
| FP163 | 0 | 1 | FALSE | 2 | 0: 173, 1: 143 |
| FP164 | 0 | 1 | FALSE | 2 | 1: 207, 0: 109 |
| FP165 | 0 | 1 | FALSE | 2 | 0: 215, 1: 101 |
| FP166 | 0 | 1 | FALSE | 2 | 0: 209, 1: 107 |
| FP167 | 0 | 1 | FALSE | 2 | 0: 221, 1: 95 |
| FP168 | 0 | 1 | FALSE | 2 | 1: 226, 0: 90 |
| FP169 | 0 | 1 | FALSE | 2 | 0: 257, 1: 59 |
| FP170 | 0 | 1 | FALSE | 2 | 0: 267, 1: 49 |
| FP171 | 0 | 1 | FALSE | 2 | 0: 275, 1: 41 |
| FP172 | 0 | 1 | FALSE | 2 | 0: 269, 1: 47 |
| FP173 | 0 | 1 | FALSE | 2 | 0: 273, 1: 43 |
| FP174 | 0 | 1 | FALSE | 2 | 0: 267, 1: 49 |
| FP175 | 0 | 1 | FALSE | 2 | 0: 274, 1: 42 |
| FP176 | 0 | 1 | FALSE | 2 | 0: 282, 1: 34 |
| FP177 | 0 | 1 | FALSE | 2 | 0: 284, 1: 32 |
| FP178 | 0 | 1 | FALSE | 2 | 0: 282, 1: 34 |
| FP179 | 0 | 1 | FALSE | 2 | 0: 272, 1: 44 |
| FP180 | 0 | 1 | FALSE | 2 | 0: 294, 1: 22 |
| FP181 | 0 | 1 | FALSE | 2 | 0: 283, 1: 33 |
| FP182 | 0 | 1 | FALSE | 2 | 0: 292, 1: 24 |
| FP183 | 0 | 1 | FALSE | 2 | 0: 274, 1: 42 |
| FP184 | 0 | 1 | FALSE | 2 | 0: 286, 1: 30 |
| FP185 | 0 | 1 | FALSE | 2 | 0: 285, 1: 31 |
| FP186 | 0 | 1 | FALSE | 2 | 0: 297, 1: 19 |
| FP187 | 0 | 1 | FALSE | 2 | 0: 295, 1: 21 |
| FP188 | 0 | 1 | FALSE | 2 | 0: 294, 1: 22 |
| FP189 | 0 | 1 | FALSE | 2 | 0: 303, 1: 13 |
| FP190 | 0 | 1 | FALSE | 2 | 0: 299, 1: 17 |
| FP191 | 0 | 1 | FALSE | 2 | 0: 298, 1: 18 |
| FP192 | 0 | 1 | FALSE | 2 | 0: 294, 1: 22 |
| FP193 | 0 | 1 | FALSE | 2 | 0: 294, 1: 22 |
| FP194 | 0 | 1 | FALSE | 2 | 0: 295, 1: 21 |
| FP195 | 0 | 1 | FALSE | 2 | 0: 300, 1: 16 |
| FP196 | 0 | 1 | FALSE | 2 | 0: 294, 1: 22 |
| FP197 | 0 | 1 | FALSE | 2 | 0: 296, 1: 20 |
| FP198 | 0 | 1 | FALSE | 2 | 0: 302, 1: 14 |
| FP201 | 0 | 1 | FALSE | 2 | 0: 303, 1: 13 |
| FP202 | 0 | 1 | FALSE | 2 | 0: 232, 1: 84 |
| FP203 | 0 | 1 | FALSE | 2 | 0: 273, 1: 43 |
| FP204 | 0 | 1 | FALSE | 2 | 0: 286, 1: 30 |
| FP205 | 0 | 1 | FALSE | 2 | 0: 291, 1: 25 |
| FP206 | 0 | 1 | FALSE | 2 | 0: 300, 1: 16 |
| FP207 | 0 | 1 | FALSE | 2 | 0: 302, 1: 14 |
| FP208 | 0 | 1 | FALSE | 2 | 0: 273, 1: 43 |
Variable type: numeric
| skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
|---|---|---|---|---|---|---|---|---|---|---|
| MolWeight | 0 | 1 | 0 | 1 | -2.46 | -0.78 | -0.06 | 0.81 | 2.18 | ▁▇▇▇▃ |
| NumBonds | 0 | 1 | 0 | 1 | -2.92 | -0.67 | 0.03 | 0.57 | 2.55 | ▁▂▇▃▂ |
| NumMultBonds | 0 | 1 | 0 | 1 | -1.24 | -1.04 | -0.06 | 0.72 | 4.06 | ▇▇▅▁▁ |
| NumRotBonds | 0 | 1 | 0 | 1 | -0.82 | -0.82 | -0.40 | 0.44 | 5.94 | ▇▁▁▁▁ |
| NumDblBonds | 0 | 1 | 0 | 1 | -0.76 | -0.76 | 0.09 | 0.09 | 4.35 | ▇▁▁▁▁ |
| NumCarbon | 0 | 1 | 0 | 1 | -2.71 | -0.70 | -0.21 | 0.56 | 2.23 | ▁▂▇▅▂ |
| NumNitrogen | 0 | 1 | 0 | 1 | -0.63 | -0.63 | -0.63 | 0.26 | 4.71 | ▇▂▁▁▁ |
| NumOxygen | 0 | 1 | 0 | 1 | -0.92 | -0.92 | -0.26 | 0.40 | 5.02 | ▇▃▁▁▁ |
| NumSulfer | 0 | 1 | 0 | 1 | -0.28 | -0.28 | -0.28 | -0.28 | 8.06 | ▇▁▁▁▁ |
| NumChlorine | 0 | 1 | 0 | 1 | -0.40 | -0.40 | -0.40 | -0.40 | 6.02 | ▇▁▁▁▁ |
| NumHalogen | 0 | 1 | 0 | 1 | -0.48 | -0.48 | -0.48 | 0.20 | 5.57 | ▇▁▁▁▁ |
| NumRings | 0 | 1 | 0 | 1 | -1.14 | -0.32 | -0.32 | 0.49 | 3.74 | ▇▃▁▁▁ |
| HydrophilicFactor | 0 | 1 | 0 | 1 | -0.90 | -0.68 | -0.30 | 0.32 | 5.19 | ▇▂▁▁▁ |
| SurfaceArea1 | 0 | 1 | 0 | 1 | -1.04 | -0.75 | -0.21 | 0.53 | 5.37 | ▇▃▁▁▁ |
| SurfaceArea2 | 0 | 1 | 0 | 1 | -1.05 | -0.77 | -0.26 | 0.52 | 5.00 | ▇▃▁▁▁ |
###################################
# Verifying the data dimensions
# for the test set
###################################
dim(PMA_PreModelling_Test)## [1] 316 2211.4 Data Exploration
Exploratory data analysis:
[A] Numeric variables which demonstrated differential relationships with the Log_Solubility_Class response variable include:
[A.1] MolWeight variable (numeric)
[A.2] NumCarbon variable (numeric)
[A.3] NumChlorine variable (numeric)
[A.4] NumHalogen variable (numeric)
[A.5] NumMultBonds variable (numeric)
[B] Factor variables which demonstrated relatively better differentiation of the Log_Solubility_Class response variable between its 1 and 0 structure levels include:
[B.1] FP207 variable (factor)
[B.2] FP190 variable (factor)
[B.3] FP197 variable (factor)
[B.4] FP196 variable (factor)
[B.5] FP193 variable (factor)
[B.6] FP184 variable (factor)
[B.7] FP172 variable (factor)
[B.8] FP149 variable (factor)
[B.9] FP112 variable (factor)
[B.10] FP107 variable (factor)
[B.11] FP089 variable (factor)
[B.12] FP079 variable (factor)
[B.13] FP076 variable (factor)
[B.14] FP072 variable (factor)
[B.15] FP071 variable (factor)
[B.16] FP070 variable (factor)
[B.17] FP065 variable (factor)
[B.18] FP059 variable (factor)
[B.19] FP054 variable (factor)
[B.20] FP056 variable (factor)
[B.21] FP053 variable (factor)
[B.22] FP049 variable (factor)
[B.23] FP044 variable (factor)
[B.24] FP041 variable (factor)
[B.25] FP039 variable (factor)
[B.26] FP014 variable (factor)
[B.27] FP013 variable (factor)
##################################
# Loading dataset
##################################
EDA <- PMA_PreModelling_Train
##################################
# Listing all predictors
##################################
EDA.Predictors <- EDA[,!names(EDA) %in% c("Log_Solubility_Class")]
##################################
# Listing all numeric predictors
##################################
EDA.Predictors.Numeric <- EDA.Predictors[,sapply(EDA.Predictors, is.numeric)]
ncol(EDA.Predictors.Numeric)## [1] 15names(EDA.Predictors.Numeric)## [1] "MolWeight" "NumBonds" "NumMultBonds"
## [4] "NumRotBonds" "NumDblBonds" "NumCarbon"
## [7] "NumNitrogen" "NumOxygen" "NumSulfer"
## [10] "NumChlorine" "NumHalogen" "NumRings"
## [13] "HydrophilicFactor" "SurfaceArea1" "SurfaceArea2"##################################
# Listing all factor predictors
##################################
EDA.Predictors.Factor <- EDA.Predictors[,sapply(EDA.Predictors, is.factor)]
ncol(EDA.Predictors.Factor)## [1] 205names(EDA.Predictors.Factor)## [1] "FP001" "FP002" "FP003" "FP004" "FP005" "FP006" "FP007" "FP008" "FP009"
## [10] "FP010" "FP011" "FP012" "FP013" "FP014" "FP015" "FP016" "FP017" "FP018"
## [19] "FP019" "FP020" "FP021" "FP022" "FP023" "FP024" "FP025" "FP026" "FP027"
## [28] "FP028" "FP029" "FP030" "FP031" "FP032" "FP033" "FP034" "FP035" "FP036"
## [37] "FP037" "FP038" "FP039" "FP040" "FP041" "FP042" "FP043" "FP044" "FP045"
## [46] "FP046" "FP047" "FP048" "FP049" "FP050" "FP051" "FP052" "FP053" "FP054"
## [55] "FP055" "FP056" "FP057" "FP058" "FP059" "FP060" "FP061" "FP062" "FP063"
## [64] "FP064" "FP065" "FP066" "FP067" "FP068" "FP069" "FP070" "FP071" "FP072"
## [73] "FP073" "FP074" "FP075" "FP076" "FP077" "FP078" "FP079" "FP080" "FP081"
## [82] "FP082" "FP083" "FP084" "FP085" "FP086" "FP087" "FP088" "FP089" "FP090"
## [91] "FP091" "FP092" "FP093" "FP094" "FP095" "FP096" "FP097" "FP098" "FP099"
## [100] "FP100" "FP101" "FP102" "FP103" "FP104" "FP105" "FP106" "FP107" "FP108"
## [109] "FP109" "FP110" "FP111" "FP112" "FP113" "FP114" "FP115" "FP116" "FP117"
## [118] "FP118" "FP119" "FP120" "FP121" "FP122" "FP123" "FP124" "FP125" "FP126"
## [127] "FP127" "FP128" "FP129" "FP130" "FP131" "FP132" "FP133" "FP134" "FP135"
## [136] "FP136" "FP137" "FP138" "FP139" "FP140" "FP141" "FP142" "FP143" "FP144"
## [145] "FP145" "FP146" "FP147" "FP148" "FP149" "FP150" "FP151" "FP152" "FP153"
## [154] "FP155" "FP156" "FP157" "FP158" "FP159" "FP160" "FP161" "FP162" "FP163"
## [163] "FP164" "FP165" "FP166" "FP167" "FP168" "FP169" "FP170" "FP171" "FP172"
## [172] "FP173" "FP174" "FP175" "FP176" "FP177" "FP178" "FP179" "FP180" "FP181"
## [181] "FP182" "FP183" "FP184" "FP185" "FP186" "FP187" "FP188" "FP189" "FP190"
## [190] "FP191" "FP192" "FP193" "FP194" "FP195" "FP196" "FP197" "FP198" "FP201"
## [199] "FP202" "FP203" "FP204" "FP205" "FP206" "FP207" "FP208"##################################
# Formulating the box plots
##################################
featurePlot(x = EDA.Predictors.Numeric,
y = EDA$Log_Solubility_Class,
plot = "box",
scales = list(x = list(relation="free", rot = 90),
y = list(relation="free")),
adjust = 1.5,
pch = "|")
##################################
# Restructuring the dataset for
# for barchart analysis
##################################
Log_Solubility_Class <- DPA$Log_Solubility_Class
EDA.Bar.Source <- as.data.frame(cbind(Log_Solubility_Class,
EDA.Predictors.Factor))
ncol(EDA.Bar.Source)## [1] 206##################################
# Creating a function to formulate
# the proportions table
##################################
EDA.PropTable.Function <- function(FactorVar) {
EDA.Bar.Source.FactorVar <- EDA.Bar.Source[,c("Log_Solubility_Class",
FactorVar)]
EDA.Bar.Source.FactorVar.Prop <- as.data.frame(prop.table(table(EDA.Bar.Source.FactorVar), 2))
names(EDA.Bar.Source.FactorVar.Prop)[2] <- "Structure"
EDA.Bar.Source.FactorVar.Prop$Variable <- rep(FactorVar,nrow(EDA.Bar.Source.FactorVar.Prop))
return(EDA.Bar.Source.FactorVar.Prop)
}
EDA.Bar.Source.FactorVar.Prop.Group5 <- rbind(EDA.PropTable.Function(names(EDA.Bar.Source)[162]),
EDA.PropTable.Function(names(EDA.Bar.Source)[163]),
EDA.PropTable.Function(names(EDA.Bar.Source)[164]),
EDA.PropTable.Function(names(EDA.Bar.Source)[165]),
EDA.PropTable.Function(names(EDA.Bar.Source)[166]),
EDA.PropTable.Function(names(EDA.Bar.Source)[167]),
EDA.PropTable.Function(names(EDA.Bar.Source)[168]),
EDA.PropTable.Function(names(EDA.Bar.Source)[169]),
EDA.PropTable.Function(names(EDA.Bar.Source)[170]),
EDA.PropTable.Function(names(EDA.Bar.Source)[171]),
EDA.PropTable.Function(names(EDA.Bar.Source)[172]),
EDA.PropTable.Function(names(EDA.Bar.Source)[173]),
EDA.PropTable.Function(names(EDA.Bar.Source)[174]),
EDA.PropTable.Function(names(EDA.Bar.Source)[175]),
EDA.PropTable.Function(names(EDA.Bar.Source)[176]),
EDA.PropTable.Function(names(EDA.Bar.Source)[177]),
EDA.PropTable.Function(names(EDA.Bar.Source)[178]),
EDA.PropTable.Function(names(EDA.Bar.Source)[179]),
EDA.PropTable.Function(names(EDA.Bar.Source)[180]),
EDA.PropTable.Function(names(EDA.Bar.Source)[181]),
EDA.PropTable.Function(names(EDA.Bar.Source)[182]),
EDA.PropTable.Function(names(EDA.Bar.Source)[183]),
EDA.PropTable.Function(names(EDA.Bar.Source)[184]),
EDA.PropTable.Function(names(EDA.Bar.Source)[185]),
EDA.PropTable.Function(names(EDA.Bar.Source)[186]),
EDA.PropTable.Function(names(EDA.Bar.Source)[187]),
EDA.PropTable.Function(names(EDA.Bar.Source)[188]),
EDA.PropTable.Function(names(EDA.Bar.Source)[189]),
EDA.PropTable.Function(names(EDA.Bar.Source)[190]),
EDA.PropTable.Function(names(EDA.Bar.Source)[191]),
EDA.PropTable.Function(names(EDA.Bar.Source)[192]),
EDA.PropTable.Function(names(EDA.Bar.Source)[193]),
EDA.PropTable.Function(names(EDA.Bar.Source)[194]),
EDA.PropTable.Function(names(EDA.Bar.Source)[195]),
EDA.PropTable.Function(names(EDA.Bar.Source)[196]),
EDA.PropTable.Function(names(EDA.Bar.Source)[197]),
EDA.PropTable.Function(names(EDA.Bar.Source)[198]),
EDA.PropTable.Function(names(EDA.Bar.Source)[199]),
EDA.PropTable.Function(names(EDA.Bar.Source)[200]),
EDA.PropTable.Function(names(EDA.Bar.Source)[201]),
EDA.PropTable.Function(names(EDA.Bar.Source)[202]),
EDA.PropTable.Function(names(EDA.Bar.Source)[203]),
EDA.PropTable.Function(names(EDA.Bar.Source)[204]),
EDA.PropTable.Function(names(EDA.Bar.Source)[205]),
EDA.PropTable.Function(names(EDA.Bar.Source)[206]))
(EDA.Barchart.FactorVar <- barchart(EDA.Bar.Source.FactorVar.Prop.Group5[,3] ~
EDA.Bar.Source.FactorVar.Prop.Group5[,2] | EDA.Bar.Source.FactorVar.Prop.Group5[,4],
data=EDA.Bar.Source.FactorVar.Prop.Group5,
groups = EDA.Bar.Source.FactorVar.Prop.Group5[,1],
stack=TRUE,
ylab = "Proportion",
xlab = "Structure",
auto.key = list(adj = 1),
layout=(c(9,5))))
EDA.Bar.Source.FactorVar.Prop.Group4 <- rbind(EDA.PropTable.Function(names(EDA.Bar.Source)[122]),
EDA.PropTable.Function(names(EDA.Bar.Source)[123]),
EDA.PropTable.Function(names(EDA.Bar.Source)[124]),
EDA.PropTable.Function(names(EDA.Bar.Source)[125]),
EDA.PropTable.Function(names(EDA.Bar.Source)[126]),
EDA.PropTable.Function(names(EDA.Bar.Source)[127]),
EDA.PropTable.Function(names(EDA.Bar.Source)[128]),
EDA.PropTable.Function(names(EDA.Bar.Source)[129]),
EDA.PropTable.Function(names(EDA.Bar.Source)[130]),
EDA.PropTable.Function(names(EDA.Bar.Source)[131]),
EDA.PropTable.Function(names(EDA.Bar.Source)[132]),
EDA.PropTable.Function(names(EDA.Bar.Source)[133]),
EDA.PropTable.Function(names(EDA.Bar.Source)[134]),
EDA.PropTable.Function(names(EDA.Bar.Source)[135]),
EDA.PropTable.Function(names(EDA.Bar.Source)[136]),
EDA.PropTable.Function(names(EDA.Bar.Source)[137]),
EDA.PropTable.Function(names(EDA.Bar.Source)[138]),
EDA.PropTable.Function(names(EDA.Bar.Source)[139]),
EDA.PropTable.Function(names(EDA.Bar.Source)[140]),
EDA.PropTable.Function(names(EDA.Bar.Source)[141]),
EDA.PropTable.Function(names(EDA.Bar.Source)[142]),
EDA.PropTable.Function(names(EDA.Bar.Source)[143]),
EDA.PropTable.Function(names(EDA.Bar.Source)[144]),
EDA.PropTable.Function(names(EDA.Bar.Source)[145]),
EDA.PropTable.Function(names(EDA.Bar.Source)[146]),
EDA.PropTable.Function(names(EDA.Bar.Source)[147]),
EDA.PropTable.Function(names(EDA.Bar.Source)[148]),
EDA.PropTable.Function(names(EDA.Bar.Source)[149]),
EDA.PropTable.Function(names(EDA.Bar.Source)[150]),
EDA.PropTable.Function(names(EDA.Bar.Source)[151]),
EDA.PropTable.Function(names(EDA.Bar.Source)[152]),
EDA.PropTable.Function(names(EDA.Bar.Source)[153]),
EDA.PropTable.Function(names(EDA.Bar.Source)[154]),
EDA.PropTable.Function(names(EDA.Bar.Source)[155]),
EDA.PropTable.Function(names(EDA.Bar.Source)[156]),
EDA.PropTable.Function(names(EDA.Bar.Source)[157]),
EDA.PropTable.Function(names(EDA.Bar.Source)[158]),
EDA.PropTable.Function(names(EDA.Bar.Source)[159]),
EDA.PropTable.Function(names(EDA.Bar.Source)[160]),
EDA.PropTable.Function(names(EDA.Bar.Source)[161]))
(EDA.Barchart.FactorVar <- barchart(EDA.Bar.Source.FactorVar.Prop.Group4[,3] ~
EDA.Bar.Source.FactorVar.Prop.Group4[,2] | EDA.Bar.Source.FactorVar.Prop.Group4[,4],
data=EDA.Bar.Source.FactorVar.Prop.Group4,
groups = EDA.Bar.Source.FactorVar.Prop.Group4[,1],
stack=TRUE,
ylab = "Proportion",
xlab = "Structure",
auto.key = list(adj = 1),
layout=(c(9,5))))
EDA.Bar.Source.FactorVar.Prop.Group3 <- rbind(EDA.PropTable.Function(names(EDA.Bar.Source)[82]),
EDA.PropTable.Function(names(EDA.Bar.Source)[83]),
EDA.PropTable.Function(names(EDA.Bar.Source)[84]),
EDA.PropTable.Function(names(EDA.Bar.Source)[85]),
EDA.PropTable.Function(names(EDA.Bar.Source)[86]),
EDA.PropTable.Function(names(EDA.Bar.Source)[87]),
EDA.PropTable.Function(names(EDA.Bar.Source)[88]),
EDA.PropTable.Function(names(EDA.Bar.Source)[89]),
EDA.PropTable.Function(names(EDA.Bar.Source)[90]),
EDA.PropTable.Function(names(EDA.Bar.Source)[91]),
EDA.PropTable.Function(names(EDA.Bar.Source)[92]),
EDA.PropTable.Function(names(EDA.Bar.Source)[93]),
EDA.PropTable.Function(names(EDA.Bar.Source)[94]),
EDA.PropTable.Function(names(EDA.Bar.Source)[95]),
EDA.PropTable.Function(names(EDA.Bar.Source)[96]),
EDA.PropTable.Function(names(EDA.Bar.Source)[97]),
EDA.PropTable.Function(names(EDA.Bar.Source)[98]),
EDA.PropTable.Function(names(EDA.Bar.Source)[99]),
EDA.PropTable.Function(names(EDA.Bar.Source)[100]),
EDA.PropTable.Function(names(EDA.Bar.Source)[101]),
EDA.PropTable.Function(names(EDA.Bar.Source)[102]),
EDA.PropTable.Function(names(EDA.Bar.Source)[103]),
EDA.PropTable.Function(names(EDA.Bar.Source)[104]),
EDA.PropTable.Function(names(EDA.Bar.Source)[105]),
EDA.PropTable.Function(names(EDA.Bar.Source)[106]),
EDA.PropTable.Function(names(EDA.Bar.Source)[107]),
EDA.PropTable.Function(names(EDA.Bar.Source)[108]),
EDA.PropTable.Function(names(EDA.Bar.Source)[109]),
EDA.PropTable.Function(names(EDA.Bar.Source)[110]),
EDA.PropTable.Function(names(EDA.Bar.Source)[111]),
EDA.PropTable.Function(names(EDA.Bar.Source)[112]),
EDA.PropTable.Function(names(EDA.Bar.Source)[113]),
EDA.PropTable.Function(names(EDA.Bar.Source)[114]),
EDA.PropTable.Function(names(EDA.Bar.Source)[115]),
EDA.PropTable.Function(names(EDA.Bar.Source)[116]),
EDA.PropTable.Function(names(EDA.Bar.Source)[117]),
EDA.PropTable.Function(names(EDA.Bar.Source)[118]),
EDA.PropTable.Function(names(EDA.Bar.Source)[119]),
EDA.PropTable.Function(names(EDA.Bar.Source)[120]),
EDA.PropTable.Function(names(EDA.Bar.Source)[121]))
(EDA.Barchart.FactorVar <- barchart(EDA.Bar.Source.FactorVar.Prop.Group3[,3] ~
EDA.Bar.Source.FactorVar.Prop.Group3[,2] | EDA.Bar.Source.FactorVar.Prop.Group3[,4],
data=EDA.Bar.Source.FactorVar.Prop.Group3,
groups = EDA.Bar.Source.FactorVar.Prop.Group3[,1],
stack=TRUE,
ylab = "Proportion",
xlab = "Structure",
auto.key = list(adj = 1),
layout=(c(9,5))))
EDA.Bar.Source.FactorVar.Prop.Group2 <- rbind(EDA.PropTable.Function(names(EDA.Bar.Source)[42]),
EDA.PropTable.Function(names(EDA.Bar.Source)[43]),
EDA.PropTable.Function(names(EDA.Bar.Source)[44]),
EDA.PropTable.Function(names(EDA.Bar.Source)[45]),
EDA.PropTable.Function(names(EDA.Bar.Source)[46]),
EDA.PropTable.Function(names(EDA.Bar.Source)[47]),
EDA.PropTable.Function(names(EDA.Bar.Source)[48]),
EDA.PropTable.Function(names(EDA.Bar.Source)[49]),
EDA.PropTable.Function(names(EDA.Bar.Source)[50]),
EDA.PropTable.Function(names(EDA.Bar.Source)[51]),
EDA.PropTable.Function(names(EDA.Bar.Source)[52]),
EDA.PropTable.Function(names(EDA.Bar.Source)[53]),
EDA.PropTable.Function(names(EDA.Bar.Source)[54]),
EDA.PropTable.Function(names(EDA.Bar.Source)[55]),
EDA.PropTable.Function(names(EDA.Bar.Source)[56]),
EDA.PropTable.Function(names(EDA.Bar.Source)[57]),
EDA.PropTable.Function(names(EDA.Bar.Source)[58]),
EDA.PropTable.Function(names(EDA.Bar.Source)[59]),
EDA.PropTable.Function(names(EDA.Bar.Source)[60]),
EDA.PropTable.Function(names(EDA.Bar.Source)[61]),
EDA.PropTable.Function(names(EDA.Bar.Source)[62]),
EDA.PropTable.Function(names(EDA.Bar.Source)[63]),
EDA.PropTable.Function(names(EDA.Bar.Source)[64]),
EDA.PropTable.Function(names(EDA.Bar.Source)[65]),
EDA.PropTable.Function(names(EDA.Bar.Source)[66]),
EDA.PropTable.Function(names(EDA.Bar.Source)[67]),
EDA.PropTable.Function(names(EDA.Bar.Source)[68]),
EDA.PropTable.Function(names(EDA.Bar.Source)[69]),
EDA.PropTable.Function(names(EDA.Bar.Source)[70]),
EDA.PropTable.Function(names(EDA.Bar.Source)[71]),
EDA.PropTable.Function(names(EDA.Bar.Source)[72]),
EDA.PropTable.Function(names(EDA.Bar.Source)[73]),
EDA.PropTable.Function(names(EDA.Bar.Source)[74]),
EDA.PropTable.Function(names(EDA.Bar.Source)[75]),
EDA.PropTable.Function(names(EDA.Bar.Source)[76]),
EDA.PropTable.Function(names(EDA.Bar.Source)[77]),
EDA.PropTable.Function(names(EDA.Bar.Source)[78]),
EDA.PropTable.Function(names(EDA.Bar.Source)[79]),
EDA.PropTable.Function(names(EDA.Bar.Source)[80]),
EDA.PropTable.Function(names(EDA.Bar.Source)[81]))
(EDA.Barchart.FactorVar <- barchart(EDA.Bar.Source.FactorVar.Prop.Group2[,3] ~
EDA.Bar.Source.FactorVar.Prop.Group2[,2] | EDA.Bar.Source.FactorVar.Prop.Group2[,4],
data=EDA.Bar.Source.FactorVar.Prop.Group2,
groups = EDA.Bar.Source.FactorVar.Prop.Group2[,1],
stack=TRUE,
ylab = "Proportion",
xlab = "Structure",
auto.key = list(adj = 1),
layout=(c(9,5))))
EDA.Bar.Source.FactorVar.Prop.Group1 <- rbind(EDA.PropTable.Function(names(EDA.Bar.Source)[2]),
EDA.PropTable.Function(names(EDA.Bar.Source)[3]),
EDA.PropTable.Function(names(EDA.Bar.Source)[4]),
EDA.PropTable.Function(names(EDA.Bar.Source)[5]),
EDA.PropTable.Function(names(EDA.Bar.Source)[6]),
EDA.PropTable.Function(names(EDA.Bar.Source)[7]),
EDA.PropTable.Function(names(EDA.Bar.Source)[8]),
EDA.PropTable.Function(names(EDA.Bar.Source)[9]),
EDA.PropTable.Function(names(EDA.Bar.Source)[10]),
EDA.PropTable.Function(names(EDA.Bar.Source)[11]),
EDA.PropTable.Function(names(EDA.Bar.Source)[12]),
EDA.PropTable.Function(names(EDA.Bar.Source)[13]),
EDA.PropTable.Function(names(EDA.Bar.Source)[14]),
EDA.PropTable.Function(names(EDA.Bar.Source)[15]),
EDA.PropTable.Function(names(EDA.Bar.Source)[16]),
EDA.PropTable.Function(names(EDA.Bar.Source)[17]),
EDA.PropTable.Function(names(EDA.Bar.Source)[18]),
EDA.PropTable.Function(names(EDA.Bar.Source)[19]),
EDA.PropTable.Function(names(EDA.Bar.Source)[20]),
EDA.PropTable.Function(names(EDA.Bar.Source)[21]),
EDA.PropTable.Function(names(EDA.Bar.Source)[22]),
EDA.PropTable.Function(names(EDA.Bar.Source)[23]),
EDA.PropTable.Function(names(EDA.Bar.Source)[24]),
EDA.PropTable.Function(names(EDA.Bar.Source)[25]),
EDA.PropTable.Function(names(EDA.Bar.Source)[26]),
EDA.PropTable.Function(names(EDA.Bar.Source)[27]),
EDA.PropTable.Function(names(EDA.Bar.Source)[28]),
EDA.PropTable.Function(names(EDA.Bar.Source)[29]),
EDA.PropTable.Function(names(EDA.Bar.Source)[30]),
EDA.PropTable.Function(names(EDA.Bar.Source)[31]),
EDA.PropTable.Function(names(EDA.Bar.Source)[32]),
EDA.PropTable.Function(names(EDA.Bar.Source)[33]),
EDA.PropTable.Function(names(EDA.Bar.Source)[34]),
EDA.PropTable.Function(names(EDA.Bar.Source)[35]),
EDA.PropTable.Function(names(EDA.Bar.Source)[36]),
EDA.PropTable.Function(names(EDA.Bar.Source)[37]),
EDA.PropTable.Function(names(EDA.Bar.Source)[38]),
EDA.PropTable.Function(names(EDA.Bar.Source)[39]),
EDA.PropTable.Function(names(EDA.Bar.Source)[40]),
EDA.PropTable.Function(names(EDA.Bar.Source)[41]))
(EDA.Barchart.FactorVar <- barchart(EDA.Bar.Source.FactorVar.Prop.Group1[,3] ~
EDA.Bar.Source.FactorVar.Prop.Group1[,2] | EDA.Bar.Source.FactorVar.Prop.Group1[,4],
data=EDA.Bar.Source.FactorVar.Prop.Group1,
groups = EDA.Bar.Source.FactorVar.Prop.Group1[,1],
stack=TRUE,
ylab = "Proportion",
xlab = "Structure",
auto.key = list(adj = 1),
layout=(c(9,5))))
1.5 Predictive Model Development
1.5.1 Logistic Regression (LR)
[A] The logistic regression model from the stats package was implemented through the caret package.
[B] The model does not contain any hyperparameter.
[C] The cross-validated model performance of the final model is summarized as follows:
[C.1] Final model configuration is fixed due to the absence of a hyperparameter
[C.2] ROC Curve AUC = 0.86164
[D] The model allows for ranking of predictors in terms of variable importance. The top-performing predictors in the model are as follows:
[D.1] FP063 (Structure=1) variable (factor)
[D.2] MolWeight variable (numeric)
[D.3] FP104 (Structure=1) variable (factor)
[D.4] FP012 (Structure=1) variable (factor)
[D.5] FP159 (Structure=1) variable (factor)
[E] The independent test model performance of the final model is summarized as follows:
[E.1] ROC Curve AUC = 0.87303
##################################
# Creating a local object
# for the train and test sets
##################################
PMA_PreModelling_Train_LR <- PMA_PreModelling_Train
PMA_PreModelling_Test_LR <- PMA_PreModelling_Test
##################################
# Creating consistent fold assignments
# for the 10-Fold Cross Validation process
##################################
set.seed(12345678)
KFold_Indices <- createFolds(PMA_PreModelling_Train_LR$Log_Solubility_Class,
k = 10,
returnTrain=TRUE)
KFold_Control <- trainControl(method="cv",
index=KFold_Indices,
summaryFunction = twoClassSummary,
classProbs = TRUE)
##################################
# Setting the conditions
# for hyperparameter tuning
##################################
# No hyperparameter tuning process conducted
# hyperparameter=intercept fixed to TRUE
##################################
# Running the logistic regression model
# by setting the caret method to 'glm'
##################################
set.seed(12345678)
LR_Tune <- train(x = PMA_PreModelling_Train_LR[,!names(PMA_PreModelling_Train_LR) %in% c("Log_Solubility_Class")],
y = PMA_PreModelling_Train_LR$Log_Solubility_Class,
method = "glm",
metric = "ROC",
trControl = KFold_Control)
##################################
# Reporting the cross-validation results
# for the train set
##################################
LR_Tune## Generalized Linear Model
##
## 951 samples
## 220 predictors
## 2 classes: 'Low', 'High'
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 857, 855, 857, 855, 856, 856, ...
## Resampling results:
##
## ROC Sens Spec
## 0.8616392 0.7961794 0.8436865LR_Tune$finalModel##
## Call: NULL
##
## Coefficients:
## (Intercept) FP0011 FP0021 FP0031
## -73.478 23.642 -63.792 29.009
## FP0041 FP0051 FP0061 FP0071
## -61.233 -10.359 126.716 4.106
## FP0081 FP0091 FP0101 FP0111
## 44.714 -148.358 32.580 -35.712
## FP0121 FP0131 FP0141 FP0151
## 150.447 100.835 -100.478 -51.850
## FP0161 FP0171 FP0181 FP0191
## 14.599 -72.252 -76.040 123.798
## FP0201 FP0211 FP0221 FP0231
## -39.270 137.655 -140.820 -33.305
## FP0241 FP0251 FP0261 FP0271
## 50.910 109.986 -59.291 -100.391
## FP0281 FP0291 FP0301 FP0311
## -53.217 120.259 -6.067 4.267
## FP0321 FP0331 FP0341 FP0351
## -142.025 154.036 91.367 -31.286
## FP0361 FP0371 FP0381 FP0391
## 3.235 76.462 4.078 35.413
## FP0401 FP0411 FP0421 FP0431
## -94.345 -143.696 114.618 -155.763
## FP0441 FP0451 FP0461 FP0471
## 11.007 50.524 72.530 -17.550
## FP0481 FP0491 FP0501 FP0511
## 19.321 -32.341 -45.643 26.443
## FP0521 FP0531 FP0541 FP0551
## 31.135 67.873 17.110 10.667
## FP0561 FP0571 FP0581 FP0591
## 23.892 -57.760 120.795 26.711
## FP0601 FP0611 FP0621 FP0631
## 16.357 -35.503 167.909 306.142
## FP0641 FP0651 FP0661 FP0671
## 21.204 3.992 -2.965 -51.198
## FP0681 FP0691 FP0701 FP0711
## -197.983 28.044 3.822 13.276
## FP0721 FP0731 FP0741 FP0751
## 96.718 9.386 6.163 62.776
## FP0761 FP0771 FP0781 FP0791
## 61.763 -1.026 -46.437 -52.010
## FP0801 FP0811 FP0821 FP0831
## 97.374 -8.238 12.896 -131.968
## FP0841 FP0851 FP0861 FP0871
## 67.549 -11.058 3.183 5.585
## FP0881 FP0891 FP0901 FP0911
## 32.577 -48.514 28.546 124.351
## FP0921 FP0931 FP0941 FP0951
## 109.202 59.604 -43.210 -69.740
## FP0961 FP0971 FP0981 FP0991
## 31.873 -63.515 -22.406 29.279
## FP1001 FP1011 FP1021 FP1031
## 124.565 -64.999 -116.518 9.557
## FP1041 FP1051 FP1061 FP1071
## -75.807 -9.512 -37.698 -40.447
## FP1081 FP1091 FP1101 FP1111
## -55.197 -24.950 -146.311 -71.819
## FP1121 FP1131 FP1141 FP1151
## -13.401 -8.784 -80.249 35.511
## FP1161 FP1171 FP1181 FP1191
## 25.361 51.423 -46.085 102.543
## FP1201 FP1211 FP1221 FP1231
## -115.444 -5.854 91.088 -47.361
## FP1241 FP1251 FP1261 FP1271
## 21.566 73.821 -83.394 17.137
## FP1281 FP1291 FP1301 FP1311
## 9.615 18.670 139.606 106.283
## FP1321 FP1331 FP1341 FP1351
## -60.900 24.554 64.458 38.337
## FP1361 FP1371 FP1381 FP1391
## -211.682 109.808 -122.970 -54.319
## FP1401 FP1411 FP1421 FP1431
## 66.218 -252.454 -43.329 126.016
## FP1441 FP1451 FP1461 FP1471
## 17.968 -18.638 -109.857 -14.412
## FP1481 FP1491 FP1501 FP1511
## -14.780 24.576 -13.686 -183.721
## FP1521 FP1531 FP1551 FP1561
## 139.475 29.879 114.250 -230.935
## FP1571 FP1581 FP1591 FP1601
## -158.006 -98.477 386.562 -85.277
## FP1611 FP1621 FP1631 FP1641
## 73.919 -12.368 -46.209 48.885
## FP1651 FP1661 FP1671 FP1681
## 35.933 -27.182 -152.769 103.681
## FP1691 FP1701 FP1711 FP1721
## -22.744 -6.383 96.779 -18.229
## FP1731 FP1741 FP1751 FP1761
## -67.084 -144.129 2.561 -107.016
## FP1771 FP1781 FP1791 FP1801
## 56.955 -58.915 62.378 -46.265
## FP1811 FP1821 FP1831 FP1841
## -79.937 -104.797 -116.208 74.850
## FP1851 FP1861 FP1871 FP1881
## 64.332 2.161 -44.703 32.183
## FP1891 FP1901 FP1911 FP1921
## -27.250 20.897 -11.267 138.402
## FP1931 FP1941 FP1951 FP1961
## 98.767 113.569 46.129 -148.367
## FP1971 FP1981 FP2011 FP2021
## -115.916 -63.312 29.714 9.347
## FP2031 FP2041 FP2051 FP2061
## -130.341 55.393 -31.422 8.553
## FP2071 FP2081 MolWeight NumBonds
## 0.389 30.840 -90.607 -122.580
## NumMultBonds NumRotBonds NumDblBonds NumCarbon
## -116.050 -31.516 78.549 65.370
## NumNitrogen NumOxygen NumSulfer NumChlorine
## 95.518 116.199 59.793 -9.772
## NumHalogen NumRings HydrophilicFactor SurfaceArea1
## -1.850 92.579 139.414 46.155
## SurfaceArea2
## -264.909
##
## Degrees of Freedom: 950 Total (i.e. Null); 730 Residual
## Null Deviance: 1308
## Residual Deviance: 1.502e-07 AIC: 442LR_Tune$results## parameter ROC Sens Spec ROCSD SensSD SpecSD
## 1 none 0.8616392 0.7961794 0.8436865 0.04359539 0.06796609 0.06105881(LR_Train_ROCCurveAUC <- LR_Tune$results$ROC)## [1] 0.8616392##################################
# Identifying and plotting the
# best model predictors
##################################
LR_VarImp <- varImp(LR_Tune, scale = TRUE)
plot(LR_VarImp,
top=25,
scales=list(y=list(cex = .95)),
main="Ranked Variable Importance : Logistic Regression",
xlab="Scaled Variable Importance Metrics",
ylab="Predictors",
cex=2,
origin=0,
alpha=0.45)
##################################
# Independently evaluating the model
# on the test set
##################################
LR_Test <- data.frame(LR_Observed = PMA_PreModelling_Test_LR$Log_Solubility_Class,
LR_Predicted = predict(LR_Tune,
PMA_PreModelling_Test_LR[,!names(PMA_PreModelling_Test_LR) %in% c("Log_Solubility_Class")],
type = "prob"))
LR_Test## LR_Observed LR_Predicted.Low LR_Predicted.High
## 20 High 2.220446e-16 1.000000e+00
## 21 High 2.220446e-16 1.000000e+00
## 23 High 2.220446e-16 1.000000e+00
## 25 High 2.220446e-16 1.000000e+00
## 28 High 5.891554e-08 9.999999e-01
## 31 High 2.220446e-16 1.000000e+00
## 32 High 2.220446e-16 1.000000e+00
## 33 High 2.220446e-16 1.000000e+00
## 34 High 2.220446e-16 1.000000e+00
## 37 High 2.220446e-16 1.000000e+00
## 38 High 2.220446e-16 1.000000e+00
## 42 High 2.220446e-16 1.000000e+00
## 49 High 2.220446e-16 1.000000e+00
## 54 High 2.220446e-16 1.000000e+00
## 55 High 2.220446e-16 1.000000e+00
## 58 High 2.220446e-16 1.000000e+00
## 60 High 2.220446e-16 1.000000e+00
## 61 High 2.220446e-16 1.000000e+00
## 65 High 2.220446e-16 1.000000e+00
## 69 High 2.220446e-16 1.000000e+00
## 73 High 2.220446e-16 1.000000e+00
## 86 High 2.220446e-16 1.000000e+00
## 90 High 2.220446e-16 1.000000e+00
## 91 High 2.220446e-16 1.000000e+00
## 93 High 2.220446e-16 1.000000e+00
## 96 High 2.220446e-16 1.000000e+00
## 98 High 2.220446e-16 1.000000e+00
## 100 High 2.220446e-16 1.000000e+00
## 104 High 2.220446e-16 1.000000e+00
## 112 High 2.220446e-16 1.000000e+00
## 115 High 2.220446e-16 1.000000e+00
## 119 High 2.220446e-16 1.000000e+00
## 128 High 2.220446e-16 1.000000e+00
## 130 High 2.220446e-16 1.000000e+00
## 139 High 2.220446e-16 1.000000e+00
## 143 High 2.220446e-16 1.000000e+00
## 145 High 2.220446e-16 1.000000e+00
## 146 High 2.220446e-16 1.000000e+00
## 149 High 2.220446e-16 1.000000e+00
## 150 High 2.220446e-16 1.000000e+00
## 152 High 2.220446e-16 1.000000e+00
## 157 High 2.220446e-16 1.000000e+00
## 161 High 2.220446e-16 1.000000e+00
## 162 High 2.220446e-16 1.000000e+00
## 166 High 2.220446e-16 1.000000e+00
## 167 High 2.220446e-16 1.000000e+00
## 173 High 2.220446e-16 1.000000e+00
## 176 High 2.220446e-16 1.000000e+00
## 182 High 2.220446e-16 1.000000e+00
## 187 High 2.220446e-16 1.000000e+00
## 190 High 2.220446e-16 1.000000e+00
## 194 High 2.220446e-16 1.000000e+00
## 195 High 2.220446e-16 1.000000e+00
## 201 High 2.220446e-16 1.000000e+00
## 207 High 2.220446e-16 1.000000e+00
## 208 High 2.220446e-16 1.000000e+00
## 215 High 2.220446e-16 1.000000e+00
## 222 High 6.031580e-02 9.396842e-01
## 224 High 2.220446e-16 1.000000e+00
## 231 High 2.220446e-16 1.000000e+00
## 236 High 2.220446e-16 1.000000e+00
## 237 High 2.220446e-16 1.000000e+00
## 240 High 2.220446e-16 1.000000e+00
## 243 High 2.220446e-16 1.000000e+00
## 248 High 2.220446e-16 1.000000e+00
## 251 High 2.220446e-16 1.000000e+00
## 256 High 1.000000e+00 2.220446e-16
## 258 High 1.321706e-07 9.999999e-01
## 262 High 2.220446e-16 1.000000e+00
## 266 High 2.220446e-16 1.000000e+00
## 272 High 2.220446e-16 1.000000e+00
## 280 High 2.220446e-16 1.000000e+00
## 283 High 2.220446e-16 1.000000e+00
## 286 High 2.220446e-16 1.000000e+00
## 287 High 9.130220e-01 8.697798e-02
## 289 High 2.220446e-16 1.000000e+00
## 290 High 9.999585e-01 4.152350e-05
## 298 High 2.220446e-16 1.000000e+00
## 305 High 2.220446e-16 1.000000e+00
## 306 High 2.220446e-16 1.000000e+00
## 312 High 2.220446e-16 1.000000e+00
## 320 High 2.220446e-16 1.000000e+00
## 325 High 1.000000e+00 2.220446e-16
## 332 High 2.220446e-16 1.000000e+00
## 333 High 2.220446e-16 1.000000e+00
## 335 High 2.220446e-16 1.000000e+00
## 339 High 1.000000e+00 1.297243e-13
## 346 High 2.220446e-16 1.000000e+00
## 347 High 2.220446e-16 1.000000e+00
## 350 High 2.220446e-16 1.000000e+00
## 353 High 2.220446e-16 1.000000e+00
## 358 High 6.755818e-11 1.000000e+00
## 365 High 2.220446e-16 1.000000e+00
## 367 High 2.220446e-16 1.000000e+00
## 370 High 2.220446e-16 1.000000e+00
## 379 High 1.000000e+00 2.220446e-16
## 386 High 2.220446e-16 1.000000e+00
## 394 High 1.000000e+00 2.220446e-16
## 396 High 2.220446e-16 1.000000e+00
## 400 High 1.153293e-10 1.000000e+00
## 404 High 2.220446e-16 1.000000e+00
## 405 High 2.305626e-02 9.769437e-01
## 413 High 2.220446e-16 1.000000e+00
## 415 High 2.220446e-16 1.000000e+00
## 417 High 1.000000e+00 2.220446e-16
## 418 High 2.220446e-16 1.000000e+00
## 423 High 2.220446e-16 1.000000e+00
## 434 High 1.124513e-07 9.999999e-01
## 437 High 1.000000e+00 2.220446e-16
## 440 High 1.000000e+00 2.220446e-16
## 449 High 2.220446e-16 1.000000e+00
## 450 High 1.000000e+00 2.220446e-16
## 457 High 2.220446e-16 1.000000e+00
## 467 High 1.000000e+00 2.220446e-16
## 469 High 2.220446e-16 1.000000e+00
## 474 High 1.000000e+00 2.220446e-16
## 475 High 1.000000e+00 2.220446e-16
## 485 High 1.000000e+00 2.220446e-16
## 504 Low 2.220446e-16 1.000000e+00
## 511 Low 1.000000e+00 2.220446e-16
## 512 Low 2.220446e-16 1.000000e+00
## 517 Low 2.220446e-16 1.000000e+00
## 519 Low 1.000000e+00 2.220446e-16
## 520 Low 1.000000e+00 2.220446e-16
## 522 Low 2.220446e-16 1.000000e+00
## 527 Low 2.220446e-16 1.000000e+00
## 528 Low 1.000000e+00 2.220446e-16
## 529 Low 1.000000e+00 2.220446e-16
## 537 Low 1.000000e+00 2.220446e-16
## 540 Low 2.220446e-16 1.000000e+00
## 541 Low 1.000000e+00 1.735441e-12
## 547 Low 1.000000e+00 2.220446e-16
## 550 Low 1.000000e+00 2.220446e-16
## 555 Low 1.000000e+00 2.220446e-16
## 564 Low 1.000000e+00 2.220446e-16
## 570 Low 1.000000e+00 2.220446e-16
## 573 Low 1.000000e+00 1.200116e-08
## 575 Low 1.000000e+00 4.090493e-11
## 578 Low 2.220446e-16 1.000000e+00
## 581 Low 2.220446e-16 1.000000e+00
## 585 Low 2.001904e-04 9.997998e-01
## 590 Low 1.000000e+00 2.220446e-16
## 601 Low 1.000000e+00 2.220446e-16
## 602 Low 2.220446e-16 1.000000e+00
## 607 Low 2.220446e-16 1.000000e+00
## 610 Low 1.000000e+00 2.220446e-16
## 618 Low 2.220446e-16 1.000000e+00
## 624 Low 1.000000e+00 2.220446e-16
## 626 Low 1.000000e+00 2.220446e-16
## 627 Low 1.000000e+00 2.220446e-16
## 634 Low 1.000000e+00 2.008828e-09
## 640 Low 1.000000e+00 2.220446e-16
## 642 Low 1.000000e+00 2.220446e-16
## 643 Low 1.000000e+00 2.220446e-16
## 644 Low 2.220446e-16 1.000000e+00
## 645 Low 2.220446e-16 1.000000e+00
## 646 Low 1.000000e+00 2.220446e-16
## 647 Low 1.000000e+00 2.220446e-16
## 652 Low 1.000000e+00 2.220446e-16
## 658 Low 1.000000e+00 2.220446e-16
## 659 Low 9.999675e-01 3.251573e-05
## 660 Low 1.000000e+00 2.220446e-16
## 664 Low 4.952152e-05 9.999505e-01
## 666 Low 1.000000e+00 2.220446e-16
## 667 Low 1.000000e+00 2.220446e-16
## 675 Low 1.000000e+00 2.220446e-16
## 680 Low 1.000000e+00 2.220446e-16
## 681 Low 9.726381e-01 2.736193e-02
## 687 Low 1.000000e+00 2.220446e-16
## 694 Low 1.000000e+00 2.220446e-16
## 697 Low 1.000000e+00 2.220446e-16
## 701 Low 1.000000e+00 2.220446e-16
## 705 Low 1.000000e+00 2.220446e-16
## 707 Low 1.000000e+00 2.220446e-16
## 710 Low 1.000000e+00 2.220446e-16
## 716 Low 1.000000e+00 1.592413e-11
## 719 Low 1.000000e+00 2.220446e-16
## 720 Low 1.000000e+00 2.220446e-16
## 725 Low 1.000000e+00 2.220446e-16
## 727 Low 1.000000e+00 2.220446e-16
## 730 Low 1.000000e+00 2.220446e-16
## 738 Low 2.220446e-16 1.000000e+00
## 745 Low 1.000000e+00 2.220446e-16
## 748 Low 1.000000e+00 2.220446e-16
## 751 Low 1.000000e+00 2.220446e-16
## 756 Low 1.000000e+00 2.220446e-16
## 766 Low 1.000000e+00 2.220446e-16
## 769 Low 1.000000e+00 2.220446e-16
## 783 Low 1.000000e+00 2.220446e-16
## 785 Low 1.000000e+00 2.220446e-16
## 790 Low 1.000000e+00 2.220446e-16
## 793 Low 1.000000e+00 2.220446e-16
## 795 Low 1.000000e+00 2.220446e-16
## 796 Low 1.000000e+00 2.220446e-16
## 797 Low 1.000000e+00 2.220446e-16
## 801 Low 1.000000e+00 2.220446e-16
## 811 Low 1.000000e+00 2.220446e-16
## 812 Low 1.000000e+00 2.220446e-16
## 815 Low 1.000000e+00 2.220446e-16
## 816 Low 1.000000e+00 2.220446e-16
## 817 Low 1.000000e+00 2.220446e-16
## 824 Low 1.000000e+00 2.220446e-16
## 825 Low 1.000000e+00 2.220446e-16
## 826 Low 1.000000e+00 2.220446e-16
## 830 Low 1.000000e+00 2.220446e-16
## 837 Low 1.000000e+00 2.220446e-16
## 838 Low 1.000000e+00 2.220446e-16
## 844 Low 1.000000e+00 2.220446e-16
## 845 Low 1.000000e+00 2.220446e-16
## 847 Low 1.000000e+00 2.220446e-16
## 850 Low 1.000000e+00 2.220446e-16
## 852 Low 1.000000e+00 2.220446e-16
## 853 Low 1.000000e+00 2.220446e-16
## 861 Low 1.000000e+00 2.220446e-16
## 868 Low 1.000000e+00 2.220446e-16
## 874 Low 1.000000e+00 2.220446e-16
## 879 High 2.220446e-16 1.000000e+00
## 895 High 2.220446e-16 1.000000e+00
## 899 High 2.220446e-16 1.000000e+00
## 903 High 2.220446e-16 1.000000e+00
## 917 High 2.220446e-16 1.000000e+00
## 927 High 2.220446e-16 1.000000e+00
## 929 High 2.220446e-16 1.000000e+00
## 931 High 2.220446e-16 1.000000e+00
## 933 High 2.220446e-16 1.000000e+00
## 944 High 2.220446e-16 1.000000e+00
## 947 High 2.220446e-16 1.000000e+00
## 949 High 2.220446e-16 1.000000e+00
## 953 High 2.220446e-16 1.000000e+00
## 958 High 1.000000e+00 5.733169e-09
## 961 High 2.220446e-16 1.000000e+00
## 963 High 2.220446e-16 1.000000e+00
## 964 High 2.220446e-16 1.000000e+00
## 973 High 2.220446e-16 1.000000e+00
## 976 High 2.220446e-16 1.000000e+00
## 977 High 2.220446e-16 1.000000e+00
## 980 High 2.220446e-16 1.000000e+00
## 983 High 2.220446e-16 1.000000e+00
## 984 High 2.220446e-16 1.000000e+00
## 986 High 2.220446e-16 1.000000e+00
## 989 High 2.220446e-16 1.000000e+00
## 991 High 2.220446e-16 1.000000e+00
## 996 High 2.220446e-16 1.000000e+00
## 997 High 1.000000e+00 2.220446e-16
## 999 High 2.220446e-16 1.000000e+00
## 1000 High 2.220446e-16 1.000000e+00
## 1003 High 2.220446e-16 1.000000e+00
## 1008 High 2.220446e-16 1.000000e+00
## 1009 High 2.220446e-16 1.000000e+00
## 1014 High 2.220446e-16 1.000000e+00
## 1015 High 2.220446e-16 1.000000e+00
## 1040 High 1.000000e+00 2.220446e-16
## 1042 High 2.220446e-16 1.000000e+00
## 1043 High 1.000000e+00 2.220446e-16
## 1050 High 1.000000e+00 2.220446e-16
## 1052 High 2.220446e-16 1.000000e+00
## 1056 High 2.220446e-16 1.000000e+00
## 1070 High 2.220446e-16 1.000000e+00
## 1073 High 1.000000e+00 2.220446e-16
## 1074 High 2.220446e-16 1.000000e+00
## 1079 High 2.220446e-16 1.000000e+00
## 1080 High 2.220446e-16 1.000000e+00
## 1085 High 2.220446e-16 1.000000e+00
## 1087 High 2.220446e-16 1.000000e+00
## 1096 High 3.436140e-12 1.000000e+00
## 1099 High 2.220446e-16 1.000000e+00
## 1100 High 1.000000e+00 5.528555e-09
## 1102 High 2.220446e-16 1.000000e+00
## 1107 Low 9.922518e-01 7.748197e-03
## 1109 Low 2.220446e-16 1.000000e+00
## 1114 Low 1.000000e+00 2.220446e-16
## 1118 Low 1.000000e+00 2.220446e-16
## 1123 Low 1.000000e+00 2.220446e-16
## 1132 Low 1.000000e+00 2.220446e-16
## 1134 Low 1.844113e-09 1.000000e+00
## 1137 Low 1.000000e+00 2.220446e-16
## 1154 Low 1.000000e+00 2.220446e-16
## 1155 Low 2.220446e-16 1.000000e+00
## 1157 Low 1.000000e+00 2.220446e-16
## 1162 Low 1.000000e+00 2.220446e-16
## 1164 Low 1.000000e+00 2.220446e-16
## 1171 Low 1.000000e+00 2.220446e-16
## 1172 Low 2.286853e-09 1.000000e+00
## 1175 Low 1.000000e+00 2.220446e-16
## 1177 Low 1.000000e+00 2.220446e-16
## 1179 Low 1.000000e+00 9.377951e-11
## 1183 Low 1.000000e+00 2.875438e-12
## 1185 Low 2.220446e-16 1.000000e+00
## 1189 Low 1.000000e+00 2.220446e-16
## 1211 Low 1.000000e+00 2.220446e-16
## 1218 Low 2.220446e-16 1.000000e+00
## 1224 Low 1.000000e+00 2.220446e-16
## 1225 Low 1.000000e+00 2.220446e-16
## 1227 Low 1.000000e+00 2.220446e-16
## 1232 Low 1.000000e+00 2.220446e-16
## 1235 Low 1.000000e+00 2.220446e-16
## 1238 Low 1.000000e+00 2.220446e-16
## 1240 Low 1.000000e+00 2.220446e-16
## 1241 Low 1.000000e+00 2.220446e-16
## 1248 Low 1.000000e+00 2.220446e-16
## 1258 Low 1.000000e+00 2.220446e-16
## 1261 Low 1.000000e+00 2.220446e-16
## 1263 Low 1.000000e+00 2.220446e-16
## 1269 Low 1.000000e+00 2.220446e-16
## 1270 Low 1.000000e+00 2.220446e-16
## 1271 Low 1.000000e+00 2.220446e-16
## 1272 Low 1.000000e+00 2.220446e-16
## 1280 Low 1.000000e+00 2.220446e-16
## 1286 Low 1.000000e+00 2.220446e-16
## 1287 Low 1.000000e+00 2.220446e-16
## 1289 Low 1.000000e+00 2.220446e-16
## 1290 Low 1.000000e+00 2.220446e-16
## 1291 High 2.220446e-16 1.000000e+00
## 1294 High 2.220446e-16 1.000000e+00
## 1305 Low 1.000000e+00 2.220446e-16
## 1308 High 1.000000e+00 2.220446e-16##################################
# Reporting the independent evaluation results
# for the test set
##################################
LR_Test_ROC <- roc(response = LR_Test$LR_Observed,
predictor = LR_Test$LR_Predicted.High,
levels = rev(levels(LR_Test$LR_Observed)))
(LR_Test_ROCCurveAUC <- auc(LR_Test_ROC)[1])## [1] 0.87303451.5.2 Linear Discriminant Analysis (LDA)
[A] The linear discriminant analysis model from the MASS package was implemented through the caret package.
[B] The model does not contain any hyperparameter.
[C] The cross-validated model performance of the final model is summarized as follows:
[C.1] Final model configuration is fixed due to the absence of a hyperparameter
[C.2] ROC Curve AUC = 0.90968
[D] The model does not allow for ranking of predictors in terms of variable importance.
[E] The independent test model performance of the final model is summarized as follows:
[E.1] ROC Curve AUC = 0.92138
##################################
# Transforming factor predictors
# as required by the nature of the model
##################################
# Creating a local object
# for the train and test sets
##################################
PMA_PreModelling_Train_LDA <- as.data.frame(lapply(PMA_PreModelling_Train[,!names(PMA_PreModelling_Train) %in%
c("Log_Solubility_Class")],
function(x) as.numeric(as.character(x))))
PMA_PreModelling_Train_LDA$Log_Solubility_Class <- PMA_PreModelling_Train$Log_Solubility_Class
dim(PMA_PreModelling_Train_LDA)## [1] 951 221PMA_PreModelling_Test_LDA <- as.data.frame(lapply(PMA_PreModelling_Test[,!names(PMA_PreModelling_Test) %in%
c("Log_Solubility_Class")],
function(x) as.numeric(as.character(x))))
PMA_PreModelling_Test_LDA$Log_Solubility_Class <- PMA_PreModelling_Test$Log_Solubility_Class
dim(PMA_PreModelling_Test_LDA)## [1] 316 221##################################
# Creating consistent fold assignments
# for the 10-Fold Cross Validation process
##################################
set.seed(12345678)
KFold_Indices <- createFolds(PMA_PreModelling_Train_LDA$Log_Solubility_Class,
k = 10,
returnTrain=TRUE)
KFold_Control <- trainControl(method="cv",
index=KFold_Indices,
summaryFunction = twoClassSummary,
classProbs = TRUE)
##################################
# Setting the conditions
# for hyperparameter tuning
##################################
# No hyperparameter tuning process conducted
##################################
# Running the linear discriminant analysis model
# by setting the caret method to 'lda'
##################################
set.seed(12345678)
LDA_Tune <- train(x = PMA_PreModelling_Train_LDA[,!names(PMA_PreModelling_Train_LDA) %in% c("Log_Solubility_Class")],
y = PMA_PreModelling_Train_LDA$Log_Solubility_Class,
method = "lda",
preProc = c("center","scale"),
metric = "ROC",
trControl = KFold_Control)
##################################
# Reporting the cross-validation results
# for the train set
##################################
LDA_Tune## Linear Discriminant Analysis
##
## 951 samples
## 220 predictors
## 2 classes: 'Low', 'High'
##
## Pre-processing: centered (220), scaled (220)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 857, 855, 857, 855, 856, 856, ...
## Resampling results:
##
## ROC Sens Spec
## 0.9096763 0.817165 0.8416909LDA_Tune$finalModel## Call:
## lda(x, y)
##
## Prior probabilities of groups:
## Low High
## 0.4490011 0.5509989
##
## Group means:
## FP001 FP002 FP003 FP004 FP005 FP006
## Low -0.04954059 0.2801751 0.007856301 -0.06481098 0.2731141 -0.1627379
## High 0.04036991 -0.2283107 -0.006401986 0.05281352 -0.2225567 0.1326128
## FP007 FP008 FP009 FP010 FP011 FP012
## Low 0.03233293 0.1438642 0.3158384 -0.09365294 -0.1402546 -0.02106485
## High -0.02634763 -0.1172328 -0.2573722 0.07631642 0.1142914 0.01716544
## FP013 FP014 FP015 FP016 FP017 FP018
## Low 0.3525294 0.3395685 -0.1976220 0.03040486 0.1365611 0.1376840
## High -0.2872711 -0.2767094 0.1610393 -0.02477648 -0.1112817 -0.1121967
## FP019 FP020 FP021 FP022 FP023 FP024
## Low -0.007754077 -0.04457870 0.05287346 -0.003457511 0.11021758 -0.01513399
## High 0.006318685 0.03632653 -0.04308582 0.002817476 -0.08981471 0.01233247
## FP025 FP026 FP027 FP028 FP029 FP030
## Low -0.04676690 0.06813605 -0.10840914 -0.03304107 0.02665863 -0.05594394
## High 0.03810967 -0.05552308 0.08834103 0.02692469 -0.02172373 0.04558790
## FP031 FP032 FP033 FP034 FP035 FP036
## Low 0.03146379 -0.07556463 -0.06110273 0.05072117 0.1716135 -0.1267802
## High -0.02563939 0.06157652 0.04979173 -0.04133194 -0.1398453 0.1033113
## FP037 FP038 FP039 FP040 FP041 FP042
## Low 0.07241315 -0.04851628 0.1791850 -0.08519871 0.1546157 -0.03283123
## High -0.05900842 0.03953522 -0.1460152 0.06942720 -0.1259941 0.02675370
## FP043 FP044 FP045 FP046 FP047 FP048
## Low 0.06317712 0.2702580 0.11430896 0.1929160 0.1027778 0.03562711
## High -0.05148211 -0.2202293 -0.09314871 -0.1572045 -0.0837521 -0.02903202
## FP049 FP050 FP051 FP052 FP053 FP054
## Low 0.2711896 0.08856849 0.11478038 -0.03298863 0.2173025 0.1652162
## High -0.2209885 -0.07217317 -0.09353287 0.02688196 -0.1770766 -0.1346323
## FP055 FP056 FP057 FP058 FP059 FP060
## Low -0.06129149 0.1722025 0.04189625 0.011124158 0.1508474 -0.1341772
## High 0.04994555 -0.1403254 -0.03414064 -0.009064915 -0.1229234 0.1093390
## FP061 FP062 FP063 FP064 FP065 FP066
## Low -0.01330222 -0.06975983 -0.08447482 -0.04655345 0.3609846 -0.002018379
## High 0.01083978 0.05684628 0.06883730 0.03793573 -0.2941611 0.001644748
## FP067 FP068 FP069 FP070 FP071 FP072
## Low -0.03901753 -0.03145129 0.04161918 0.3288123 0.2861991 -0.2569933
## High 0.03179482 0.02562920 -0.03391486 -0.2679444 -0.2332195 0.2094201
## FP073 FP074 FP075 FP076 FP077 FP078
## Low -0.1389273 -0.04868503 -0.07210725 0.4980956 0.07048212 0.02157141
## High 0.1132098 0.03967273 0.05875916 -0.4058909 -0.05743486 -0.01757823
## FP079 FP080 FP081 FP082 FP083 FP084
## Low 0.3463924 -0.05762649 0.07838924 0.3373452 -0.1404314 -0.03174270
## High -0.2822702 0.04695899 -0.06387826 -0.2748977 0.1144355 0.02586667
## FP085 FP086 FP087 FP088 FP089 FP090
## Low 0.3053243 0.10584011 0.3032336 -0.10767772 0.4204845 0.1059896
## High -0.2488043 -0.08624757 -0.2471007 0.08774501 -0.3426467 -0.0863694
## FP091 FP092 FP093 FP094 FP095 FP096
## Low 0.005121802 0.3533487 0.1680405 0.001219888 -0.04432336 0.0513720
## High -0.004173682 -0.2879388 -0.1369338 -0.000994069 0.03611847 -0.0418623
## FP097 FP098 FP099 FP100 FP101 FP102
## Low 0.2946914 -0.05760012 0.1732751 -0.07094028 -0.03318476 0.1329019
## High -0.2401397 0.04693750 -0.1411994 0.05780820 0.02704178 -0.1082999
## FP103 FP104 FP105 FP106 FP107 FP108
## Low 0.12235122 0.10579469 0.1648155 0.09092851 0.2794970 -0.003218840
## High -0.09970223 -0.08621056 -0.1343058 -0.07409632 -0.2277581 0.002622986
## FP109 FP110 FP111 FP112 FP113 FP114
## Low 0.1016844 -0.06946341 0.02377356 0.3898869 -0.07974936 0.06165111
## High -0.0828611 0.05660473 -0.01937273 -0.3177132 0.06498660 -0.05023859
## FP115 FP116 FP117 FP118 FP119 FP120
## Low 0.02852821 -0.03068122 0.10794595 -0.05443201 -0.02278350 -0.05623436
## High -0.02324722 0.02500168 -0.08796359 0.04435586 0.01856594 0.04582457
## FP121 FP122 FP123 FP124 FP125 FP126
## Low 0.11663727 0.006041735 0.1543669 -0.03269777 -0.02874788 -0.002036287
## High -0.09504602 -0.004923322 -0.1257913 0.02664494 0.02342623 0.001659341
## FP127 FP128 FP129 FP130 FP131 FP132
## Low -0.06557830 -0.06131717 0.1268166 0.06943777 0.007894091 -0.1233146
## High 0.05343881 0.04996647 -0.1033410 -0.05658383 -0.006432780 0.1004873
## FP133 FP134 FP135 FP136 FP137 FP138
## Low -0.02030227 0.10305010 0.007894091 -0.01173875 0.09228709 0.07739663
## High 0.01654402 -0.08397403 -0.006432780 0.00956574 -0.07520341 -0.06306939
## FP139 FP140 FP141 FP142 FP143 FP144
## Low 0.03393326 -0.05648327 0.1251016 0.03227952 0.04656681 -0.08010303
## High -0.02765172 0.04602740 -0.1019434 -0.02630411 -0.03794661 0.06527480
## FP145 FP146 FP147 FP148 FP149 FP150
## Low -0.04944482 0.2078579 -0.02212958 -0.03538806 0.2479928 -0.01454711
## High 0.04029187 -0.1693804 0.01803307 0.02883722 -0.2020858 0.01185423
## FP151 FP152 FP153 FP155 FP156 FP157
## Low -0.01833621 0.05952448 0.07666591 0.1875793 0.08155977 0.01464155
## High 0.01494191 -0.04850564 -0.06247394 -0.1528556 -0.06646187 -0.01193119
## FP158 FP159 FP160 FP161 FP162 FP163
## Low -0.07168155 0.07241315 0.007559130 -0.1721042 0.2505609 -0.07216223
## High 0.05841225 -0.05900842 -0.006159826 0.1402452 -0.2041784 0.05880396
## FP164 FP165 FP166 FP167 FP168 FP169
## Low 0.3096359 -0.03470786 0.1669255 -0.04032322 0.3362988 0.327927
## High -0.2523178 0.02828293 -0.1360252 0.03285881 -0.2740450 -0.267223
## FP170 FP171 FP172 FP173 FP174 FP175
## Low 0.11733598 -0.09542927 0.3613895 0.1501297 0.07871463 0.010478627
## High -0.09561539 0.07776393 -0.2944911 -0.1223385 -0.06414341 -0.008538881
## FP176 FP177 FP178 FP179 FP180 FP181
## Low -0.0006016742 0.02415692 0.1246648 0.06495599 -0.05898743 0.2012292
## High 0.0004902956 -0.01968512 -0.1015875 -0.05293170 0.04806800 -0.1639787
## FP182 FP183 FP184 FP185 FP186 FP187
## Low -0.03298749 -0.06484156 0.2620897 0.1478417 -0.02441762 0.009194087
## High 0.02688103 0.05283845 -0.2135731 -0.1204740 0.01989757 -0.007492128
## FP188 FP189 FP190 FP191 FP192 FP193
## Low -0.07592293 0.08109314 0.2167300 -0.01905305 0.08761784 0.2572220
## High 0.06186849 -0.06608162 -0.1766101 0.01552606 -0.07139851 -0.2096065
## FP194 FP195 FP196 FP197 FP198 FP201
## Low -0.02131844 -0.1471268 0.2099093 0.1945447 -0.08340218 -0.06764568
## High 0.01737209 0.1198915 -0.1710521 -0.1585317 0.06796323 0.05512348
## FP202 FP203 FP204 FP205 FP206 FP207
## Low 0.1551880 0.007780434 0.10033971 0.1640452 0.10262214 0.2099093
## High -0.1264604 -0.006340163 -0.08176537 -0.1336781 -0.08362529 -0.1710521
## FP208 MolWeight NumBonds NumMultBonds NumRotBonds NumDblBonds
## Low 0.01449529 0.6447051 0.5260887 0.4454402 0.2155584 0.07217700
## High -0.01181200 -0.5253608 -0.4287020 -0.3629828 -0.1756554 -0.05881599
## NumCarbon NumNitrogen NumOxygen NumSulfer NumChlorine NumHalogen
## Low 0.6263249 -0.02976857 -0.03406840 0.11971764 0.3118792 0.3385013
## High -0.5103830 0.02425798 0.02776184 -0.09755617 -0.2541458 -0.2758398
## NumRings HydrophilicFactor SurfaceArea1 SurfaceArea2
## Low 0.4841073 -0.2459915 -0.09225436 -0.04168274
## High -0.3944921 0.2004549 0.07517674 0.03396666
##
## Coefficients of linear discriminants:
## LD1
## FP001 0.012875326
## FP002 -0.248225553
## FP003 -0.187395370
## FP004 -0.433046298
## FP005 -0.362154129
## FP006 -0.020171530
## FP007 0.023306160
## FP008 -0.032081948
## FP009 -0.717769114
## FP010 0.110779863
## FP011 0.258826748
## FP012 0.209427218
## FP013 0.019882720
## FP014 -0.057333713
## FP015 -0.080915412
## FP016 -0.130667605
## FP017 -0.227574267
## FP018 -0.255928604
## FP019 -0.181709412
## FP020 -0.215412670
## FP021 0.501216467
## FP022 -0.357311775
## FP023 -0.052913180
## FP024 0.035967510
## FP025 0.177343692
## FP026 -0.323519114
## FP027 -0.007178850
## FP028 -0.032975063
## FP029 0.145296265
## FP030 -0.161155803
## FP031 0.046337595
## FP032 -0.743681838
## FP033 0.311424434
## FP034 0.094788437
## FP035 -0.202694496
## FP036 -0.032828299
## FP037 0.260679548
## FP038 -0.128056904
## FP039 0.089605500
## FP040 0.071442073
## FP041 -0.067564396
## FP042 0.930984536
## FP043 -0.169567237
## FP044 0.243967686
## FP045 0.080382127
## FP046 0.030736083
## FP047 -0.057942188
## FP048 0.008206059
## FP049 -0.037741091
## FP050 -0.147981935
## FP051 0.134845376
## FP052 0.176151364
## FP053 0.231774338
## FP054 -0.070601965
## FP055 0.014143815
## FP056 -0.095182501
## FP057 -0.007420043
## FP058 0.535139988
## FP059 -0.014252609
## FP060 -0.065950196
## FP061 -0.122312068
## FP062 0.393612442
## FP063 0.930813438
## FP064 0.065441624
## FP065 0.186805195
## FP066 0.167958525
## FP067 -0.212616346
## FP068 -0.519887504
## FP069 0.090686177
## FP070 0.200155899
## FP071 0.088134834
## FP072 0.908780645
## FP073 -0.250802725
## FP074 -0.082227983
## FP075 0.057002521
## FP076 0.013837596
## FP077 0.094264936
## FP078 -0.242277204
## FP079 -0.023865803
## FP080 0.439565858
## FP081 -0.077157657
## FP082 0.091106844
## FP083 -0.064042942
## FP084 -0.176819154
## FP085 -0.268673937
## FP086 0.030390219
## FP087 -0.194957587
## FP088 0.163794423
## FP089 -0.282944026
## FP090 0.009357220
## FP091 0.285834751
## FP092 0.459990457
## FP093 0.104850491
## FP094 -0.073168130
## FP095 -0.319889448
## FP096 0.066474232
## FP097 -0.136110771
## FP098 0.147457368
## FP099 0.211568568
## FP100 -0.076438380
## FP101 0.077177684
## FP102 -0.338795554
## FP103 0.006792125
## FP104 -0.386425756
## FP105 -0.069381157
## FP106 -0.058498907
## FP107 -0.230462820
## FP108 -0.094827896
## FP109 0.299118672
## FP110 -0.372150175
## FP111 -0.098659228
## FP112 -0.283228997
## FP113 0.093992519
## FP114 -0.140293999
## FP115 -0.049811746
## FP116 0.425814720
## FP117 -0.003831833
## FP118 -0.128014629
## FP119 0.484681499
## FP120 -0.328296417
## FP121 0.131825432
## FP122 0.193654715
## FP123 -0.192192593
## FP124 -0.084615248
## FP125 0.077673681
## FP126 -0.290792002
## FP127 0.058235282
## FP128 0.316749603
## FP129 0.376783202
## FP130 0.248127770
## FP131 0.282887048
## FP132 0.082237362
## FP133 0.077683007
## FP134 0.113216796
## FP135 -0.051285300
## FP136 -0.326880813
## FP137 0.145941700
## FP138 -0.178259305
## FP139 -0.320335708
## FP140 0.445465221
## FP141 -0.395738194
## FP142 -0.041396998
## FP143 0.224994152
## FP144 0.070763526
## FP145 -0.029325224
## FP146 -0.141322324
## FP147 0.107304633
## FP148 -0.056022933
## FP149 0.052097963
## FP150 0.087748229
## FP151 -0.015973030
## FP152 0.017502434
## FP153 0.049739096
## FP155 0.136703365
## FP156 -0.333916842
## FP157 -0.295929021
## FP158 -0.049526714
## FP159 0.333650313
## FP160 0.198974937
## FP161 -0.005771305
## FP162 0.065758353
## FP163 -0.274695492
## FP164 0.518357241
## FP165 0.159032681
## FP166 0.038381456
## FP167 -0.329079325
## FP168 -0.047259271
## FP169 -0.088937588
## FP170 0.163658892
## FP171 0.216749476
## FP172 0.009570624
## FP173 -0.085144281
## FP174 -0.031642714
## FP175 0.047375613
## FP176 -0.087959080
## FP177 0.229511308
## FP178 0.042694344
## FP179 0.290071401
## FP180 0.152923230
## FP181 -0.192565242
## FP182 -0.176167992
## FP183 0.412115851
## FP184 0.199266994
## FP185 0.167423298
## FP186 0.070957356
## FP187 -0.391419133
## FP188 -0.016694210
## FP189 -0.100533547
## FP190 -0.063175723
## FP191 0.038411139
## FP192 0.131234896
## FP193 0.014403687
## FP194 -0.627900664
## FP195 0.084256288
## FP196 -0.217704936
## FP197 -0.301977667
## FP198 0.056480096
## FP201 -0.009941918
## FP202 0.165033685
## FP203 -0.135845702
## FP204 -0.099068181
## FP205 0.005210160
## FP206 -0.001473758
## FP207 0.052079412
## FP208 -0.364736773
## MolWeight -0.879499894
## NumBonds -1.047867086
## NumMultBonds -0.325380591
## NumRotBonds -0.336768637
## NumDblBonds -0.182263696
## NumCarbon 0.625278394
## NumNitrogen 0.675860288
## NumOxygen 1.146841627
## NumSulfer 0.581387772
## NumChlorine -0.024337219
## NumHalogen 0.145791905
## NumRings -0.144261011
## HydrophilicFactor -0.100865167
## SurfaceArea1 0.980164468
## SurfaceArea2 -1.522398889LDA_Tune$results## parameter ROC Sens Spec ROCSD SensSD SpecSD
## 1 none 0.9096763 0.817165 0.8416909 0.02903576 0.06810246 0.05240927(LDA_Train_ROCCurveAUC <- LDA_Tune$results$ROC)## [1] 0.9096763##################################
# Identifying and plotting the
# best model predictors
##################################
# model does not support variable importance measurement
##################################
# Independently evaluating the model
# on the test set
##################################
LDA_Test <- data.frame(LDA_Observed = PMA_PreModelling_Test_LDA$Log_Solubility_Class,
LDA_Predicted = predict(LDA_Tune,
PMA_PreModelling_Test_LDA[,!names(PMA_PreModelling_Test_LDA) %in% c("Log_Solubility_Class")],
type = "prob"))
LDA_Test## LDA_Observed LDA_Predicted.Low LDA_Predicted.High
## 1 High 6.101853e-06 9.999939e-01
## 2 High 5.801348e-04 9.994199e-01
## 3 High 8.333462e-04 9.991667e-01
## 4 High 1.274634e-02 9.872537e-01
## 5 High 2.342759e-03 9.976572e-01
## 6 High 9.489361e-07 9.999991e-01
## 7 High 2.843413e-05 9.999716e-01
## 8 High 2.055907e-05 9.999794e-01
## 9 High 9.993396e-06 9.999900e-01
## 10 High 2.407199e-02 9.759280e-01
## 11 High 3.553017e-02 9.644698e-01
## 12 High 2.005432e-02 9.799457e-01
## 13 High 5.819250e-05 9.999418e-01
## 14 High 6.854088e-05 9.999315e-01
## 15 High 1.557334e-02 9.844267e-01
## 16 High 2.624025e-04 9.997376e-01
## 17 High 6.220519e-06 9.999938e-01
## 18 High 2.021402e-05 9.999798e-01
## 19 High 6.765133e-02 9.323487e-01
## 20 High 1.128928e-03 9.988711e-01
## 21 High 1.864596e-04 9.998135e-01
## 22 High 1.529233e-05 9.999847e-01
## 23 High 6.770491e-04 9.993230e-01
## 24 High 3.604555e-03 9.963954e-01
## 25 High 1.535838e-03 9.984642e-01
## 26 High 1.035444e-03 9.989646e-01
## 27 High 3.685756e-04 9.996314e-01
## 28 High 2.446010e-07 9.999998e-01
## 29 High 2.138715e-01 7.861285e-01
## 30 High 4.879130e-02 9.512087e-01
## 31 High 9.314797e-04 9.990685e-01
## 32 High 3.083479e-04 9.996917e-01
## 33 High 1.931832e-04 9.998068e-01
## 34 High 9.522193e-06 9.999905e-01
## 35 High 8.879957e-06 9.999911e-01
## 36 High 4.334430e-02 9.566557e-01
## 37 High 1.929392e-05 9.999807e-01
## 38 High 4.094468e-04 9.995906e-01
## 39 High 2.575069e-04 9.997425e-01
## 40 High 2.006488e-03 9.979935e-01
## 41 High 4.442402e-04 9.995558e-01
## 42 High 1.555145e-01 8.444855e-01
## 43 High 3.391193e-03 9.966088e-01
## 44 High 4.363344e-04 9.995637e-01
## 45 High 4.146480e-04 9.995854e-01
## 46 High 1.935511e-03 9.980645e-01
## 47 High 8.212070e-03 9.917879e-01
## 48 High 1.611458e-03 9.983885e-01
## 49 High 1.929248e-03 9.980708e-01
## 50 High 5.943037e-04 9.994057e-01
## 51 High 9.963823e-01 3.617746e-03
## 52 High 5.850619e-04 9.994149e-01
## 53 High 4.364703e-03 9.956353e-01
## 54 High 1.270009e-02 9.872999e-01
## 55 High 3.224993e-02 9.677501e-01
## 56 High 7.489621e-02 9.251038e-01
## 57 High 8.807745e-03 9.911923e-01
## 58 High 2.252293e-03 9.977477e-01
## 59 High 9.138841e-03 9.908612e-01
## 60 High 2.602806e-01 7.397194e-01
## 61 High 2.115881e-05 9.999788e-01
## 62 High 2.325644e-03 9.976744e-01
## 63 High 8.351655e-04 9.991648e-01
## 64 High 3.301942e-04 9.996698e-01
## 65 High 5.307614e-03 9.946924e-01
## 66 High 2.388042e-03 9.976120e-01
## 67 High 9.615860e-01 3.841395e-02
## 68 High 2.402377e-01 7.597623e-01
## 69 High 2.867821e-01 7.132179e-01
## 70 High 2.487167e-02 9.751283e-01
## 71 High 1.001441e-03 9.989986e-01
## 72 High 5.553754e-02 9.444625e-01
## 73 High 3.565931e-02 9.643407e-01
## 74 High 3.939077e-01 6.060923e-01
## 75 High 2.345573e-02 9.765443e-01
## 76 High 3.751948e-01 6.248052e-01
## 77 High 4.575808e-01 5.424192e-01
## 78 High 2.276101e-02 9.772390e-01
## 79 High 7.403096e-03 9.925969e-01
## 80 High 9.682064e-02 9.031794e-01
## 81 High 1.108423e-03 9.988916e-01
## 82 High 5.691326e-01 4.308674e-01
## 83 High 6.199096e-01 3.800904e-01
## 84 High 4.581526e-02 9.541847e-01
## 85 High 1.245892e-01 8.754108e-01
## 86 High 5.959941e-03 9.940401e-01
## 87 High 9.864226e-01 1.357740e-02
## 88 High 1.726463e-01 8.273537e-01
## 89 High 4.407236e-01 5.592764e-01
## 90 High 2.761076e-02 9.723892e-01
## 91 High 2.677744e-02 9.732226e-01
## 92 High 1.071287e-01 8.928713e-01
## 93 High 1.705059e-01 8.294941e-01
## 94 High 2.482345e-02 9.751766e-01
## 95 High 8.511602e-05 9.999149e-01
## 96 High 9.118778e-02 9.088122e-01
## 97 High 1.391049e-01 8.608951e-01
## 98 High 9.973670e-01 2.632968e-03
## 99 High 6.721581e-02 9.327842e-01
## 100 High 3.625039e-02 9.637496e-01
## 101 High 2.277153e-01 7.722847e-01
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## 217 High 1.858673e-03 9.981413e-01
## 218 High 1.076282e-04 9.998924e-01
## 219 High 6.564478e-02 9.343552e-01
## 220 High 4.736164e-05 9.999526e-01
## 221 High 4.085723e-04 9.995914e-01
## 222 High 3.018304e-04 9.996982e-01
## 223 High 7.478741e-04 9.992521e-01
## 224 High 2.669598e-04 9.997330e-01
## 225 High 9.323018e-01 6.769815e-02
## 226 High 4.174843e-03 9.958252e-01
## 227 High 1.457604e-03 9.985424e-01
## 228 High 9.260600e-04 9.990739e-01
## 229 High 2.989736e-04 9.997010e-01
## 230 High 1.228192e-04 9.998772e-01
## 231 High 3.120396e-02 9.687960e-01
## 232 High 1.124519e-02 9.887548e-01
## 233 High 1.594777e-03 9.984052e-01
## 234 High 2.933700e-04 9.997066e-01
## 235 High 8.034844e-02 9.196516e-01
## 236 High 1.543943e-03 9.984561e-01
## 237 High 8.995170e-01 1.004830e-01
## 238 High 1.399792e-02 9.860021e-01
## 239 High 4.364703e-03 9.956353e-01
## 240 High 1.467963e-03 9.985320e-01
## 241 High 4.529777e-04 9.995470e-01
## 242 High 4.518727e-01 5.481273e-01
## 243 High 1.543381e-02 9.845662e-01
## 244 High 9.528498e-01 4.715025e-02
## 245 High 9.421706e-02 9.057829e-01
## 246 High 1.036434e-04 9.998964e-01
## 247 High 1.832249e-03 9.981678e-01
## 248 High 3.351149e-03 9.966489e-01
## 249 High 6.478475e-03 9.935215e-01
## 250 High 1.257219e-01 8.742781e-01
## 251 High 6.252382e-03 9.937476e-01
## 252 High 2.190669e-02 9.780933e-01
## 253 High 2.724629e-01 7.275371e-01
## 254 High 7.200249e-01 2.799751e-01
## 255 High 6.241526e-01 3.758474e-01
## 256 High 2.442795e-02 9.755721e-01
## 257 High 2.769711e-05 9.999723e-01
## 258 High 4.861685e-02 9.513831e-01
## 259 High 9.940406e-01 5.959380e-03
## 260 High 5.298627e-03 9.947014e-01
## 261 High 1.096083e-01 8.903917e-01
## 262 High 1.955142e-03 9.980449e-01
## 263 High 1.019986e-01 8.980014e-01
## 264 High 4.602847e-01 5.397153e-01
## 265 High 8.446951e-01 1.553049e-01
## 266 High 5.435098e-05 9.999456e-01
## 267 High 9.187425e-02 9.081257e-01
## 268 High 2.927730e-03 9.970723e-01
## 269 Low 4.564682e-01 5.435318e-01
## 270 Low 8.441996e-01 1.558004e-01
## 271 Low 7.399371e-01 2.600629e-01
## 272 Low 9.671848e-01 3.281523e-02
## 273 Low 9.948918e-01 5.108168e-03
## 274 Low 9.856775e-01 1.432246e-02
## 275 Low 1.122599e-01 8.877401e-01
## 276 Low 9.855100e-01 1.449000e-02
## 277 Low 9.816237e-01 1.837628e-02
## 278 Low 4.574519e-01 5.425481e-01
## 279 Low 9.994376e-01 5.624466e-04
## 280 Low 7.320493e-01 2.679507e-01
## 281 Low 5.528278e-01 4.471722e-01
## 282 Low 9.976586e-01 2.341403e-03
## 283 Low 9.753766e-01 2.462343e-02
## 284 Low 9.945286e-01 5.471402e-03
## 285 Low 9.898977e-01 1.010230e-02
## 286 Low 3.919536e-01 6.080464e-01
## 287 Low 9.062465e-01 9.375346e-02
## 288 Low 1.543449e-03 9.984566e-01
## 289 Low 9.963301e-01 3.669899e-03
## 290 Low 9.982430e-01 1.756953e-03
## 291 Low 9.719170e-01 2.808300e-02
## 292 Low 9.950976e-01 4.902382e-03
## 293 Low 8.423258e-01 1.576742e-01
## 294 Low 9.977819e-01 2.218137e-03
## 295 Low 9.986966e-01 1.303430e-03
## 296 Low 2.435234e-01 7.564766e-01
## 297 Low 9.993080e-01 6.919813e-04
## 298 Low 9.982025e-01 1.797495e-03
## 299 Low 9.993432e-01 6.568128e-04
## 300 Low 9.984324e-01 1.567643e-03
## 301 Low 9.999403e-01 5.966629e-05
## 302 Low 9.990657e-01 9.342658e-04
## 303 Low 9.971222e-01 2.877827e-03
## 304 Low 9.968341e-01 3.165885e-03
## 305 Low 9.999922e-01 7.806887e-06
## 306 Low 9.983887e-01 1.611304e-03
## 307 Low 9.996808e-01 3.192036e-04
## 308 Low 9.999521e-01 4.787311e-05
## 309 Low 9.999946e-01 5.401102e-06
## 310 Low 9.999974e-01 2.565390e-06
## 311 Low 9.999764e-01 2.356976e-05
## 312 Low 9.989466e-01 1.053401e-03
## 313 High 4.702359e-03 9.952976e-01
## 314 High 6.414674e-02 9.358533e-01
## 315 Low 8.828822e-01 1.171178e-01
## 316 High 9.992564e-01 7.435747e-04##################################
# Reporting the independent evaluation results
# for the test set
##################################
LDA_Test_ROC <- roc(response = LDA_Test$LDA_Observed,
predictor = LDA_Test$LDA_Predicted.High,
levels = rev(levels(LDA_Test$LDA_Observed)))
(LDA_Test_ROCCurveAUC <- auc(LDA_Test_ROC)[1])## [1] 0.92137921.5.3 Flexible Discriminant Analysis (FDA)
[A] The flexible discriminant analysis model from the earth and mda packages was implemented through the caret package.
[B] The model contains 2 hyperparameters:
[B.1] degree = product degree held constant at a value of 1
[B.2] nprune = number of terms made to vary across a range of values equal to 2 to 25
[C] The cross-validated model performance of the final model is summarized as follows:
[C.1] Final model configuration involves degree=1 and nprune=24
[C.2] ROC Curve AUC = 0.94949
[D] The model allows for ranking of predictors in terms of variable importance. The top-performing predictors in the model are as follows:
[D.1] MolWeight variable (numeric)
[D.2] HydrophilicFactor variable (numeric)
[D.3] NumOxygen variable (numeric)
[D.4] FP070 (Structure=1) variable (factor)
[D.5] FP075 (Structure=1) variable (factor)
[E] The independent test model performance of the final model is summarized as follows:
[E.1] ROC Curve AUC = 0.95933
##################################
# Creating a local object
# for the train and test sets
##################################
PMA_PreModelling_Train_FDA <- PMA_PreModelling_Train
PMA_PreModelling_Test_FDA <- PMA_PreModelling_Test
##################################
# Creating consistent fold assignments
# for the 10-Fold Cross Validation process
##################################
set.seed(12345678)
KFold_Indices <- createFolds(PMA_PreModelling_Train_FDA$Log_Solubility_Class,
k = 10,
returnTrain=TRUE)
KFold_Control <- trainControl(method="cv",
index=KFold_Indices,
summaryFunction = twoClassSummary,
classProbs = TRUE)
##################################
# Setting the conditions
# for hyperparameter tuning
##################################
FDA_Grid = expand.grid(degree = 1, nprune = 2:25)
##################################
# Running the flexible discriminant analysis model
# by setting the caret method to 'fda'
##################################
set.seed(12345678)
FDA_Tune <- train(x = PMA_PreModelling_Train_FDA[,!names(PMA_PreModelling_Train_FDA) %in% c("Log_Solubility_Class")],
y = PMA_PreModelling_Train_FDA$Log_Solubility_Class,
method = "fda",
tuneGrid = FDA_Grid,
metric = "ROC",
trControl = KFold_Control)
##################################
# Reporting the cross-validation results
# for the train set
##################################
FDA_Tune## Flexible Discriminant Analysis
##
## 951 samples
## 220 predictors
## 2 classes: 'Low', 'High'
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 857, 855, 857, 855, 856, 856, ...
## Resampling results across tuning parameters:
##
## nprune ROC Sens Spec
## 2 0.8419414 0.7117386 0.8341074
## 3 0.9106928 0.8057032 0.8627721
## 4 0.9227555 0.8053710 0.8742380
## 5 0.9269196 0.8243079 0.8720972
## 6 0.9326890 0.8291251 0.8855225
## 7 0.9353226 0.8384275 0.8835994
## 8 0.9377446 0.8360465 0.8644775
## 9 0.9412788 0.8501107 0.8760160
## 10 0.9412875 0.8429679 0.8722424
## 11 0.9424124 0.8451827 0.8703193
## 12 0.9433294 0.8452935 0.8760885
## 13 0.9420364 0.8570321 0.8797170
## 14 0.9424613 0.8430233 0.8739840
## 15 0.9419380 0.8524363 0.8683237
## 16 0.9420235 0.8500000 0.8664369
## 17 0.9423609 0.8523810 0.8664369
## 18 0.9457102 0.8475083 0.8779390
## 19 0.9482061 0.8522148 0.8855951
## 20 0.9476880 0.8474529 0.8931785
## 21 0.9492896 0.8591916 0.8798621
## 22 0.9494056 0.8591916 0.8817489
## 23 0.9488624 0.8568106 0.8760522
## 24 0.9494893 0.8497785 0.8779390
## 25 0.9477070 0.8616833 0.8893324
##
## Tuning parameter 'degree' was held constant at a value of 1
## ROC was used to select the optimal model using the largest value.
## The final values used for the model were degree = 1 and nprune = 24.FDA_Tune$finalModel## Call:
## mda::fda(formula = .outcome ~ ., data = dat, weights = wts, method = earth::earth,
## degree = param$degree, nprune = param$nprune)
##
## Dimension: 1
##
## Percent Between-Group Variance Explained:
## v1
## 100
##
## Training Misclassification Error: 0.08623 ( N = 951 )FDA_Tune$results## degree nprune ROC Sens Spec ROCSD SensSD SpecSD
## 1 1 2 0.8419414 0.7117386 0.8341074 0.03896762 0.09489524 0.06239354
## 2 1 3 0.9106928 0.8057032 0.8627721 0.02242246 0.07519247 0.06804707
## 3 1 4 0.9227555 0.8053710 0.8742380 0.02195624 0.06249717 0.05802672
## 4 1 5 0.9269196 0.8243079 0.8720972 0.01802883 0.04334609 0.05514159
## 5 1 6 0.9326890 0.8291251 0.8855225 0.01780746 0.03617307 0.04943403
## 6 1 7 0.9353226 0.8384275 0.8835994 0.01303631 0.04171346 0.04724288
## 7 1 8 0.9377446 0.8360465 0.8644775 0.01248855 0.05823961 0.05536583
## 8 1 9 0.9412788 0.8501107 0.8760160 0.01455529 0.03670488 0.05254503
## 9 1 10 0.9412875 0.8429679 0.8722424 0.01545052 0.05450548 0.04888567
## 10 1 11 0.9424124 0.8451827 0.8703193 0.01618394 0.05283938 0.05936728
## 11 1 12 0.9433294 0.8452935 0.8760885 0.01751110 0.05677991 0.05600524
## 12 1 13 0.9420364 0.8570321 0.8797170 0.02077095 0.06745409 0.05434716
## 13 1 14 0.9424613 0.8430233 0.8739840 0.02012156 0.07140365 0.05302971
## 14 1 15 0.9419380 0.8524363 0.8683237 0.01729176 0.06118946 0.05069259
## 15 1 16 0.9420235 0.8500000 0.8664369 0.01659259 0.07343215 0.05493565
## 16 1 17 0.9423609 0.8523810 0.8664369 0.01745948 0.05510654 0.05105891
## 17 1 18 0.9457102 0.8475083 0.8779390 0.01604604 0.05923356 0.06134573
## 18 1 19 0.9482061 0.8522148 0.8855951 0.01423424 0.05130079 0.05982429
## 19 1 20 0.9476880 0.8474529 0.8931785 0.01548466 0.05944141 0.05733283
## 20 1 21 0.9492896 0.8591916 0.8798621 0.01736480 0.05482756 0.05841022
## 21 1 22 0.9494056 0.8591916 0.8817489 0.01727343 0.05692662 0.05320937
## 22 1 23 0.9488624 0.8568106 0.8760522 0.01612087 0.05671808 0.05342934
## 23 1 24 0.9494893 0.8497785 0.8779390 0.01369371 0.05853053 0.04782343
## 24 1 25 0.9477070 0.8616833 0.8893324 0.01488523 0.05605751 0.04936318(FDA_Train_ROCCurveAUC <- FDA_Tune$results[FDA_Tune$results$degree==FDA_Tune$bestTune$degree &
FDA_Tune$results$nprune==FDA_Tune$bestTune$nprune,
c("ROC")])## [1] 0.9494893##################################
# Identifying and plotting the
# best model predictors
##################################
FDA_VarImp <- varImp(FDA_Tune, scale = TRUE)
plot(FDA_VarImp,
top=25,
scales=list(y=list(cex = .95)),
main="Ranked Variable Importance : Flexible Discriminant Analysis",
xlab="Scaled Variable Importance Metrics",
ylab="Predictors",
cex=2,
origin=0,
alpha=0.45)
##################################
# Independently evaluating the model
# on the test set
##################################
FDA_Test <- data.frame(FDA_Observed = PMA_PreModelling_Test_FDA$Log_Solubility_Class,
FDA_Predicted = predict(FDA_Tune,
PMA_PreModelling_Test_FDA[,!names(PMA_PreModelling_Test_FDA) %in% c("Log_Solubility_Class")],
type = "prob"))
FDA_Test## FDA_Observed FDA_Predicted.Low FDA_Predicted.High
## 1 High 3.690766e-04 9.996309e-01
## 2 High 7.423450e-04 9.992577e-01
## 3 High 1.699865e-03 9.983001e-01
## 4 High 1.452439e-02 9.854756e-01
## 5 High 4.908517e-03 9.950915e-01
## 6 High 5.230972e-04 9.994769e-01
## 7 High 2.320216e-03 9.976798e-01
## 8 High 1.311373e-04 9.998689e-01
## 9 High 4.142991e-03 9.958570e-01
## 10 High 2.556431e-02 9.744357e-01
## 11 High 2.556431e-02 9.744357e-01
## 12 High 9.277825e-02 9.072217e-01
## 13 High 2.599678e-03 9.974003e-01
## 14 High 5.670742e-03 9.943293e-01
## 15 High 9.824829e-03 9.901752e-01
## 16 High 1.921582e-03 9.980784e-01
## 17 High 4.593616e-04 9.995406e-01
## 18 High 4.142991e-03 9.958570e-01
## 19 High 5.262656e-03 9.947373e-01
## 20 High 1.432298e-02 9.856770e-01
## 21 High 4.023503e-04 9.995976e-01
## 22 High 6.763996e-04 9.993236e-01
## 23 High 3.336696e-03 9.966633e-01
## 24 High 7.349325e-04 9.992651e-01
## 25 High 3.254626e-03 9.967454e-01
## 26 High 7.349325e-04 9.992651e-01
## 27 High 4.669673e-04 9.995330e-01
## 28 High 1.870383e-03 9.981296e-01
## 29 High 1.193320e-01 8.806680e-01
## 30 High 2.834895e-03 9.971651e-01
## 31 High 7.976461e-01 2.023539e-01
## 32 High 4.081256e-03 9.959187e-01
## 33 High 4.081256e-03 9.959187e-01
## 34 High 3.809269e-04 9.996191e-01
## 35 High 3.809269e-04 9.996191e-01
## 36 High 8.172885e-03 9.918271e-01
## 37 High 1.014634e-03 9.989854e-01
## 38 High 4.081256e-03 9.959187e-01
## 39 High 7.245229e-04 9.992755e-01
## 40 High 9.893476e-03 9.901065e-01
## 41 High 4.142991e-03 9.958570e-01
## 42 High 3.427320e-01 6.572680e-01
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## 219 High 1.958320e-04 9.998042e-01
## 220 High 8.363020e-03 9.916370e-01
## 221 High 6.566203e-04 9.993434e-01
## 222 High 1.540351e-03 9.984596e-01
## 223 High 1.475592e-02 9.852441e-01
## 224 High 5.670742e-03 9.943293e-01
## 225 High 7.096778e-01 2.903222e-01
## 226 High 2.135624e-03 9.978644e-01
## 227 High 9.048039e-04 9.990952e-01
## 228 High 5.473683e-03 9.945263e-01
## 229 High 1.287000e-03 9.987130e-01
## 230 High 3.266078e-02 9.673392e-01
## 231 High 1.850478e-01 8.149522e-01
## 232 High 2.381172e-03 9.976188e-01
## 233 High 1.879250e-03 9.981208e-01
## 234 High 1.457875e-03 9.985421e-01
## 235 High 2.743915e-03 9.972561e-01
## 236 High 2.501833e-03 9.974982e-01
## 237 High 9.847491e-01 1.525093e-02
## 238 High 1.978247e-02 9.802175e-01
## 239 High 2.501833e-03 9.974982e-01
## 240 High 3.554147e-03 9.964459e-01
## 241 High 5.571878e-03 9.944281e-01
## 242 High 3.214995e-02 9.678501e-01
## 243 High 8.130724e-03 9.918693e-01
## 244 High 6.582718e-03 9.934173e-01
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## 246 High 1.998389e-04 9.998002e-01
## 247 High 4.367589e-03 9.956324e-01
## 248 High 2.727005e-03 9.972730e-01
## 249 High 7.010362e-02 9.298964e-01
## 250 High 1.609613e-01 8.390387e-01
## 251 High 6.746265e-01 3.253735e-01
## 252 High 7.872232e-03 9.921278e-01
## 253 High 3.121653e-01 6.878347e-01
## 254 High 5.845846e-01 4.154154e-01
## 255 High 2.665529e-01 7.334471e-01
## 256 High 5.787852e-04 9.994212e-01
## 257 High 2.648977e-02 9.735102e-01
## 258 High 3.150072e-01 6.849928e-01
## 259 High 3.336151e-01 6.663849e-01
## 260 High 6.803261e-03 9.931967e-01
## 261 High 1.095579e-01 8.904421e-01
## 262 High 1.706943e-01 8.293057e-01
## 263 High 4.729980e-02 9.527002e-01
## 264 High 6.225764e-02 9.377424e-01
## 265 High 4.459511e-01 5.540489e-01
## 266 High 3.348277e-01 6.651723e-01
## 267 High 9.334114e-02 9.066589e-01
## 268 High 9.489563e-01 5.104370e-02
## 269 Low 9.922257e-01 7.774338e-03
## 270 Low 8.731715e-01 1.268285e-01
## 271 Low 9.883396e-01 1.166037e-02
## 272 Low 6.468122e-01 3.531878e-01
## 273 Low 9.984132e-01 1.586838e-03
## 274 Low 9.988656e-01 1.134392e-03
## 275 Low 1.252445e-01 8.747555e-01
## 276 Low 9.418795e-01 5.812049e-02
## 277 Low 9.956807e-01 4.319262e-03
## 278 Low 2.847007e-01 7.152993e-01
## 279 Low 9.932363e-01 6.763709e-03
## 280 Low 9.994836e-01 5.163749e-04
## 281 Low 9.732999e-01 2.670008e-02
## 282 Low 9.889232e-01 1.107676e-02
## 283 Low 9.941472e-01 5.852827e-03
## 284 Low 9.954809e-01 4.519077e-03
## 285 Low 9.801197e-01 1.988031e-02
## 286 Low 6.355589e-01 3.644411e-01
## 287 Low 9.903434e-01 9.656559e-03
## 288 Low 8.261194e-01 1.738806e-01
## 289 Low 9.946350e-01 5.364997e-03
## 290 Low 9.998786e-01 1.214263e-04
## 291 Low 9.950626e-01 4.937433e-03
## 292 Low 8.690051e-01 1.309949e-01
## 293 Low 9.972415e-01 2.758533e-03
## 294 Low 9.984568e-01 1.543181e-03
## 295 Low 9.982758e-01 1.724221e-03
## 296 Low 2.870159e-01 7.129841e-01
## 297 Low 9.852478e-01 1.475222e-02
## 298 Low 9.991623e-01 8.377175e-04
## 299 Low 9.998786e-01 1.214263e-04
## 300 Low 9.999956e-01 4.418394e-06
## 301 Low 9.905874e-01 9.412579e-03
## 302 Low 9.953501e-01 4.649855e-03
## 303 Low 9.953203e-01 4.679661e-03
## 304 Low 8.241165e-01 1.758835e-01
## 305 Low 9.977351e-01 2.264928e-03
## 306 Low 9.985056e-01 1.494411e-03
## 307 Low 9.990729e-01 9.270714e-04
## 308 Low 9.995931e-01 4.068867e-04
## 309 Low 9.999975e-01 2.470773e-06
## 310 Low 9.999946e-01 5.393850e-06
## 311 Low 9.997960e-01 2.039678e-04
## 312 Low 9.990729e-01 9.270714e-04
## 313 High 3.025030e-02 9.697497e-01
## 314 High 4.288205e-01 5.711795e-01
## 315 Low 9.615043e-01 3.849566e-02
## 316 High 9.936174e-01 6.382574e-03##################################
# Reporting the independent evaluation results
# for the test set
##################################
FDA_Test_ROC <- roc(response = FDA_Test$FDA_Observed,
predictor = FDA_Test$FDA_Predicted.High,
levels = rev(levels(FDA_Test$FDA_Observed)))
(FDA_Test_ROCCurveAUC <- auc(FDA_Test_ROC)[1])## [1] 0.95933551.5.4 Mixture Discriminant Analysis (MDA)
[A] The mixture discriminant analysis model from the mda package was implemented through the caret package.
[B] The model contains 1 hyperparameter:
[B.1] subclasses = number of subclasses per class made to vary across a range of values equal to 1 to 8
[C] The cross-validated model performance of the final model is summarized as follows:
[C.1] Final model configuration involves subclasses=1
[C.2] ROC Curve AUC = 0.90659
[D] The model does not allow for ranking of predictors in terms of variable importance.
[E] The independent test model performance of the final model is summarized as follows:
[E.1] ROC Curve AUC = 0.92138
##################################
# Creating a local object
# for the train and test sets
##################################
PMA_PreModelling_Train_MDA <- PMA_PreModelling_Train
PMA_PreModelling_Test_MDA <- PMA_PreModelling_Test
##################################
# Creating consistent fold assignments
# for the 10-Fold Cross Validation process
##################################
set.seed(12345678)
KFold_Indices <- createFolds(PMA_PreModelling_Train_MDA$Log_Solubility_Class,
k = 10,
returnTrain=TRUE)
KFold_Control <- trainControl(method="cv",
index=KFold_Indices,
summaryFunction = twoClassSummary,
classProbs = TRUE)
##################################
# Setting the conditions
# for hyperparameter tuning
##################################
MDA_Grid = expand.grid(subclasses = 1:8)
##################################
# Running the mixture discriminant analysis model
# by setting the caret method to 'mda'
##################################
set.seed(12345678)
MDA_Tune <- train(x = PMA_PreModelling_Train_MDA[,!names(PMA_PreModelling_Train_MDA) %in% c("Log_Solubility_Class")],
y = PMA_PreModelling_Train_MDA$Log_Solubility_Class,
method = "mda",
tuneGrid = MDA_Grid,
tries = 40,
metric = "ROC",
trControl = KFold_Control)
##################################
# Reporting the cross-validation results
# for the train set
##################################
MDA_Tune## Mixture Discriminant Analysis
##
## 951 samples
## 220 predictors
## 2 classes: 'Low', 'High'
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 857, 855, 857, 855, 856, 856, ...
## Resampling results across tuning parameters:
##
## subclasses ROC Sens Spec
## 1 0.9065884 0.8216362 0.8381713
## 2 0.9061159 0.8009413 0.8356313
## 3 0.8990602 0.7688261 0.8595791
## 4 0.9018378 0.7868217 0.8642507
## 5 0.9053039 0.8010105 0.8642961
## 6 0.9064374 0.7924972 0.8688770
## 7 0.9054071 0.8012182 0.8618922
## 8 0.8961314 0.7866833 0.8618922
##
## ROC was used to select the optimal model using the largest value.
## The final value used for the model was subclasses = 1.MDA_Tune$finalModel## Call:
## mda::mda(formula = as.formula(".outcome ~ ."), data = dat, subclasses = param$subclasses,
## tries = 40)
##
## Dimension: 1
##
## Percent Between-Group Variance Explained:
## v1
## 100
##
## Degrees of Freedom (per dimension): 221
##
## Training Misclassification Error: 0.06309 ( N = 951 )
##
## Deviance: 274.654MDA_Tune$results## subclasses ROC Sens Spec ROCSD SensSD SpecSD
## 1 1 0.9065884 0.8216362 0.8381713 0.03141234 0.06913201 0.05860299
## 2 2 0.9061159 0.8009413 0.8356313 0.02183807 0.06191089 0.04609250
## 3 3 0.8990602 0.7688261 0.8595791 0.02739762 0.07985827 0.02857108
## 4 4 0.9018378 0.7868217 0.8642507 0.02721217 0.08855550 0.02797936
## 5 5 0.9053039 0.8010105 0.8642961 0.02369782 0.06038734 0.03748632
## 6 6 0.9064374 0.7924972 0.8688770 0.02150088 0.07067420 0.04319700
## 7 7 0.9054071 0.8012182 0.8618922 0.02223467 0.04285442 0.04280862
## 8 8 0.8961314 0.7866833 0.8618922 0.02455558 0.05138028 0.04538396(MDA_Train_ROCCurveAUC <- MDA_Tune$results[MDA_Tune$results$subclasses==MDA_Tune$bestTune$subclasses,
c("ROC")])## [1] 0.9065884##################################
# Identifying and plotting the
# best model predictors
##################################
# model does not support variable importance measurement
##################################
# Independently evaluating the model
# on the test set
##################################
MDA_Test <- data.frame(MDA_Observed = PMA_PreModelling_Test_MDA$Log_Solubility_Class,
MDA_Predicted = predict(MDA_Tune,
PMA_PreModelling_Test_MDA[,!names(PMA_PreModelling_Test_MDA) %in% c("Log_Solubility_Class")],
type = "prob"))
MDA_Test## MDA_Observed MDA_Predicted.Low MDA_Predicted.High
## 1 High 5.951955e-06 9.999940e-01
## 2 High 5.713468e-04 9.994287e-01
## 3 High 8.213523e-04 9.991786e-01
## 4 High 1.263688e-02 9.873631e-01
## 5 High 2.314122e-03 9.976859e-01
## 6 High 9.220012e-07 9.999991e-01
## 7 High 2.782574e-05 9.999722e-01
## 8 High 2.010542e-05 9.999799e-01
## 9 High 9.758039e-06 9.999902e-01
## 10 High 2.389943e-02 9.761006e-01
## 11 High 3.530722e-02 9.646928e-01
## 12 High 1.990229e-02 9.800977e-01
## 13 High 5.703342e-05 9.999430e-01
## 14 High 6.719888e-05 9.999328e-01
## 15 High 1.544650e-02 9.845535e-01
## 16 High 2.579946e-04 9.997420e-01
## 17 High 6.067952e-06 9.999939e-01
## 18 High 1.976728e-05 9.999802e-01
## 19 High 6.733053e-02 9.326695e-01
## 20 High 1.113397e-03 9.988866e-01
## 21 High 1.831952e-04 9.998168e-01
## 22 High 1.494558e-05 9.999851e-01
## 23 High 6.670111e-04 9.993330e-01
## 24 High 3.563783e-03 9.964362e-01
## 25 High 1.515700e-03 9.984843e-01
## 26 High 1.021011e-03 9.989790e-01
## 27 High 3.626444e-04 9.996374e-01
## 28 High 2.369801e-07 9.999998e-01
## 29 High 2.134831e-01 7.865169e-01
## 30 High 4.852152e-02 9.514785e-01
## 31 High 9.182902e-04 9.990817e-01
## 32 High 3.032715e-04 9.996967e-01
## 33 High 1.898153e-04 9.998102e-01
## 34 High 9.296987e-06 9.999907e-01
## 35 High 8.668665e-06 9.999913e-01
## 36 High 4.309249e-02 9.569075e-01
## 37 High 1.886567e-05 9.999811e-01
## 38 High 4.029474e-04 9.995971e-01
## 39 High 2.531711e-04 9.997468e-01
## 40 High 1.981306e-03 9.980187e-01
## 41 High 4.372638e-04 9.995627e-01
## 42 High 1.551033e-01 8.448967e-01
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## 302 Low 9.990798e-01 9.202490e-04
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## 314 High 6.383425e-02 9.361657e-01
## 315 Low 8.833661e-01 1.166339e-01
## 316 High 9.992679e-01 7.320644e-04##################################
# Reporting the independent evaluation results
# for the test set
##################################
MDA_Test_ROC <- roc(response = MDA_Test$MDA_Observed,
predictor = MDA_Test$MDA_Predicted.High,
levels = rev(levels(MDA_Test$MDA_Observed)))
(MDA_Test_ROCCurveAUC <- auc(MDA_Test_ROC)[1])## [1] 0.92137921.5.5 Naive Bayes (NB)
[A] The naive bayes model from the klaR package was implemented through the caret package.
[B] The model contains 3 hyperparameters:
[B.1] fL = laplace correction held constant at a value of 2
[B.2] adjust = bandwidth adjustment held constant at a value of FALSE
[B.3] usekernel = distribution type made to vary across a range of levels equal to TRUE and FALSE
[C] The cross-validated model performance of the final model is summarized as follows:
[C.1] Final model configuration involves fL=2, adjust=FALSE and usekernel=FALSE
[C.2] ROC Curve AUC = 0.88182
[D] The model does not allow for ranking of predictors in terms of variable importance.
[E] The independent test model performance of the final model is summarized as follows:
[E.1] ROC Curve AUC = 0.88561
##################################
# Creating a local object
# for the train and test sets
##################################
PMA_PreModelling_Train_NB <- PMA_PreModelling_Train
PMA_PreModelling_Test_NB <- PMA_PreModelling_Test
##################################
# Creating consistent fold assignments
# for the 10-Fold Cross Validation process
##################################
set.seed(12345678)
KFold_Indices <- createFolds(PMA_PreModelling_Train_NB$Log_Solubility_Class,
k = 10,
returnTrain=TRUE)
KFold_Control <- trainControl(method="cv",
index=KFold_Indices,
summaryFunction = twoClassSummary,
classProbs = TRUE)
##################################
# Setting the conditions
# for hyperparameter tuning
##################################
NB_Grid = data.frame(usekernel = c(TRUE, FALSE), fL = 2, adjust = FALSE)
##################################
# Running the naive bayes model
# by setting the caret method to 'nb'
##################################
set.seed(12345678)
NB_Tune <- train(x = PMA_PreModelling_Train_NB[,!names(PMA_PreModelling_Train_NB) %in% c("Log_Solubility_Class")],
y = PMA_PreModelling_Train_NB$Log_Solubility_Class,
method = "nb",
tuneGrid = NB_Grid,
metric = "ROC",
trControl = KFold_Control)
##################################
# Reporting the cross-validation results
# for the train set
##################################
NB_Tune## Naive Bayes
##
## 951 samples
## 220 predictors
## 2 classes: 'Low', 'High'
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 857, 855, 857, 855, 856, 856, ...
## Resampling results across tuning parameters:
##
## usekernel ROC Sens Spec
## FALSE 0.8818276 0.7772979 0.8072932
## TRUE NaN NaN NaN
##
## Tuning parameter 'fL' was held constant at a value of 2
## Tuning
## parameter 'adjust' was held constant at a value of FALSE
## ROC was used to select the optimal model using the largest value.
## The final values used for the model were fL = 2, usekernel = FALSE and adjust
## = FALSE.NB_Tune$finalModel## $apriori
## grouping
## Low High
## 0.4490011 0.5509989
##
## $tables
## $tables$FP001
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##
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##
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##
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##
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##
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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##
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## var
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## var
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## var
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## var
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##
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## var
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## var
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## var
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## var
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## var
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##
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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##
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## var
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## var
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## var
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##
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## var
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## var
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##
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## High 0.8731061 0.1268939
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## var
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## $tables$FP161
## var
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## var
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## var
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## var
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## var
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## $tables$FP166
## var
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## var
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## var
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##
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## var
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## var
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## var
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## $tables$FP172
## var
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## $tables$FP173
## var
## grouping 0 1
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## $tables$FP174
## var
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## var
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## $tables$FP176
## var
## grouping 0 1
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## $tables$FP177
## var
## grouping 0 1
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## $tables$FP178
## var
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## High 0.90909091 0.09090909
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## $tables$FP179
## var
## grouping 0 1
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## High 0.91477273 0.08522727
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## $tables$FP180
## var
## grouping 0 1
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## High 0.87500000 0.12500000
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## $tables$FP181
## var
## grouping 0 1
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## $tables$FP182
## var
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##
## $tables$FP183
## var
## grouping 0 1
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## $tables$FP184
## var
## grouping 0 1
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## var
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## $tables$FP186
## var
## grouping 0 1
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##
## $tables$FP187
## var
## grouping 0 1
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## $tables$FP188
## var
## grouping 0 1
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## High 0.91287879 0.08712121
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## $tables$FP189
## var
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## High 0.9375000 0.0625000
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## var
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## High 0.96969697 0.03030303
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## $tables$FP191
## var
## grouping 0 1
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## $tables$FP192
## var
## grouping 0 1
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## High 0.95265152 0.04734848
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## $tables$FP193
## var
## grouping 0 1
## Low 0.87238979 0.12761021
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## $tables$FP194
## var
## grouping 0 1
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## $tables$FP195
## var
## grouping 0 1
## Low 0.96983759 0.03016241
## High 0.90719697 0.09280303
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## $tables$FP196
## var
## grouping 0 1
## Low 0.89095128 0.10904872
## High 0.97916667 0.02083333
##
## $tables$FP197
## var
## grouping 0 1
## Low 0.90023202 0.09976798
## High 0.97916667 0.02083333
##
## $tables$FP198
## var
## grouping 0 1
## Low 0.95823666 0.04176334
## High 0.92424242 0.07575758
##
## $tables$FP201
## var
## grouping 0 1
## Low 0.95823666 0.04176334
## High 0.93181818 0.06818182
##
## $tables$FP202
## var
## grouping 0 1
## Low 0.6728538 0.3271462
## High 0.7954545 0.2045455
##
## $tables$FP203
## var
## grouping 0 1
## Low 0.8793503 0.1206497
## High 0.8844697 0.1155303
##
## $tables$FP204
## var
## grouping 0 1
## Low 0.86774942 0.13225058
## High 0.92234848 0.07765152
##
## $tables$FP205
## var
## grouping 0 1
## Low 0.87470998 0.12529002
## High 0.95454545 0.04545455
##
## $tables$FP206
## var
## grouping 0 1
## Low 0.91183295 0.08816705
## High 0.95643939 0.04356061
##
## $tables$FP207
## var
## grouping 0 1
## Low 0.89095128 0.10904872
## High 0.97916667 0.02083333
##
## $tables$FP208
## var
## grouping 0 1
## Low 0.8793503 0.1206497
## High 0.8882576 0.1117424
##
## $tables$MolWeight
## [,1] [,2]
## Low 0.6447051 0.8127549
## High -0.5253608 0.8139447
##
## $tables$NumBonds
## [,1] [,2]
## Low 0.5260887 0.9212852
## High -0.4287020 0.8455727
##
## $tables$NumMultBonds
## [,1] [,2]
## Low 0.4454402 1.0735331
## High -0.3629828 0.7640112
##
## $tables$NumRotBonds
## [,1] [,2]
## Low 0.2155584 1.1862560
## High -0.1756554 0.7754882
##
## $tables$NumDblBonds
## [,1] [,2]
## Low 0.07217700 1.1166156
## High -0.05881599 0.8905851
##
## $tables$NumCarbon
## [,1] [,2]
## Low 0.6263249 0.8520677
## High -0.5103830 0.8023791
##
## $tables$NumNitrogen
## [,1] [,2]
## Low -0.02976857 1.0250998
## High 0.02425798 0.9793858
##
## $tables$NumOxygen
## [,1] [,2]
## Low -0.03406840 1.0954990
## High 0.02776184 0.9149808
##
## $tables$NumSulfer
## [,1] [,2]
## Low 0.11971764 1.2230290
## High -0.09755617 0.7594935
##
## $tables$NumChlorine
## [,1] [,2]
## Low 0.3118792 1.3422891
## High -0.2541458 0.4524838
##
## $tables$NumHalogen
## [,1] [,2]
## Low 0.3385013 1.3025157
## High -0.2758398 0.5145567
##
## $tables$NumRings
## [,1] [,2]
## Low 0.4841073 1.0815485
## High -0.3944921 0.7185989
##
## $tables$HydrophilicFactor
## [,1] [,2]
## Low -0.2459915 0.7233875
## High 0.2004549 1.1404141
##
## $tables$SurfaceArea1
## [,1] [,2]
## Low -0.09225436 1.0302674
## High 0.07517674 0.9691477
##
## $tables$SurfaceArea2
## [,1] [,2]
## Low -0.04168274 1.0668148
## High 0.03396666 0.9417302
##
##
## $levels
## [1] "Low" "High"
##
## $call
## NaiveBayes.default(x = x, grouping = y, usekernel = FALSE, fL = param$fL)
##
## $x
## FP001 FP002 FP003 FP004 FP005 FP006 FP007 FP008 FP009 FP010 FP011 FP012
## X661 0 1 0 0 1 0 0 1 0 0 0 0
## X662 0 1 0 1 1 1 1 1 0 0 1 0
## X663 1 1 1 1 1 0 0 1 0 1 0 0
## X665 0 0 1 0 0 0 1 0 0 0 0 0
## X668 0 0 1 1 1 1 0 0 1 0 0 0
## X669 1 0 1 1 0 0 0 0 1 0 0 1
## X670 0 1 0 1 1 0 0 1 1 0 0 0
## X671 1 0 1 1 0 0 1 0 0 0 0 1
## X672 1 0 1 1 0 1 1 0 1 0 1 0
## X673 1 1 1 1 1 1 1 0 0 0 0 0
## X674 1 1 1 1 1 0 0 1 0 0 0 0
## X676 1 0 1 1 0 1 1 0 0 0 1 0
## X677 0 1 0 0 1 0 0 1 0 0 0 0
## X678 0 1 0 0 1 0 0 0 1 0 0 0
## X679 0 1 1 0 1 0 1 1 0 0 0 0
## X682 1 1 1 1 1 0 0 1 0 1 0 0
## X683 1 0 1 1 1 1 1 1 0 0 0 0
## X684 0 1 0 1 1 1 1 0 1 0 1 0
## X685 1 0 1 1 0 1 1 0 0 0 1 0
## X686 0 1 1 0 1 0 0 1 0 0 0 0
## X688 1 1 0 1 1 1 0 1 1 0 1 1
## X689 0 1 0 1 1 0 1 1 0 0 0 0
## X690 1 1 1 1 1 0 1 1 1 0 0 1
## X691 1 0 0 1 0 1 0 0 1 0 0 0
## X692 1 1 1 1 1 1 0 1 0 0 0 1
## X693 1 1 0 1 1 1 1 1 0 0 0 0
## X695 0 1 1 1 1 0 0 0 0 0 0 0
## X696 0 1 0 0 1 1 0 0 0 0 0 0
## X698 1 1 1 1 1 1 0 1 0 0 0 0
## X699 0 1 0 0 1 0 0 1 1 0 0 0
## X700 0 0 1 0 0 0 1 0 0 0 0 0
## X702 0 0 1 0 0 0 1 0 0 0 0 0
## X703 0 0 1 0 0 0 1 0 0 0 0 0
## X704 0 1 0 0 1 0 0 1 0 0 0 0
## X706 1 1 1 1 1 0 0 1 0 0 0 0
## X708 0 1 0 0 1 0 0 0 0 0 0 0
## X709 0 0 1 0 0 0 1 0 0 0 0 0
## X711 1 0 1 1 0 1 1 0 0 1 1 0
## X712 0 1 1 0 1 0 1 1 0 1 0 0
## X713 1 1 0 1 1 1 0 1 1 1 0 0
## X714 1 0 1 1 0 1 1 0 0 0 1 1
## X715 1 1 0 1 1 1 0 0 1 0 0 1
## X717 0 1 0 0 1 0 0 0 1 0 0 0
## X718 0 1 0 1 1 0 1 0 1 0 0 0
## X721 0 0 1 0 1 1 0 0 1 0 0 0
## X722 1 1 0 1 1 0 0 1 1 0 0 0
## X723 0 0 1 0 0 0 1 0 0 0 0 0
## X724 0 1 0 1 1 0 0 0 0 0 0 0
## X726 0 1 0 1 1 0 0 0 1 1 0 0
## X728 1 1 1 1 1 0 0 1 1 1 0 0
## X729 0 1 0 0 1 0 0 0 1 0 0 0
## X731 0 0 1 0 0 0 1 0 0 0 0 0
## X732 0 1 0 0 1 0 0 0 1 0 0 0
## X733 0 0 1 0 1 1 0 0 1 0 0 0
## X734 0 1 0 0 1 0 0 0 1 0 0 0
## X735 1 0 1 1 0 1 1 0 0 0 1 0
## X736 1 1 1 1 1 1 1 1 0 0 0 1
## X737 1 1 0 1 1 0 0 0 0 0 0 0
## X739 1 1 1 1 1 0 1 1 1 0 0 1
## X740 1 1 0 1 1 0 0 1 1 1 0 0
## X741 1 0 1 1 0 0 1 0 0 1 0 0
## X742 1 0 1 1 0 0 1 0 0 0 0 1
## X743 0 1 0 0 1 0 0 0 1 0 0 0
## X744 0 1 0 0 1 0 0 1 0 0 0 0
## X746 1 1 1 1 1 0 0 1 0 0 0 1
## X747 0 0 1 0 0 1 1 0 0 0 1 0
## X749 1 1 1 1 1 0 1 0 1 0 0 1
## X752 1 0 1 1 0 1 1 0 1 0 1 1
## X753 0 0 1 0 0 0 1 0 0 0 0 0
## X754 0 1 0 1 1 0 1 0 0 0 0 0
## X755 0 1 0 0 1 0 0 1 0 0 0 0
## X757 0 0 1 0 0 0 1 0 1 0 0 0
## X758 0 1 0 1 1 0 0 1 0 0 0 0
## X759 1 0 1 1 0 0 0 0 0 0 0 0
## X760 0 1 0 0 1 0 0 0 1 0 0 0
## X761 1 0 1 1 0 1 1 0 1 0 1 1
## X762 0 1 0 0 1 0 0 1 0 0 0 0
## X763 0 1 0 0 1 1 0 0 1 0 0 0
## X764 0 1 0 0 1 0 0 1 0 0 0 0
## X765 1 1 1 1 1 1 0 1 1 0 1 1
## X767 1 0 1 1 0 0 1 0 1 0 0 1
## X768 0 1 0 0 1 0 0 0 0 0 0 0
## X770 0 1 0 1 1 0 1 0 1 0 0 0
## X771 1 1 0 1 1 1 0 1 1 0 0 0
## X772 0 1 0 0 1 0 0 0 1 0 0 0
## X773 0 0 1 0 0 0 1 0 0 0 0 0
## X774 0 0 1 0 0 0 1 0 1 0 0 0
## X775 1 1 0 1 1 0 1 1 0 1 0 0
## X776 1 1 0 1 1 1 1 1 1 0 0 0
## X777 1 0 1 1 0 0 1 0 0 0 0 1
## X778 1 0 1 1 0 1 1 0 0 1 1 0
## X779 0 1 0 0 1 1 0 0 0 0 0 0
## X780 0 0 0 0 0 0 0 0 1 0 0 0
## X781 1 0 1 1 0 0 1 0 0 0 0 1
## X782 1 1 0 1 1 0 0 1 0 0 0 0
## X784 1 1 0 1 1 1 0 1 1 1 1 0
## X786 0 0 1 0 0 0 1 0 0 0 0 0
## X787 0 1 0 0 1 0 0 0 1 0 0 0
## X788 1 0 1 1 0 0 1 0 0 0 0 0
## X789 0 1 0 0 1 0 0 0 1 0 0 0
## X791 0 1 0 0 1 0 0 0 1 0 0 0
## X792 0 1 0 1 1 0 1 1 1 0 0 0
## X794 1 0 1 1 0 0 1 0 0 1 0 0
## X798 0 1 0 0 1 0 0 0 0 0 0 0
## X799 1 0 0 1 0 0 1 0 1 0 0 0
## X800 0 0 1 1 0 1 1 0 0 0 1 1
## X804 0 1 0 1 1 0 0 1 0 0 0 0
## X805 1 0 1 1 0 1 1 0 0 0 1 1
## X807 1 0 1 1 0 0 0 0 0 0 0 1
## X808 1 1 0 1 1 0 0 1 0 1 0 0
## X809 1 1 1 1 1 0 1 1 0 0 0 1
## X810 0 0 0 0 0 0 1 0 1 0 0 0
## X813 1 0 1 1 0 0 1 0 0 1 0 0
## X814 1 1 1 1 1 0 0 0 1 0 0 1
## X818 0 1 0 0 1 0 0 0 1 0 0 0
## X819 1 1 0 1 1 1 0 1 1 0 0 0
## X820 0 0 1 0 0 1 1 0 0 0 1 0
## X821 0 1 0 0 1 0 0 0 1 0 0 0
## X822 0 1 0 0 1 0 0 0 0 0 0 0
## X823 0 1 0 0 1 1 0 0 0 0 0 0
## X827 0 0 0 1 0 0 1 0 1 0 0 1
## X828 0 1 0 0 1 0 0 0 1 0 0 0
## X829 1 1 1 1 1 0 0 1 1 0 0 1
## X831 0 1 0 0 1 0 0 1 1 0 0 0
## X832 0 1 0 0 1 0 0 0 1 0 0 0
## X833 0 1 0 0 1 0 0 0 1 0 0 0
## X834 0 1 0 0 1 0 0 1 1 0 0 0
## X835 0 1 0 0 1 0 0 0 1 0 0 0
## X836 0 1 0 0 1 0 0 0 1 0 0 0
## X839 0 1 0 0 1 0 0 1 0 0 0 0
## X840 0 1 0 0 1 0 0 0 0 0 0 0
## X841 0 1 0 0 1 0 0 0 1 0 0 0
## X842 0 1 1 0 1 0 0 1 0 0 0 0
## X843 0 1 0 0 1 0 0 1 1 0 0 0
## X846 0 1 0 0 1 0 0 0 0 0 0 0
## X848 0 1 0 0 1 0 0 0 1 0 0 0
## X849 0 1 0 0 1 0 0 0 1 0 0 0
## X851 0 0 1 1 0 1 1 0 0 0 1 1
## X854 0 1 0 0 1 0 0 0 1 0 0 0
## X855 0 1 0 0 1 0 0 0 0 0 0 0
## X856 0 1 0 0 1 0 0 0 1 0 0 0
## X857 0 1 0 0 1 0 0 0 1 0 0 0
## X858 0 1 0 0 1 0 0 0 1 0 0 0
## X859 0 1 0 0 1 0 0 0 1 0 0 0
## X860 0 1 0 0 1 0 0 0 1 0 0 0
## X862 0 1 0 0 1 0 0 0 1 0 0 0
## X863 0 1 0 0 1 0 0 0 1 0 0 0
## X864 0 1 0 0 1 0 0 1 0 0 0 0
## X865 0 1 0 0 1 0 0 0 0 0 0 0
## X866 0 1 0 0 1 0 0 0 1 0 0 0
## X867 0 1 0 0 1 0 0 0 0 0 0 0
## X869 0 1 0 0 1 0 0 1 1 0 0 0
## X870 0 1 0 0 1 0 0 0 1 0 0 0
## X871 0 1 0 0 1 0 0 0 1 0 0 0
## X872 0 1 0 0 1 0 0 0 1 0 0 0
## X873 0 1 0 0 1 0 0 0 0 0 0 0
## X875 0 1 0 0 1 0 0 0 1 0 0 0
## X876 0 1 0 0 1 0 0 0 1 0 0 0
## X877 0 0 0 0 1 0 0 0 1 0 0 0
## X1190 0 1 0 1 1 0 0 0 0 0 0 0
## X1191 0 0 1 0 0 0 1 0 1 0 0 0
## X1192 1 0 1 1 0 1 1 0 0 0 1 0
## X1193 0 1 0 0 1 0 0 1 0 0 0 0
## X1194 1 0 1 1 0 1 1 0 0 0 1 1
## X1195 0 1 0 0 1 0 0 0 1 0 0 0
## X1197 0 1 1 0 1 0 1 1 0 0 0 0
## X1198 0 1 0 0 1 0 0 0 1 0 0 0
## X1199 0 0 1 1 1 1 0 0 0 0 0 0
## X1200 1 0 1 1 0 0 0 0 0 0 0 1
## X1201 1 1 0 1 1 0 0 1 0 0 0 1
## X1202 1 0 1 1 0 1 1 0 1 0 1 1
## X1203 0 0 0 0 0 0 1 0 0 0 0 0
## X1204 1 1 0 1 1 1 0 1 0 1 0 0
## X1205 1 1 0 1 1 1 0 1 1 1 0 0
## X1206 0 0 0 0 0 0 0 0 1 0 0 0
## X1207 0 1 1 1 1 0 0 0 0 0 0 0
## X1208 1 0 1 1 0 0 1 0 0 0 0 1
## X1209 0 0 0 0 1 0 0 0 1 1 0 0
## X1210 1 0 1 1 0 1 1 0 0 1 1 0
## X1212 0 1 1 0 1 1 1 1 0 1 1 0
## X1213 0 1 0 1 1 0 1 0 0 0 0 0
## X1215 1 0 1 1 0 1 1 0 1 0 1 1
## X1216 0 1 0 0 1 0 0 0 0 0 0 0
## X1217 0 1 0 0 1 1 0 1 1 0 1 0
## X1219 0 1 1 0 1 0 1 1 0 1 0 0
## X1220 1 1 0 1 1 1 1 1 1 0 1 0
## X1221 0 0 1 0 0 0 1 0 1 0 0 0
## X1222 0 1 0 0 1 0 1 1 0 0 0 0
## X1226 0 1 0 1 1 0 1 1 1 0 0 0
## X1228 1 1 0 1 1 0 0 1 0 0 0 1
## X1229 1 0 1 1 0 1 1 0 0 0 1 1
## X1230 1 1 0 1 1 0 0 1 0 0 0 1
## X1231 0 1 0 0 1 0 0 1 0 0 0 0
## X1233 1 0 1 1 0 1 1 0 0 0 1 0
## X1234 0 1 0 0 1 0 0 1 0 0 0 0
## X1236 1 0 1 1 0 0 1 0 0 0 0 1
## X1237 1 1 0 1 1 0 0 0 1 0 0 1
## X1239 1 0 1 1 0 0 0 0 1 0 0 1
## X1242 0 0 0 0 0 0 0 0 1 0 0 0
## X1244 0 1 0 0 1 0 0 0 1 0 0 0
## X1245 0 1 1 0 1 0 1 1 0 0 0 0
## X1246 1 1 1 1 1 0 1 1 0 1 0 0
## X1247 1 1 1 1 1 0 0 1 0 0 0 1
## X1249 1 1 1 1 1 0 0 1 1 0 0 1
## X1250 0 0 0 0 0 1 0 0 1 0 1 0
## X1251 0 0 0 0 1 0 0 1 1 0 0 0
## X1253 1 1 1 1 1 0 0 0 1 0 0 1
## X1254 0 1 0 0 1 0 0 0 1 0 0 0
## X1255 0 1 0 0 1 0 0 1 0 0 0 0
## X1256 0 1 0 0 1 0 1 1 0 0 0 0
## X1257 0 1 0 0 1 0 0 0 1 0 0 0
## X1259 0 0 0 1 0 0 1 0 1 0 0 1
## X1260 0 1 0 0 1 0 0 0 1 0 0 0
## X1262 1 1 1 1 1 0 0 1 1 0 0 1
## X1264 0 0 0 0 0 0 0 0 1 0 0 0
## X1265 0 1 0 0 1 0 0 0 1 0 0 0
## X1266 0 1 0 0 1 0 0 1 1 0 0 0
## X1267 1 1 0 1 1 0 0 1 0 1 0 0
## X1268 1 0 1 1 0 0 1 0 0 1 0 0
## X1273 0 1 0 0 1 0 0 0 1 0 0 0
## X1274 0 0 1 0 0 1 1 0 0 0 1 0
## X1275 0 0 0 0 0 0 1 0 1 0 0 0
## X1276 0 1 0 0 1 0 0 0 0 0 0 0
## X1277 0 1 0 0 1 0 0 0 1 0 0 0
## X1278 0 1 0 0 1 0 0 1 0 0 0 0
## X1279 0 1 0 0 1 0 0 0 0 0 0 0
## X1281 0 1 0 0 1 0 0 0 1 0 0 0
## X1282 0 1 0 0 1 0 0 0 1 0 0 0
## X1283 0 1 0 0 1 0 0 0 0 0 0 0
## X1284 0 1 0 0 1 0 0 0 0 0 0 0
## X1285 0 1 0 0 1 0 0 0 1 0 0 0
## X1288 0 1 0 0 1 0 0 0 1 0 0 0
## X1299 1 1 0 1 1 1 0 1 0 0 0 0
## X1301 1 0 1 1 0 1 1 0 0 0 1 0
## X1302 0 0 0 0 0 0 0 0 1 0 0 0
## X1307 1 1 1 1 1 0 0 0 1 0 0 1
## X1309 0 1 0 0 1 0 0 1 1 0 0 0
## X1310 0 0 0 0 0 0 1 0 1 0 0 0
## X447 1 1 0 1 1 0 0 0 1 1 0 0
## X448 1 1 0 1 1 1 1 1 1 1 1 0
## X451 0 0 1 0 0 0 1 0 0 0 0 0
## X452 0 1 0 0 1 0 0 1 1 0 0 0
## X453 0 1 0 0 1 0 0 0 0 1 0 0
## X454 1 1 0 1 1 1 0 1 0 0 0 0
## X455 1 1 1 1 1 0 0 1 1 1 0 0
## X456 1 1 1 1 1 1 1 0 0 0 0 1
## X458 1 1 0 1 1 1 0 1 0 0 0 0
## X459 1 0 1 1 0 0 1 0 0 0 0 0
## X460 0 0 0 0 0 0 1 0 0 0 0 0
## X461 1 1 0 1 1 0 0 1 1 1 0 0
## X462 0 1 1 0 1 0 0 0 0 0 0 0
## X463 0 1 0 1 1 1 0 1 0 0 0 0
## X464 0 0 0 0 0 0 0 0 1 0 0 0
## X465 0 1 0 1 1 1 1 1 0 0 1 0
## X466 1 1 0 1 1 0 0 0 1 1 0 0
## X468 1 0 1 1 0 1 1 0 0 0 1 1
## X471 1 1 1 1 1 1 1 1 0 0 0 0
## X472 0 0 1 0 0 0 1 0 1 0 0 0
## X473 0 0 0 0 0 0 1 0 0 0 0 0
## X476 1 1 0 1 1 0 0 1 0 1 0 0
## X477 1 1 1 1 1 1 0 1 0 0 0 0
## X478 0 0 0 0 0 0 1 0 0 0 0 0
## X479 0 0 1 0 0 0 1 0 0 0 0 0
## X480 0 1 0 0 1 0 0 0 0 0 0 0
## X482 0 0 1 0 0 0 0 0 1 0 0 0
## X483 0 0 1 0 0 0 0 0 1 0 0 0
## X484 0 1 0 0 1 1 0 0 0 0 0 0
## X486 1 0 1 1 0 0 1 0 0 0 0 1
## X487 1 1 1 1 1 0 0 1 0 0 0 1
## X488 1 1 1 1 1 0 1 1 0 1 0 1
## X489 1 1 0 1 1 0 0 1 1 1 0 0
## X490 1 1 1 1 1 0 0 1 1 0 0 1
## X491 0 0 1 0 0 0 1 0 1 0 0 0
## X492 1 0 1 1 0 1 1 0 0 0 0 0
## X493 1 0 1 1 0 0 1 0 0 1 0 0
## X494 1 0 0 1 1 1 0 0 1 1 0 0
## X495 0 1 0 1 1 1 1 1 0 0 1 0
## X496 1 0 0 1 1 1 0 0 0 0 0 0
## X497 0 1 0 0 1 0 0 0 0 0 0 0
## X498 0 1 0 0 1 0 0 1 1 1 0 0
## X499 0 1 0 0 1 0 0 1 0 0 0 0
## X501 1 1 0 1 1 0 0 0 1 0 0 0
## X502 0 1 0 0 1 0 0 1 0 0 0 0
## X503 0 1 1 1 1 1 1 1 0 0 1 0
## X505 1 1 1 1 1 1 0 0 1 0 0 0
## X506 1 1 0 1 1 1 0 1 0 0 0 0
## X507 0 1 0 1 1 1 0 1 0 0 0 0
## X508 1 1 0 1 1 1 0 1 1 1 1 0
## X509 1 1 1 1 1 1 0 1 0 1 1 0
## X510 1 1 0 1 1 1 0 0 1 0 1 0
## X513 0 0 1 0 0 0 1 0 1 0 0 0
## X514 1 1 0 1 1 1 0 1 0 0 0 0
## X515 0 1 0 0 1 0 0 0 0 1 0 0
## X516 0 1 0 1 1 0 0 1 0 0 0 0
## X518 1 1 1 1 1 1 0 0 0 0 0 0
## X521 1 1 0 1 1 1 0 1 0 0 0 0
## X523 1 1 1 1 1 0 0 1 0 0 0 1
## X524 1 1 1 1 1 1 1 0 1 0 0 0
## X525 1 0 1 1 0 1 1 0 0 0 0 0
## X526 0 0 1 0 0 1 1 0 0 0 1 0
## X530 0 1 1 1 1 0 0 0 0 0 0 0
## X531 1 1 1 1 1 1 0 1 0 1 0 0
## X532 0 0 1 1 1 1 0 0 0 0 0 0
## X533 1 1 0 1 1 1 0 1 1 0 1 0
## X534 1 1 1 1 1 1 1 1 0 0 0 0
## X535 0 1 0 0 1 0 0 0 1 0 0 0
## X536 0 1 0 0 1 1 1 1 0 0 1 0
## X538 1 1 0 1 1 0 0 1 0 1 0 0
## X539 0 1 0 0 1 1 1 1 0 0 1 0
## X542 1 0 1 1 0 1 1 0 0 0 1 0
## X543 0 0 1 0 0 0 1 0 1 0 0 0
## X544 1 1 1 1 1 1 1 1 0 1 1 0
## X545 0 0 1 0 0 0 1 0 0 0 0 0
## X546 0 0 0 0 0 0 0 0 1 0 0 0
## X548 0 1 1 1 1 0 0 1 0 0 0 0
## X549 0 1 0 0 1 0 0 0 1 0 0 0
## X551 0 0 0 0 0 0 0 0 1 0 0 0
## X552 1 1 0 1 1 0 0 1 0 0 0 1
## X553 1 1 1 1 1 1 0 0 0 0 0 1
## X554 0 0 1 0 1 1 0 0 1 0 0 0
## X556 1 1 0 1 1 0 0 1 0 1 0 0
## X557 1 1 1 1 1 1 0 1 1 0 0 0
## X558 0 1 0 1 1 0 0 0 0 0 0 0
## X559 0 0 1 0 0 0 1 0 0 0 0 0
## X560 0 1 0 0 1 0 0 1 0 0 0 0
## X561 0 1 0 0 1 0 0 0 1 0 0 0
## X562 0 1 1 0 1 0 0 1 0 0 0 0
## X563 1 1 0 1 1 0 0 1 0 1 0 0
## X565 0 0 1 0 0 0 1 0 0 0 0 0
## X566 0 1 0 0 1 1 0 0 1 0 0 0
## X567 1 1 1 1 1 1 0 1 1 0 0 0
## X568 1 1 1 1 1 1 0 0 1 0 0 0
## X569 1 1 1 1 1 0 0 1 1 0 0 1
## X571 1 1 0 1 1 1 0 1 1 0 0 1
## X572 1 1 1 1 1 1 1 1 0 0 0 1
## X574 0 0 1 0 0 0 1 0 0 0 0 0
## X576 1 1 0 1 1 1 0 1 0 0 0 0
## X577 1 1 0 1 1 1 0 0 0 0 0 0
## X579 1 1 0 1 1 1 0 1 0 0 0 0
## X580 1 1 0 1 1 0 0 1 1 1 0 0
## X582 1 0 1 1 0 0 1 0 0 0 0 0
## X583 0 1 0 0 1 0 0 1 0 0 0 0
## X584 1 1 0 1 1 0 1 1 0 0 0 1
## X586 1 1 1 1 1 0 0 1 0 0 0 1
## X587 0 1 0 0 1 0 0 0 0 0 0 0
## X588 1 0 1 1 0 1 1 0 0 0 0 0
## X589 1 0 1 1 0 1 1 0 0 1 1 0
## X591 0 1 0 1 1 1 1 1 0 0 1 0
## X592 0 1 1 0 1 0 1 1 0 0 0 0
## X593 0 1 0 0 1 1 0 1 1 0 1 0
## X594 1 0 1 1 0 0 1 0 0 0 0 1
## X595 1 0 1 1 0 0 0 0 1 0 0 1
## X596 1 1 1 1 1 1 1 1 0 0 0 0
## X597 0 1 0 1 1 0 1 1 0 0 0 0
## X598 1 0 0 1 0 0 1 0 0 1 0 0
## X599 0 1 0 0 1 0 0 1 0 0 0 0
## X600 1 1 1 1 1 0 0 1 0 0 0 1
## X603 1 0 1 1 0 0 1 0 0 1 0 0
## X604 1 0 1 1 0 1 1 0 0 0 0 0
## X605 1 0 1 1 0 0 1 0 0 0 0 0
## X606 1 1 1 1 1 0 1 1 0 0 0 1
## X608 0 1 0 0 1 0 0 0 1 0 0 0
## X609 1 1 0 1 1 1 0 1 0 0 0 0
## X611 0 0 0 0 0 0 1 0 0 0 0 0
## X612 1 1 0 1 1 1 0 0 1 0 0 0
## X613 0 1 0 0 1 0 0 1 1 0 0 0
## X614 0 1 0 0 1 0 0 1 1 0 0 0
## X616 0 0 1 0 0 0 1 0 0 0 0 0
## X617 1 1 1 1 1 0 0 0 0 0 0 0
## X619 1 1 0 1 1 1 0 1 1 0 1 0
## X620 0 1 0 0 1 0 0 0 1 0 0 0
## X621 1 1 0 1 1 1 0 1 0 1 0 0
## X622 0 1 0 0 1 0 0 0 0 0 0 0
## X623 1 1 0 1 1 1 0 1 1 0 1 0
## X625 1 1 1 1 1 0 0 0 1 0 0 0
## X628 1 0 1 1 0 1 1 0 1 0 1 0
## X629 1 0 1 1 0 1 1 0 0 1 1 0
## X630 0 1 0 1 1 1 1 1 0 0 0 0
## X631 0 0 1 0 0 0 1 0 0 0 0 0
## X632 0 0 0 0 0 0 0 0 1 0 0 0
## X633 1 1 0 1 1 0 1 0 1 1 0 0
## X635 1 1 0 1 1 1 1 1 0 0 0 0
## X636 1 0 1 1 0 1 1 0 1 0 1 0
## X637 1 0 1 1 0 0 1 0 0 0 0 0
## X638 1 1 1 1 1 0 0 1 0 1 0 0
## X639 1 1 0 1 1 1 0 1 0 0 0 0
## X641 1 1 1 1 1 0 1 0 0 1 0 0
## X648 1 1 0 1 1 1 0 1 1 1 1 0
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## X829 0 0 0 0 0 0 1 0 0 0 0 0
## X831 0 0 0 0 0 0 1 0 0 0 0 1
## X832 0 0 0 0 0 0 1 1 0 0 0 0
## X833 0 0 0 0 0 0 0 0 0 1 0 1
## X834 0 0 0 0 0 0 1 0 0 0 0 1
## X835 0 0 0 0 0 0 0 0 0 0 0 1
## X836 0 0 0 0 0 0 0 0 0 0 0 1
## X839 0 0 0 0 0 0 1 0 0 0 0 0
## X840 0 0 0 0 0 0 1 0 0 0 0 0
## X841 0 0 0 0 0 0 0 0 0 1 0 1
## X842 0 0 0 0 0 0 1 0 0 0 0 0
## X843 0 0 0 0 0 0 0 0 0 0 0 1
## X846 0 0 0 0 0 0 1 1 0 0 0 0
## X848 0 0 0 0 0 0 1 0 0 0 0 0
## X849 0 0 0 0 0 0 0 0 0 0 0 1
## X851 0 0 1 0 0 0 0 0 0 0 0 0
## X854 0 0 0 0 0 0 0 0 0 1 0 0
## X855 0 0 0 0 0 0 1 0 0 0 0 0
## X856 0 0 0 0 0 0 0 0 0 0 0 1
## X857 0 0 0 0 0 0 1 0 0 0 0 0
## X858 0 0 0 0 0 0 0 0 0 0 0 0
## X859 0 0 0 0 0 0 0 0 0 0 0 1
## X860 0 0 0 0 0 0 0 0 0 0 0 1
## X862 0 0 0 0 0 0 1 1 0 0 0 0
## X863 0 0 0 0 0 0 0 0 0 0 0 0
## X864 0 0 0 1 0 0 1 0 0 0 0 0
## X865 0 0 0 0 0 0 1 0 0 1 0 0
## X866 0 0 0 0 0 0 0 0 0 0 0 0
## X867 0 0 0 0 0 0 1 0 0 1 0 0
## X869 0 0 0 0 0 0 1 1 0 1 0 0
## X870 0 0 0 0 0 0 0 0 0 0 0 0
## X871 0 0 0 0 0 0 0 0 0 1 0 0
## X872 0 0 0 0 0 0 0 0 0 0 0 0
## X873 0 0 0 0 0 0 0 0 0 1 0 0
## X875 0 0 0 0 0 0 0 0 0 0 0 0
## X876 0 0 0 0 0 0 0 0 0 0 0 0
## X877 0 0 0 0 0 0 0 0 0 0 0 0
## X1190 0 0 0 0 0 0 1 1 0 0 0 0
## X1191 0 0 0 0 0 0 0 0 1 0 1 0
## X1192 0 0 1 1 0 0 0 0 0 0 0 0
## X1193 0 0 0 0 0 0 0 0 0 0 0 0
## X1194 0 0 1 1 0 0 0 0 0 0 0 0
## X1195 0 0 0 0 0 0 0 0 0 1 0 0
## X1197 0 0 0 0 0 0 1 1 1 0 0 0
## X1198 0 0 0 0 0 0 0 0 0 0 0 0
## X1199 0 0 0 0 0 0 0 0 0 0 0 0
## X1200 0 0 0 0 0 0 0 0 0 0 0 0
## X1201 0 0 0 1 0 0 0 0 0 0 0 0
## X1202 0 0 1 1 0 0 0 0 0 0 0 0
## X1203 0 0 0 0 0 0 0 0 0 0 0 0
## X1204 0 0 0 0 0 1 1 0 0 0 0 0
## X1205 0 0 0 0 0 1 0 0 0 1 0 0
## X1206 0 0 0 0 0 0 0 0 0 0 0 0
## X1207 0 0 0 0 0 0 1 0 0 0 0 0
## X1208 0 0 1 1 0 0 0 0 0 0 0 0
## X1209 0 0 0 0 0 0 0 0 0 0 0 0
## X1210 0 0 1 0 0 0 0 0 0 0 0 0
## X1212 0 0 1 1 0 0 0 0 0 0 0 0
## X1213 0 0 0 0 0 0 1 0 0 0 0 0
## X1215 0 0 1 1 1 0 0 0 0 0 0 0
## X1216 0 0 0 0 0 0 1 0 0 0 0 0
## X1217 0 0 0 0 0 0 1 0 0 0 0 1
## X1219 0 0 0 0 0 0 0 0 0 0 0 0
## X1220 0 0 0 0 0 0 0 0 0 0 0 1
## X1221 0 0 0 0 0 0 0 0 1 0 1 0
## X1222 0 0 0 1 0 0 1 0 0 0 0 0
## X1226 0 0 0 0 0 0 1 0 0 0 0 0
## X1228 0 0 0 0 0 0 0 0 0 0 0 0
## X1229 0 0 1 1 0 0 0 0 0 0 0 0
## X1230 0 0 0 0 0 0 1 1 0 0 0 0
## X1231 0 0 0 0 0 0 1 1 0 0 0 0
## X1233 0 0 1 0 0 0 0 0 0 0 0 0
## X1234 0 0 0 0 0 0 1 0 0 0 0 0
## X1236 0 0 1 1 0 0 0 0 0 0 0 0
## X1237 0 0 0 0 0 0 0 0 0 0 0 0
## X1239 0 0 0 0 0 0 0 0 0 0 0 0
## X1242 0 0 0 0 0 0 0 0 0 0 0 0
## X1244 0 0 0 0 0 0 1 1 0 0 0 1
## X1245 0 0 0 0 0 0 1 1 1 0 1 0
## X1246 0 0 1 1 0 0 0 0 0 0 0 0
## X1247 0 0 1 0 0 0 1 1 0 1 0 0
## X1249 0 0 0 0 0 0 0 0 0 0 0 0
## X1250 0 0 0 0 0 0 0 0 0 0 0 0
## X1251 0 0 0 0 0 0 0 0 0 0 0 0
## X1253 0 0 0 0 0 0 0 0 0 0 0 1
## X1254 0 0 0 0 0 0 0 0 0 1 0 0
## X1255 0 0 0 0 0 0 1 0 0 0 0 0
## X1256 0 0 0 1 0 0 0 0 0 0 0 0
## X1257 0 0 0 0 0 0 1 0 0 0 0 1
## X1259 0 0 0 0 0 0 0 0 0 0 0 0
## X1260 0 0 0 0 0 0 0 0 0 0 0 1
## X1262 0 0 1 0 0 0 1 1 0 1 0 0
## X1264 0 0 0 0 0 0 0 0 0 0 0 0
## X1265 0 0 0 0 0 0 0 0 0 0 0 1
## X1266 0 0 0 0 0 0 1 0 0 0 0 1
## X1267 0 0 0 0 0 0 0 0 0 1 0 0
## X1268 0 0 0 0 0 0 0 0 1 0 1 0
## X1273 0 0 0 0 0 0 1 1 0 0 0 0
## X1274 0 0 0 0 1 0 0 0 1 0 1 0
## X1275 0 0 0 0 0 0 0 0 0 0 0 0
## X1276 0 0 0 0 0 0 1 0 0 1 0 0
## X1277 0 0 0 0 0 0 0 0 0 0 0 1
## X1278 0 0 0 0 0 0 1 0 0 0 0 0
## X1279 0 0 0 0 0 0 1 0 0 0 0 0
## X1281 0 0 0 0 0 0 0 0 0 0 0 0
## X1282 0 0 0 0 0 0 0 0 0 1 0 0
## X1283 0 0 0 0 0 0 1 0 0 1 0 0
## X1284 0 0 0 0 0 0 1 0 0 0 0 0
## X1285 0 0 0 0 0 0 0 0 0 0 0 0
## X1288 0 0 0 0 0 0 0 0 0 0 0 0
## X1299 0 1 0 0 0 0 1 1 0 0 0 0
## X1301 0 0 1 1 0 0 0 0 0 0 0 0
## X1302 0 0 0 0 0 0 0 0 0 0 0 0
## X1307 0 0 0 0 0 0 0 0 0 0 0 0
## X1309 0 0 0 0 0 0 0 0 0 0 0 1
## X1310 0 0 0 0 0 0 0 0 0 0 0 0
## X447 0 0 0 0 0 0 0 0 0 0 0 1
## X448 0 0 0 0 0 0 0 0 0 0 0 0
## X451 0 0 0 0 0 0 0 0 0 0 0 0
## X452 0 0 0 0 0 0 0 0 0 0 0 0
## X453 0 0 0 0 0 1 0 0 0 1 0 0
## X454 1 0 0 0 0 0 0 0 0 0 0 0
## X455 0 0 0 0 0 0 0 0 0 0 0 1
## X456 0 0 0 1 0 0 1 1 0 0 0 0
## X458 1 0 0 0 0 1 0 0 0 0 0 0
## X459 0 0 0 0 0 0 0 0 1 0 1 0
## X460 0 0 0 0 0 0 0 0 0 0 0 0
## X461 0 0 0 0 0 0 0 0 0 1 0 0
## X462 0 0 0 0 0 0 0 0 0 0 0 0
## X463 0 1 0 0 0 0 1 1 0 0 0 0
## X464 0 0 0 0 0 0 0 0 0 0 0 0
## X465 0 0 0 0 0 0 0 0 0 0 0 0
## X466 0 0 0 0 0 0 0 0 0 1 0 0
## X468 0 0 0 0 0 0 0 0 1 0 1 0
## X471 1 0 0 0 0 0 0 0 0 0 0 0
## X472 0 0 0 0 0 0 0 0 0 0 0 0
## X473 0 0 0 0 0 0 0 0 0 0 0 0
## X476 0 0 0 0 0 0 1 0 0 1 0 0
## X477 0 1 0 0 0 0 1 0 0 0 0 0
## X478 0 0 0 0 0 0 0 0 0 0 0 0
## X479 0 0 0 0 0 0 0 0 0 0 0 0
## X480 0 0 0 0 0 1 0 0 0 0 0 0
## X482 0 0 0 0 0 0 0 0 0 0 0 0
## X483 0 0 0 0 0 0 0 0 0 0 0 0
## X484 1 0 0 0 0 0 0 0 0 0 0 0
## X486 0 0 0 0 0 0 0 0 1 0 1 0
## X487 0 0 0 0 0 0 0 0 0 0 0 0
## X488 0 0 0 0 0 0 0 0 1 0 0 0
## X489 0 0 0 0 0 0 1 0 0 0 0 0
## X490 0 0 0 0 0 0 0 0 0 1 0 0
## X491 0 0 0 0 0 0 0 0 1 0 1 0
## X492 0 1 1 1 0 0 0 0 0 0 0 0
## X493 0 0 0 0 0 0 0 0 1 0 1 0
## X494 1 0 0 0 0 0 0 0 0 0 0 0
## X495 0 0 0 0 0 1 0 0 0 0 0 0
## X496 0 1 0 0 0 1 0 0 0 0 0 0
## X497 0 0 0 0 0 1 1 0 0 0 0 0
## X498 0 0 0 0 0 0 0 0 0 0 0 0
## X499 0 0 0 0 0 0 1 0 0 0 0 0
## X501 0 0 0 0 0 0 0 0 0 0 0 0
## X502 0 0 0 0 0 0 0 0 0 1 0 0
## X503 0 0 0 0 0 0 1 0 0 0 0 0
## X505 0 0 0 0 0 0 0 0 0 0 0 1
## X506 1 0 0 0 0 1 0 0 0 0 0 0
## X507 1 0 0 0 0 1 0 0 0 0 0 0
## X508 0 0 0 0 0 0 0 0 0 0 0 0
## X509 0 0 0 0 0 0 0 0 0 1 0 0
## X510 1 0 0 0 0 0 1 1 0 0 0 0
## X513 0 0 0 0 0 0 0 0 0 0 0 0
## X514 1 0 0 0 0 0 0 0 0 0 0 0
## X515 0 0 0 0 0 0 0 0 0 1 0 0
## X516 0 0 0 0 0 0 0 0 0 0 0 0
## X518 0 0 0 0 0 0 0 0 0 1 0 0
## X521 1 0 0 0 0 0 0 0 0 0 0 0
## X523 0 0 0 0 0 0 1 1 0 0 0 0
## X524 0 0 0 0 0 0 0 0 0 0 0 0
## X525 0 1 0 1 0 0 0 0 0 0 0 0
## X526 0 0 0 0 1 0 0 0 1 0 1 0
## X530 0 0 0 0 0 0 1 1 0 0 0 0
## X531 0 0 0 0 0 0 0 0 0 0 0 0
## X532 0 0 0 0 0 0 0 0 0 0 0 0
## X533 0 1 0 0 0 0 0 0 0 0 0 0
## X534 0 0 0 0 0 0 1 1 1 0 0 0
## X535 0 0 0 0 0 0 1 0 0 0 0 0
## X536 0 0 0 0 0 1 1 0 0 0 0 0
## X538 0 0 0 0 0 0 0 0 0 0 0 0
## X539 0 0 0 0 0 1 1 0 0 0 0 0
## X542 0 0 1 1 1 0 0 0 0 0 0 0
## X543 0 0 0 0 0 0 0 0 1 0 1 0
## X544 0 0 1 0 0 0 0 0 0 1 0 0
## X545 0 0 0 0 0 0 0 0 1 0 0 0
## X546 0 0 0 0 0 0 0 0 0 0 0 0
## X548 0 0 0 0 0 0 0 0 0 0 0 0
## X549 0 0 0 0 0 0 0 0 0 0 0 0
## X551 0 0 0 0 0 0 0 0 0 0 0 0
## X552 0 0 0 1 0 0 0 0 0 0 0 0
## X553 0 0 0 0 0 0 1 1 0 0 0 0
## X554 0 0 0 0 0 0 0 0 0 0 0 0
## X556 0 0 0 0 0 0 1 1 0 0 0 0
## X557 1 0 0 0 0 0 0 0 0 0 0 0
## X558 0 0 0 0 0 0 1 0 0 0 0 0
## X559 0 0 0 0 0 0 0 0 1 0 0 0
## X560 0 0 0 0 0 0 0 0 0 1 0 0
## X561 0 0 0 0 0 0 0 0 0 1 0 0
## X562 0 0 0 0 0 0 1 0 0 0 0 0
## X563 0 0 0 0 0 0 1 1 0 0 0 0
## X565 0 0 0 0 0 0 0 0 1 0 0 0
## X566 1 0 0 0 0 0 0 0 0 0 0 0
## X567 0 0 0 0 0 0 0 0 0 0 0 0
## X568 0 0 0 0 0 0 0 0 0 0 0 0
## X569 0 0 0 0 0 0 0 0 0 1 0 0
## X571 1 0 0 0 0 0 0 0 0 0 0 0
## X572 1 0 0 0 0 0 0 0 1 0 1 0
## X574 0 0 0 1 0 0 0 0 0 0 0 0
## X576 1 0 0 0 0 0 0 0 0 0 0 0
## X577 0 0 0 0 0 0 1 0 0 1 0 0
## X579 0 0 0 0 0 0 1 1 0 0 0 0
## X580 0 0 0 0 0 0 0 0 0 0 0 0
## X582 0 0 0 0 0 0 0 0 1 0 1 0
## X583 0 0 0 0 0 0 0 0 0 0 0 0
## X584 0 0 0 0 0 0 1 0 0 0 0 0
## X586 0 0 0 0 0 0 1 0 0 0 0 0
## X587 0 0 0 0 0 1 1 0 0 0 0 0
## X588 0 1 0 0 0 0 0 0 0 0 0 0
## X589 0 0 1 0 0 0 0 0 0 0 0 0
## X591 0 0 0 0 0 1 0 0 0 0 0 0
## X592 0 0 0 0 0 0 1 1 0 0 0 0
## X593 0 0 0 0 0 0 1 0 0 0 0 0
## X594 0 0 0 0 0 0 0 0 1 0 1 0
## X595 0 0 0 0 0 0 0 0 0 0 0 0
## X596 0 0 0 0 0 0 0 0 1 0 0 0
## X597 0 0 0 0 0 0 1 0 0 0 0 0
## X598 0 0 0 0 0 0 0 0 0 0 0 0
## X599 0 0 0 0 0 0 0 0 0 0 0 0
## X600 0 0 1 0 0 0 0 0 0 0 0 0
## X603 0 0 0 0 0 0 0 0 1 0 1 0
## X604 0 1 0 0 0 0 0 0 0 0 0 0
## X605 0 0 1 1 0 0 0 0 0 0 0 0
## X606 0 0 0 0 0 0 1 1 1 0 0 0
## X608 0 0 0 0 0 0 1 0 0 0 0 0
## X609 1 0 0 0 0 1 0 0 0 0 0 0
## X611 0 0 0 0 0 0 0 0 0 0 0 0
## X612 0 0 0 0 0 0 0 0 0 0 0 0
## X613 0 0 0 0 0 0 0 0 0 1 0 0
## X614 0 0 0 0 0 0 1 0 0 0 0 0
## X616 0 0 0 0 0 0 0 0 0 0 0 0
## X617 0 0 0 0 0 0 1 0 0 1 0 0
## X619 0 1 0 0 0 0 1 1 0 0 0 0
## X620 0 0 0 0 0 0 0 0 0 0 0 1
## X621 0 0 0 0 0 0 1 1 0 0 0 0
## X622 0 0 0 0 0 0 1 0 0 0 0 0
## X623 0 1 0 0 0 0 1 0 0 0 0 1
## X625 0 0 0 0 0 0 0 0 0 0 0 1
## X628 0 0 1 1 1 0 0 0 0 0 0 0
## X629 0 0 1 0 0 0 0 0 0 0 0 0
## X630 0 0 0 1 0 0 1 0 0 0 0 0
## X631 0 0 0 0 0 0 0 0 1 0 1 0
## X632 0 0 0 0 0 0 0 0 0 0 0 0
## X633 0 0 0 0 0 0 0 0 0 0 0 1
## X635 0 0 0 0 0 0 0 0 0 0 0 0
## X636 0 0 1 1 1 0 0 0 0 0 0 0
## X637 0 0 1 1 0 0 0 0 0 0 0 0
## X638 0 0 0 0 0 0 1 1 0 1 0 0
## X639 1 0 0 0 0 1 0 0 0 0 0 0
## X641 0 0 0 0 0 0 1 1 1 0 0 0
## X648 0 0 0 0 0 0 0 0 0 1 0 0
## X650 0 0 0 0 0 0 0 0 0 0 0 0
## X651 0 0 0 0 0 0 1 1 1 0 0 0
## X653 0 0 1 0 0 0 0 0 0 0 0 0
## X654 0 0 0 0 0 0 0 0 1 0 0 0
## X655 0 0 0 0 0 0 1 1 0 0 0 0
## X656 0 0 0 0 0 0 1 0 0 1 0 0
## X657 1 0 0 0 0 0 0 0 1 0 1 0
## X1082 0 0 0 0 0 0 0 0 0 0 0 0
## X1083 0 0 0 0 0 0 1 1 0 0 0 0
## X1084 0 0 0 0 0 0 0 0 0 0 0 0
## X1086 0 0 0 0 0 0 1 1 0 0 0 0
## X1088 0 0 0 0 0 0 0 0 0 0 0 1
## X1089 0 0 0 0 0 0 1 0 0 0 0 0
## X1090 0 0 0 0 0 0 0 0 0 0 0 0
## X1091 0 0 0 0 0 0 0 0 1 0 1 0
## X1092 0 0 0 0 0 0 0 0 1 0 0 0
## X1093 0 0 1 0 0 0 0 0 0 0 0 0
## X1094 0 0 0 0 0 0 0 0 0 0 0 0
## X1095 0 1 0 0 0 0 1 0 0 0 0 0
## X1097 0 0 0 0 0 0 0 0 0 0 0 0
## X1098 0 1 0 0 0 0 0 0 0 0 0 0
## X1101 0 1 0 0 0 0 0 0 0 0 0 0
## X1103 0 0 0 0 0 0 0 0 0 0 0 0
## X1104 1 0 0 0 0 1 1 0 0 0 0 0
## X1105 0 1 0 0 0 1 0 0 0 0 0 0
## X1106 0 0 0 0 0 0 0 0 1 0 1 0
## X1108 0 0 0 0 0 0 0 0 0 0 0 0
## X1110 0 0 0 0 0 0 1 1 0 0 0 0
## X1112 1 0 0 0 0 1 0 0 0 0 0 0
## X1113 0 0 0 0 0 0 0 0 0 0 0 0
## X1115 0 0 0 0 0 0 1 1 0 0 0 0
## X1116 0 0 0 0 0 0 0 0 0 0 0 1
## X1117 0 0 0 0 0 0 1 0 0 0 0 0
## X1119 0 0 0 0 0 0 0 0 0 0 0 0
## X1120 0 0 1 1 1 0 0 0 0 0 0 0
## X1121 0 1 0 0 0 1 0 0 0 0 0 0
## X1122 0 0 1 0 1 0 0 0 0 0 0 0
## X1124 0 0 0 0 0 0 1 0 0 0 0 0
## X1125 0 0 0 0 0 0 0 0 0 0 0 0
## X1126 0 0 0 0 0 0 0 0 0 1 0 0
## X1127 0 0 0 1 0 0 1 0 0 0 0 0
## X1128 0 0 0 0 0 0 0 0 0 0 0 0
## X1129 0 0 0 0 0 0 0 0 0 0 0 1
## X1130 0 0 0 0 0 0 0 0 0 0 0 0
## X1131 0 0 0 0 0 0 0 0 0 0 0 0
## X1133 1 0 0 0 0 0 1 1 0 0 0 0
## X1135 0 0 0 0 0 0 0 0 1 0 1 0
## X1136 0 0 0 0 0 0 0 0 0 0 0 0
## X1138 0 0 0 0 0 0 0 0 0 0 0 0
## X1139 0 0 1 1 1 0 0 0 0 0 0 0
## X1141 0 0 0 0 0 0 0 0 0 0 0 0
## X1142 0 0 0 0 0 0 0 0 0 0 0 1
## X1143 0 0 0 0 0 0 1 1 0 0 0 0
## X1144 0 0 0 0 0 0 0 0 0 0 0 0
## X1145 0 1 0 0 0 0 0 0 0 0 0 0
## X1146 0 0 0 0 0 0 0 0 1 0 1 0
## X1147 0 0 0 0 0 0 0 0 1 0 0 0
## X1149 0 0 0 0 0 0 0 0 0 1 0 0
## X1150 0 0 0 0 0 0 0 0 1 0 1 0
## X1151 0 0 0 0 0 0 0 0 0 0 0 0
## X1152 0 0 0 0 0 0 0 0 0 0 0 0
## X1153 0 0 0 0 0 0 0 0 0 0 0 0
## X1156 0 0 0 0 0 0 0 0 1 0 1 0
## X1158 0 0 0 0 0 0 0 0 0 0 0 0
## X1159 0 0 0 0 0 0 0 0 0 0 0 0
## X1160 0 0 0 0 0 0 1 0 0 0 0 0
## FP208 MolWeight NumBonds NumMultBonds NumRotBonds NumDblBonds
## X661 0 0.304017769 0.49840233 1.90489650 -0.9347280 -0.831341597
## X662 0 1.474751336 1.69828720 1.32482715 0.7260405 -0.831341597
## X663 0 0.284237960 0.69697444 0.16468846 0.7260405 -0.005212173
## X665 0 -0.579130036 0.20728011 -0.80209379 -0.5195359 0.820917251
## X668 0 0.508214019 0.56629095 -0.02866799 1.1412327 -0.831341597
## X669 0 0.846130172 0.56629095 -0.80209379 1.1412327 0.820917251
## X670 0 1.343679568 0.99793817 2.29160940 -0.5195359 -0.005212173
## X671 0 0.223329553 0.94039386 -0.99545024 3.2171934 -0.005212173
## X672 0 1.536294032 1.99292450 -0.41538089 -0.5195359 2.473176098
## X673 1 0.531725024 0.99793817 0.16468846 -0.1043438 -0.005212173
## X674 0 0.513009822 0.63244961 0.55140136 -0.1043438 1.647046674
## X676 0 0.981923863 1.69828720 -0.80209379 -0.9347280 0.820917251
## X677 0 -0.294344540 0.12893412 0.93811425 -0.9347280 -0.831341597
## X678 0 -0.211043577 -0.40240913 0.93811425 -0.9347280 -0.831341597
## X679 1 -0.403319666 0.28325136 -0.02866799 -0.1043438 -0.831341597
## X682 0 0.513009822 0.63244961 1.13147070 0.3108484 -0.005212173
## X683 0 1.174798750 1.36999732 0.35804491 2.3868091 0.820917251
## X684 0 1.683069116 1.87027471 1.13147070 1.5564248 -0.831341597
## X685 0 0.996447520 1.78555525 -0.99545024 -0.9347280 -0.005212173
## X686 0 -0.294344540 0.12893412 0.93811425 -0.5195359 -0.831341597
## X688 0 0.880198541 0.63244961 1.32482715 -0.1043438 -0.005212173
## X689 0 0.923239370 1.46773946 1.13147070 0.7260405 -0.831341597
## X690 0 1.144391553 1.46773946 0.16468846 2.3868091 -0.005212173
## X691 0 1.836745684 0.88159159 -0.80209379 0.7260405 0.820917251
## X692 1 1.649573481 1.46773946 0.55140136 3.2171934 1.647046674
## X693 0 1.038577746 1.16359252 0.55140136 0.3108484 1.647046674
## X695 0 1.252510849 1.56220886 1.13147070 1.1412327 -0.831341597
## X696 0 0.158871193 0.28325136 1.90489650 -0.9347280 -0.831341597
## X698 0 0.792852769 1.31981693 0.16468846 0.7260405 -0.005212173
## X699 0 -0.094205025 -1.09071695 0.16468846 -0.9347280 -0.831341597
## X700 0 -0.771172819 0.04803954 -0.99545024 1.1412327 -0.831341597
## X702 0 -1.218301524 -0.12219740 -1.18880668 -0.1043438 -0.831341597
## X703 0 -0.982753213 0.04803954 -1.18880668 -0.9347280 -0.831341597
## X704 0 -0.294344540 0.12893412 0.93811425 -0.9347280 -0.831341597
## X706 0 0.636103875 0.82146772 0.55140136 0.3108484 1.647046674
## X708 1 -0.321429192 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X709 0 -0.982753213 0.04803954 -1.18880668 -0.9347280 -0.831341597
## X711 0 1.706734262 2.47286768 -0.99545024 0.7260405 -0.005212173
## X712 0 0.831678296 1.16359252 1.32482715 0.7260405 -0.005212173
## X713 0 0.929168040 0.56629095 1.32482715 0.3108484 -0.005212173
## X714 0 1.675379106 2.11068236 -0.22202444 0.7260405 3.299305521
## X715 0 0.750468797 0.12893412 0.35804491 0.3108484 -0.005212173
## X717 0 0.291891037 -0.40240913 0.93811425 -0.9347280 -0.831341597
## X718 0 1.522316745 1.69828720 1.13147070 0.7260405 -0.831341597
## X721 0 0.508214019 0.56629095 -0.02866799 0.7260405 -0.831341597
## X722 1 1.257699471 1.10948462 1.71154005 -0.1043438 1.647046674
## X723 0 -0.982753213 -0.03559810 -0.99545024 1.1412327 -0.005212173
## X724 1 0.026037466 0.12893412 1.32482715 -0.1043438 -0.005212173
## X726 0 0.989629709 0.12893412 1.13147070 -0.1043438 -0.831341597
## X728 1 0.635848282 0.63244961 1.32482715 0.3108484 -0.005212173
## X729 0 1.163654675 -1.22934392 -0.02866799 -0.9347280 -0.831341597
## X731 0 -1.218301524 -0.12219740 -1.18880668 0.7260405 -0.831341597
## X732 1 0.098097256 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X733 0 0.237099891 0.12893412 -0.02866799 0.7260405 -0.831341597
## X734 0 0.378611406 -1.22934392 -0.02866799 -0.9347280 -0.831341597
## X735 0 1.052782459 1.65364219 -0.60873734 -0.9347280 0.820917251
## X736 0 0.558425111 0.99793817 0.16468846 2.3868091 -0.005212173
## X737 0 0.060245711 -0.21200528 1.32482715 -0.5195359 0.820917251
## X739 0 1.400858350 1.26871571 0.55140136 0.3108484 1.647046674
## X740 0 1.430265786 1.26871571 2.29160940 0.7260405 0.820917251
## X741 0 0.223329553 0.94039386 -0.99545024 3.2171934 -0.005212173
## X742 0 0.072232210 0.75995351 -0.99545024 2.8020012 -0.005212173
## X743 0 0.378611406 -1.22934392 -0.02866799 -0.9347280 -0.831341597
## X744 0 -0.321429192 0.04803954 0.93811425 -0.9347280 -0.831341597
## X746 0 0.907820092 1.21665476 0.35804491 2.3868091 0.820917251
## X747 0 0.072790642 0.99793817 -1.18880668 3.2171934 -0.831341597
## X749 0 1.889098307 2.07194628 1.32482715 2.3868091 -0.005212173
## X752 0 2.027107324 2.54041376 -0.22202444 1.9716169 3.299305521
## X753 0 -0.982753213 0.04803954 -1.18880668 -0.1043438 -0.831341597
## X754 0 1.135094949 1.46773946 1.13147070 -0.1043438 -0.831341597
## X755 0 -0.294344540 0.12893412 0.93811425 -0.9347280 -0.831341597
## X757 0 0.475066868 -0.12219740 -1.18880668 0.7260405 -0.831341597
## X758 0 0.201609653 0.49840233 1.13147070 -0.1043438 -0.831341597
## X759 0 1.039771029 0.82146772 -0.80209379 1.9716169 0.820917251
## X760 1 0.098097256 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X761 0 1.834687162 2.22396656 -0.22202444 0.7260405 3.299305521
## X762 0 -0.165345469 0.12893412 1.13147070 -0.9347280 -0.831341597
## X763 0 0.710001130 0.28325136 1.13147070 -0.5195359 -0.831341597
## X764 0 -0.115366351 0.35700394 0.93811425 -0.9347280 -0.831341597
## X765 0 1.803708352 1.05428349 1.32482715 1.1412327 -0.005212173
## X767 0 1.677549637 1.95260717 -0.02866799 0.3108484 4.125434945
## X768 0 -0.152986644 0.04803954 1.71154005 -0.9347280 -0.831341597
## X770 0 1.190653352 1.21665476 1.13147070 0.7260405 -0.831341597
## X771 0 1.188302449 0.20728011 0.74475780 -0.5195359 2.473176098
## X772 0 1.163654675 -1.22934392 -0.02866799 -0.9347280 -0.831341597
## X773 0 -0.737607576 0.20728011 -0.99545024 1.5564248 -0.005212173
## X774 0 0.147051515 0.12893412 -1.18880668 1.1412327 -0.831341597
## X775 1 0.719516934 0.75995351 1.51818360 1.1412327 0.820917251
## X776 0 2.101817743 2.14892180 1.90489650 2.3868091 2.473176098
## X777 0 1.162199568 1.26871571 -0.99545024 4.0475776 -0.005212173
## X778 0 1.978779123 2.70310385 -0.80209379 1.5564248 0.820917251
## X779 0 0.148236508 0.35700394 1.90489650 -0.9347280 -0.831341597
## X780 0 0.865295430 -1.37754378 -0.80209379 -0.9347280 0.820917251
## X781 0 1.135296034 1.82822307 -0.60873734 3.6323855 1.647046674
## X782 0 0.303418106 0.20728011 1.51818360 -0.9347280 0.820917251
## X784 0 2.675894881 0.88159159 1.32482715 1.1412327 -0.005212173
## X786 0 -0.945628244 0.12893412 -1.18880668 1.1412327 -0.831341597
## X787 1 0.447081835 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X788 0 1.327364381 2.03269881 -0.41538089 -0.5195359 2.473176098
## X789 0 0.447081835 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X791 0 0.447081835 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X792 0 1.398910560 1.36999732 1.13147070 0.7260405 -0.831341597
## X794 0 0.496130384 1.26871571 -0.99545024 4.0475776 -0.005212173
## X798 0 0.735984417 0.82146772 3.06503519 -0.5195359 -0.831341597
## X799 0 1.378795179 0.35700394 -0.60873734 -0.1043438 1.647046674
## X800 0 1.108515489 1.82822307 -1.18880668 -0.9347280 -0.831341597
## X804 0 1.017548306 1.41929339 1.51818360 0.7260405 0.820917251
## X805 0 1.956176482 2.60651481 -0.41538089 1.5564248 2.473176098
## X807 0 1.580162693 1.10948462 -0.80209379 4.0475776 0.820917251
## X808 1 1.380821445 1.46773946 2.48496584 1.1412327 1.647046674
## X809 1 1.147725526 1.31981693 1.51818360 2.8020012 0.820917251
## X810 0 1.317009930 0.04803954 -0.80209379 -0.9347280 0.820917251
## X813 0 0.953373701 1.82822307 -0.99545024 5.7083462 -0.005212173
## X814 0 1.355892859 1.16359252 0.35804491 0.7260405 0.820917251
## X818 0 0.745867382 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X819 0 1.136435150 0.56629095 1.51818360 -0.1043438 0.820917251
## X820 0 0.364681635 1.31981693 -1.18880668 4.0475776 -0.831341597
## X821 1 0.745867382 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X822 0 0.242973688 0.42867850 2.48496584 -0.9347280 -0.831341597
## X823 0 0.627652706 0.82146772 2.87167874 -0.9347280 -0.831341597
## X827 0 1.560421390 0.56629095 -0.99545024 -0.9347280 -0.005212173
## X828 0 0.745867382 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X829 0 1.630165630 1.16359252 0.55140136 1.9716169 1.647046674
## X831 0 1.184902006 0.28325136 1.32482715 -0.1043438 -0.005212173
## X832 1 0.447081835 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X833 0 1.007095938 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X834 0 1.198080407 0.42867850 1.13147070 -0.1043438 -0.831341597
## X835 0 0.447081835 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X836 0 1.007095938 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X839 0 0.382560531 0.63244961 2.09825295 -0.9347280 -0.831341597
## X840 0 0.495036672 0.69697444 2.87167874 -0.9347280 -0.831341597
## X841 0 1.007095938 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X842 0 0.284137074 0.63244961 1.90489650 -0.5195359 -0.831341597
## X843 0 1.184902006 0.28325136 1.32482715 -0.1043438 -0.005212173
## X846 1 0.513371322 0.75995351 2.29160940 -0.1043438 -0.831341597
## X848 0 1.239163633 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X849 0 1.007095938 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X851 0 1.737322938 2.63904482 -0.99545024 -0.9347280 -0.005212173
## X854 0 1.007095938 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X855 0 0.823597252 0.99793817 3.64510454 -0.9347280 -0.831341597
## X856 0 1.447932035 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X857 0 1.239163633 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X858 0 1.447932035 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X859 0 1.447932035 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X860 0 1.007095938 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X862 1 1.239163633 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X863 0 1.637655670 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X864 0 0.831600743 1.16359252 2.87167874 -0.9347280 -0.831341597
## X865 0 0.703248097 0.88159159 3.45174809 -0.9347280 -0.831341597
## X866 0 1.447932035 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X867 0 0.703248097 0.88159159 3.45174809 -0.9347280 -0.831341597
## X869 1 1.552263693 1.46773946 3.25839164 0.7260405 -0.831341597
## X870 0 1.447932035 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X871 0 1.447932035 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X872 0 1.447932035 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X873 0 0.703248097 0.88159159 3.45174809 -0.9347280 -0.831341597
## X875 0 1.811520606 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X876 0 1.811520606 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X877 0 2.120939599 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X1190 1 -0.115977627 0.04803954 1.13147070 -0.1043438 -0.831341597
## X1191 0 -0.603559640 -0.12219740 -1.18880668 0.7260405 -0.831341597
## X1192 0 1.080766715 1.82822307 -0.80209379 -0.9347280 0.820917251
## X1193 0 -0.403319666 0.28325136 -0.02866799 -0.9347280 -0.831341597
## X1194 0 1.675379106 2.11068236 -0.22202444 0.7260405 3.299305521
## X1195 0 0.016880687 -1.22934392 -0.02866799 -0.9347280 -0.831341597
## X1197 1 -0.610215946 0.04803954 -0.02866799 0.3108484 -0.831341597
## X1198 0 0.563194962 -1.22934392 -0.02866799 -0.9347280 -0.831341597
## X1199 0 0.611250316 0.82146772 -0.02866799 1.1412327 -0.831341597
## X1200 0 0.769013180 0.42867850 -0.99545024 2.3868091 -0.005212173
## X1201 0 1.574200229 1.74225056 1.32482715 0.3108484 -0.005212173
## X1202 0 2.035474501 2.33314222 -0.02866799 1.5564248 4.125434945
## X1203 0 -0.982753213 0.04803954 -1.18880668 -0.9347280 -0.831341597
## X1204 0 1.270551909 0.99793817 1.90489650 -0.1043438 2.473176098
## X1205 0 0.936481465 0.49840233 1.32482715 0.3108484 -0.005212173
## X1206 0 0.476723028 -1.70965649 -0.80209379 -0.5195359 0.820917251
## X1207 0 0.952788440 1.21665476 1.13147070 0.3108484 -0.831341597
## X1208 0 1.747037108 2.22396656 -0.41538089 -0.1043438 2.473176098
## X1209 0 0.815641020 -1.09071695 -0.02866799 -0.9347280 -0.831341597
## X1210 0 1.623602913 2.43853015 -0.99545024 0.7260405 -0.005212173
## X1212 0 1.038647958 1.56220886 0.16468846 -0.9347280 -0.831341597
## X1213 0 0.952788440 1.21665476 1.13147070 0.7260405 -0.831341597
## X1215 0 1.834687162 2.26079827 -0.41538089 -0.1043438 2.473176098
## X1216 0 0.049093577 -0.03559810 1.71154005 -0.9347280 -0.831341597
## X1217 0 1.269483899 0.88159159 2.29160940 0.3108484 -0.831341597
## X1219 0 0.847285078 1.26871571 1.13147070 1.1412327 -0.831341597
## X1220 0 1.532919242 1.65364219 1.32482715 1.5564248 -0.005212173
## X1221 0 -0.009904078 -0.12219740 -1.18880668 0.7260405 -0.831341597
## X1222 0 0.900780208 1.41929339 1.32482715 0.3108484 -0.005212173
## X1226 0 1.701175131 1.82822307 1.13147070 0.7260405 -0.831341597
## X1228 0 0.907670555 0.56629095 0.16468846 1.1412327 -0.005212173
## X1229 0 1.882368345 2.43853015 -0.22202444 1.1412327 3.299305521
## X1230 1 0.448387506 0.35700394 1.51818360 -0.5195359 0.820917251
## X1231 1 0.026494249 0.42867850 1.13147070 0.3108484 -0.831341597
## X1233 0 1.175127549 1.95260717 -0.80209379 -0.5195359 0.820917251
## X1234 0 -0.294344540 0.12893412 0.93811425 -0.9347280 -0.831341597
## X1236 0 1.327058775 1.87027471 -0.41538089 -0.1043438 1.647046674
## X1237 0 1.214275611 -0.03559810 0.16468846 0.7260405 -0.005212173
## X1239 0 1.095780590 0.56629095 -0.80209379 1.1412327 0.820917251
## X1242 0 0.771569118 -1.70965649 -0.80209379 -0.5195359 0.820917251
## X1244 1 0.098097256 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X1245 1 -0.215143211 0.49840233 -0.02866799 1.1412327 -0.831341597
## X1246 0 0.815953602 1.16359252 1.13147070 -0.9347280 -0.005212173
## X1247 1 1.387244764 1.78555525 1.51818360 1.9716169 0.820917251
## X1249 0 1.459034034 1.05428349 0.55140136 1.5564248 1.647046674
## X1250 0 1.413034907 0.12893412 -0.80209379 -0.9347280 0.820917251
## X1251 0 0.812356063 -0.96037479 0.35804491 -0.9347280 -0.831341597
## X1253 0 1.341677499 0.75995351 0.16468846 2.3868091 -0.005212173
## X1254 0 0.447081835 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X1255 0 0.137547205 0.42867850 1.90489650 -0.9347280 -0.831341597
## X1256 0 0.304417449 0.82146772 0.93811425 -0.9347280 -0.831341597
## X1257 0 0.745867382 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X1259 0 1.560421390 0.56629095 -0.99545024 -0.9347280 -0.005212173
## X1260 0 0.745867382 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X1262 1 1.616540792 1.51536781 1.51818360 1.9716169 0.820917251
## X1264 0 1.518473204 0.04803954 -0.80209379 -0.9347280 0.820917251
## X1265 0 1.007095938 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X1266 0 1.410804929 0.42867850 1.13147070 -0.1043438 -0.831341597
## X1267 0 1.745837809 1.69828720 2.48496584 1.5564248 -0.005212173
## X1268 0 0.737283220 1.56220886 -0.99545024 4.8779619 -0.005212173
## X1273 1 1.007095938 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X1274 0 0.620626671 1.60829128 -1.18880668 4.8779619 -0.831341597
## X1275 0 1.471104074 0.42867850 -0.80209379 -0.9347280 0.820917251
## X1276 0 0.703248097 0.88159159 3.45174809 -0.9347280 -0.831341597
## X1277 0 1.239163633 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X1278 0 0.382560531 0.63244961 2.09825295 -0.9347280 -0.831341597
## X1279 0 0.495036672 0.69697444 2.87167874 -0.9347280 -0.831341597
## X1281 0 1.447932035 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X1282 0 1.447932035 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X1283 0 0.703248097 0.88159159 3.45174809 -0.9347280 -0.831341597
## X1284 0 0.495036672 0.69697444 2.87167874 -0.9347280 -0.831341597
## X1285 0 1.447932035 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X1288 0 1.971974745 -0.03559810 1.13147070 -0.5195359 -0.831341597
## X1299 1 0.703000619 0.69697444 1.51818360 -0.1043438 0.820917251
## X1301 0 0.981923863 1.69828720 -0.80209379 -0.9347280 0.820917251
## X1302 0 0.998810596 -0.50369472 -1.18880668 -0.9347280 -0.831341597
## X1307 0 1.387897880 0.42867850 0.16468846 1.5564248 -0.005212173
## X1309 0 1.410804929 0.42867850 1.13147070 -0.1043438 -0.831341597
## X1310 0 1.712430972 0.20728011 -0.99545024 -0.9347280 -0.005212173
## X447 0 0.427774521 -0.40240913 0.16468846 0.3108484 -0.005212173
## X448 0 1.975155875 1.87027471 0.93811425 -0.1043438 3.299305521
## X451 0 -1.960986946 -0.96037479 -0.99545024 -0.5195359 -0.005212173
## X452 0 -0.455773295 -0.83728034 -0.02866799 -0.9347280 -0.831341597
## X453 0 -0.447297107 -0.40240913 0.93811425 -0.9347280 -0.831341597
## X454 0 1.024063318 0.82146772 1.51818360 0.7260405 0.820917251
## X455 0 0.366815837 0.12893412 0.16468846 0.3108484 -0.005212173
## X456 1 0.392161232 0.63244961 0.35804491 -0.1043438 0.820917251
## X458 0 0.922422855 0.63244961 1.51818360 0.7260405 0.820917251
## X459 0 -0.489295914 0.28325136 -0.99545024 1.5564248 -0.005212173
## X460 0 -1.632068261 -0.72058540 -0.99545024 -0.9347280 -0.005212173
## X461 0 -0.289953121 -0.83728034 0.16468846 -0.5195359 -0.005212173
## X462 0 -0.983309595 -0.83728034 -0.22202444 -0.5195359 -0.831341597
## X463 1 0.808360205 1.16359252 1.32482715 1.1412327 -0.005212173
## X464 0 0.243179485 -2.10721958 -1.18880668 -0.9347280 -0.831341597
## X465 0 0.736065616 0.94039386 1.13147070 0.7260405 -0.831341597
## X466 0 0.630729830 -0.12219740 0.35804491 -0.1043438 0.820917251
## X468 0 -0.254497849 0.28325136 -0.99545024 1.9716169 -0.005212173
## X471 0 -0.390166117 -0.12219740 0.16468846 -0.1043438 -0.005212173
## X472 0 -1.089862985 -0.72058540 -1.18880668 -0.1043438 -0.831341597
## X473 0 -1.960986946 -0.83728034 -1.18880668 -0.9347280 -0.831341597
## X476 0 0.071003132 0.12893412 1.13147070 -0.1043438 -0.005212173
## X477 0 0.601744921 0.42867850 0.55140136 -0.5195359 1.647046674
## X478 0 -1.632068261 -0.83728034 -0.80209379 0.3108484 0.820917251
## X479 0 -1.960986946 -0.96037479 -0.99545024 -0.1043438 -0.005212173
## X480 0 0.002838576 0.04803954 1.90489650 -0.9347280 -0.831341597
## X482 0 -0.507220812 -0.72058540 -1.18880668 -0.5195359 -0.831341597
## X483 0 -0.725281754 -1.09071695 -1.18880668 -0.5195359 -0.831341597
## X484 0 0.048980624 0.28325136 1.13147070 -0.5195359 -0.831341597
## X486 0 -0.267476312 0.35700394 -0.99545024 1.9716169 -0.005212173
## X487 0 0.808360205 1.21665476 0.16468846 2.8020012 -0.005212173
## X488 0 0.158871193 0.35700394 0.16468846 1.1412327 -0.005212173
## X489 0 0.667472628 -0.83728034 0.16468846 -0.5195359 -0.005212173
## X490 0 0.948173754 1.16359252 0.16468846 1.1412327 -0.005212173
## X491 0 -1.089862985 -0.72058540 -1.18880668 -0.1043438 -0.831341597
## X492 0 0.566721151 0.75995351 -0.41538089 -0.5195359 2.473176098
## X493 0 -0.267476312 0.35700394 -0.99545024 1.9716169 -0.005212173
## X494 0 0.611681349 -0.72058540 0.16468846 -0.5195359 -0.005212173
## X495 0 1.226628531 1.65364219 1.13147070 0.7260405 -0.005212173
## X496 0 -0.190792410 -0.72058540 0.35804491 -0.9347280 0.820917251
## X497 0 -0.008626296 0.12893412 1.90489650 -0.9347280 -0.831341597
## X498 0 -0.289288562 -0.40240913 -0.02866799 -0.9347280 -0.831341597
## X499 0 -1.098274791 -0.50369472 -0.02866799 -0.9347280 -0.831341597
## X501 0 0.774201646 -0.03559810 0.35804491 -0.5195359 0.820917251
## X502 0 -1.098274791 -0.50369472 -0.02866799 -0.9347280 -0.831341597
## X503 0 1.239546173 1.82822307 -0.02866799 -0.5195359 -0.831341597
## X505 0 -0.123326972 -0.40240913 0.16468846 -0.5195359 -0.005212173
## X506 0 0.800109202 0.56629095 1.51818360 0.3108484 0.820917251
## X507 0 0.995515874 1.10948462 1.13147070 1.1412327 -0.831341597
## X508 0 1.827201901 0.04803954 0.16468846 0.3108484 -0.005212173
## X509 0 1.881712881 1.99292450 0.93811425 -0.1043438 3.299305521
## X510 1 0.433604324 0.04803954 0.55140136 -0.5195359 1.647046674
## X513 0 -0.364519110 -0.72058540 -1.18880668 -0.5195359 -0.831341597
## X514 0 0.823597252 0.63244961 1.32482715 0.3108484 0.820917251
## X515 0 -0.242509175 -0.21200528 0.93811425 -0.9347280 -0.831341597
## X516 0 -0.404021657 -0.03559810 0.16468846 0.3108484 -0.005212173
## X518 0 0.915283282 1.16359252 0.35804491 0.7260405 0.820917251
## X521 0 1.134223355 0.88159159 1.51818360 1.1412327 0.820917251
## X523 1 -0.043759055 0.12893412 0.35804491 0.7260405 0.820917251
## X524 0 0.399810034 -0.12219740 0.16468846 -0.1043438 -0.005212173
## X525 0 0.686767950 0.94039386 -0.41538089 -0.1043438 2.473176098
## X526 0 -0.459952245 0.42867850 -1.18880668 1.9716169 -0.831341597
## X530 1 -0.389468783 0.20728011 -0.02866799 0.3108484 -0.831341597
## X531 0 0.430503397 0.82146772 0.16468846 0.7260405 -0.005212173
## X532 0 0.486632405 0.63244961 -0.02866799 1.1412327 -0.831341597
## X533 0 1.033797758 0.04803954 0.93811425 -0.5195359 3.299305521
## X534 1 0.736309194 0.69697444 0.55140136 1.1412327 1.647046674
## X535 0 -0.421224013 -1.22934392 -0.02866799 -0.9347280 -0.831341597
## X536 0 1.024487502 1.46773946 1.13147070 0.3108484 -0.005212173
## X538 0 1.079045894 0.75995351 1.51818360 -0.5195359 0.820917251
## X539 0 1.024487502 1.46773946 1.13147070 0.3108484 -0.005212173
## X542 0 1.445796891 1.91172984 -0.41538089 -0.1043438 2.473176098
## X543 0 -0.832540404 -0.40240913 -1.18880668 0.3108484 -0.831341597
## X544 0 1.881712881 1.99292450 0.93811425 -0.1043438 3.299305521
## X545 0 0.061817968 1.05428349 -1.18880668 2.8020012 -0.831341597
## X546 0 -0.107436062 -2.10721958 -1.18880668 -0.9347280 -0.831341597
## X548 0 -0.404021657 -0.03559810 0.16468846 -0.1043438 -0.005212173
## X549 0 0.436794393 -1.22934392 -0.02866799 -0.9347280 -0.831341597
## X551 0 1.271995992 -2.92387959 -1.18880668 -0.9347280 -0.831341597
## X552 0 1.731140385 1.91172984 1.32482715 0.7260405 -0.005212173
## X553 1 0.558159799 0.49840233 0.35804491 -0.1043438 0.820917251
## X554 0 0.605379378 0.42867850 0.16468846 0.7260405 -0.831341597
## X556 1 0.362642398 0.28325136 1.32482715 0.3108484 -0.005212173
## X557 0 1.062383808 1.21665476 0.16468846 1.9716169 -0.005212173
## X558 0 -0.152364404 -0.72058540 0.74475780 -0.9347280 -0.831341597
## X559 0 -1.901900752 -0.72058540 -1.18880668 -0.1043438 -0.831341597
## X560 0 -0.839972199 -0.21200528 -0.02866799 -0.9347280 -0.831341597
## X561 0 0.128651681 -1.22934392 -0.02866799 -0.9347280 -0.831341597
## X562 0 -0.839972199 -0.21200528 -0.02866799 -0.5195359 -0.831341597
## X563 1 0.343414497 0.42867850 1.32482715 0.3108484 -0.005212173
## X565 0 -1.581515202 -0.60958681 -0.99545024 0.3108484 -0.005212173
## X566 0 -0.218737027 -0.96037479 -0.02866799 -0.9347280 -0.831341597
## X567 0 1.133955099 0.69697444 0.55140136 0.3108484 1.647046674
## X568 0 0.774201646 -0.40240913 0.16468846 -0.5195359 -0.005212173
## X569 0 0.842661605 0.99793817 0.16468846 1.1412327 -0.005212173
## X571 0 0.418526237 -0.30530231 0.16468846 -0.1043438 -0.005212173
## X572 0 0.687183627 1.10948462 0.16468846 2.8020012 -0.005212173
## X574 0 -1.303931995 -0.40240913 -0.99545024 -0.9347280 -0.005212173
## X576 0 0.922422855 0.63244961 1.51818360 0.7260405 0.820917251
## X577 0 0.232450944 0.28325136 1.13147070 -0.1043438 -0.005212173
## X579 1 0.232450944 0.28325136 1.13147070 -0.1043438 -0.005212173
## X580 0 1.609081003 -0.72058540 0.16468846 -0.5195359 -0.005212173
## X582 0 -0.293545411 0.49840233 -0.99545024 1.9716169 -0.005212173
## X583 0 -0.839972199 -0.21200528 -0.02866799 -0.9347280 -0.831341597
## X584 0 1.289745203 1.74225056 0.35804491 -0.9347280 0.820917251
## X586 0 1.058701570 0.75995351 0.55140136 1.1412327 1.647046674
## X587 0 -0.008626296 0.12893412 1.90489650 -0.9347280 -0.831341597
## X588 0 0.619596479 0.75995351 -0.60873734 0.7260405 1.647046674
## X589 0 1.706734262 2.47286768 -0.99545024 0.7260405 -0.005212173
## X591 0 1.226628531 1.65364219 1.13147070 0.7260405 -0.005212173
## X592 1 -0.839972199 -0.21200528 -0.02866799 -0.1043438 -0.831341597
## X593 0 1.072631922 0.94039386 2.09825295 0.7260405 -0.831341597
## X594 0 -0.267476312 0.35700394 -0.99545024 1.9716169 -0.005212173
## X595 0 0.453788004 0.12893412 -0.80209379 1.1412327 0.820917251
## X596 0 0.847208104 0.88159159 0.55140136 1.1412327 1.647046674
## X597 0 0.915506765 1.31981693 1.32482715 0.3108484 -0.005212173
## X598 0 0.049545329 0.63244961 -0.80209379 2.8020012 0.820917251
## X599 0 -0.839972199 -0.21200528 -0.02866799 -0.9347280 -0.831341597
## X600 0 0.966789467 0.99793817 0.35804491 0.7260405 0.820917251
## X603 0 -0.090698960 0.56629095 -0.99545024 2.3868091 -0.005212173
## X604 0 0.720253413 0.82146772 -0.41538089 1.1412327 2.473176098
## X605 0 1.066475255 1.56220886 -0.41538089 -0.9347280 2.473176098
## X606 1 -0.020037904 0.28325136 0.16468846 1.1412327 -0.005212173
## X608 0 0.563194962 -1.22934392 -0.02866799 -0.9347280 -0.831341597
## X609 0 0.686601657 0.35700394 1.51818360 0.3108484 0.820917251
## X611 0 -1.260676413 -0.21200528 -1.18880668 -0.9347280 -0.831341597
## X612 0 0.676599640 0.12893412 0.16468846 -0.1043438 -0.005212173
## X613 0 -0.105975307 -0.83728034 -0.02866799 -0.9347280 -0.831341597
## X614 0 -0.732339628 -0.83728034 -0.02866799 -0.9347280 -0.831341597
## X616 0 -1.532160955 -0.40240913 -1.18880668 -0.5195359 -0.831341597
## X617 0 0.854891424 1.21665476 1.13147070 1.1412327 -0.005212173
## X619 1 1.771027243 1.26871571 1.90489650 0.3108484 2.473176098
## X620 0 0.016880687 -1.22934392 -0.02866799 -0.9347280 -0.831341597
## X621 1 0.353099452 0.35700394 1.32482715 -0.1043438 -0.005212173
## X622 0 -0.706360421 -0.40240913 0.93811425 -0.9347280 -0.831341597
## X623 0 1.205416250 0.69697444 1.51818360 -0.5195359 0.820917251
## X625 0 1.019887558 0.94039386 1.13147070 1.1412327 -0.005212173
## X628 0 1.622913686 2.03269881 -0.41538089 -0.1043438 2.473176098
## X629 0 1.623602913 2.43853015 -0.99545024 0.7260405 -0.005212173
## X630 0 0.816422389 1.31981693 1.13147070 0.7260405 -0.831341597
## X631 0 -1.020552429 -0.21200528 -0.99545024 0.7260405 -0.831341597
## X632 0 0.570417230 -2.10721958 -1.18880668 -0.9347280 -0.831341597
## X633 0 0.676516088 0.12893412 0.16468846 1.1412327 -0.005212173
## X635 0 1.141453232 1.26871571 0.55140136 0.3108484 1.647046674
## X636 0 1.633333725 1.95260717 -0.41538089 -0.1043438 2.473176098
## X637 0 0.967298146 1.60829128 -0.60873734 -0.9347280 1.647046674
## X638 1 0.719516934 0.75995351 1.51818360 0.7260405 0.820917251
## X639 0 0.686601657 0.35700394 1.51818360 0.3108484 0.820917251
## X641 1 1.226307769 1.41929339 1.51818360 1.1412327 0.820917251
## X648 0 1.412917599 1.05428349 1.71154005 0.3108484 1.647046674
## X650 0 0.752403196 0.28325136 1.13147070 0.3108484 0.820917251
## X651 1 1.121037974 1.36999732 1.51818360 1.1412327 0.820917251
## X653 0 1.623602913 2.43853015 -0.99545024 0.7260405 -0.005212173
## X654 0 1.017548306 1.51536781 0.16468846 3.6323855 -0.005212173
## X655 1 -0.610215946 0.04803954 -0.02866799 -0.1043438 -0.831341597
## X656 0 -0.211043577 -0.40240913 0.93811425 -0.9347280 -0.831341597
## X657 0 0.430503397 0.82146772 0.16468846 1.9716169 -0.005212173
## X1082 0 -1.089862985 -0.72058540 -1.18880668 -0.5195359 -0.831341597
## X1083 1 0.201609653 0.49840233 1.13147070 0.3108484 -0.831341597
## X1084 0 -0.293545411 0.56629095 -1.18880668 -0.5195359 -0.831341597
## X1086 1 -0.284112271 -1.22934392 -0.02866799 -0.9347280 -0.831341597
## X1088 0 0.366912794 0.12893412 0.16468846 -0.1043438 -0.005212173
## X1089 0 0.094121874 0.56629095 0.74475780 0.3108484 -0.831341597
## X1090 0 0.014240641 0.04803954 0.16468846 0.3108484 -0.005212173
## X1091 0 0.159406860 0.63244961 -0.02866799 1.1412327 -0.831341597
## X1092 0 -0.489295914 0.28325136 -0.99545024 1.5564248 -0.005212173
## X1093 0 0.188446950 -0.60958681 -0.80209379 -0.9347280 0.820917251
## X1094 0 -0.580658068 -0.50369472 0.16468846 -0.5195359 -0.005212173
## X1095 0 -0.419242736 -0.60958681 0.35804491 -0.9347280 0.820917251
## X1097 0 -1.089862985 -0.72058540 -1.18880668 -0.1043438 -0.831341597
## X1098 0 0.784301940 1.05428349 -0.41538089 -0.1043438 2.473176098
## X1101 0 1.559218908 0.42867850 0.74475780 -0.5195359 2.473176098
## X1103 0 1.065435819 0.94039386 0.74475780 -0.9347280 2.473176098
## X1104 0 0.678353466 0.42867850 1.51818360 0.3108484 0.820917251
## X1105 0 -0.190792410 -0.72058540 0.35804491 -0.9347280 0.820917251
## X1106 0 -0.688575293 0.28325136 -1.18880668 1.5564248 -0.831341597
## X1108 0 -1.098274791 -0.50369472 -0.02866799 -0.9347280 -0.831341597
## X1110 1 0.260904394 -1.22934392 -0.02866799 -0.9347280 -0.831341597
## X1112 0 0.800109202 0.56629095 1.51818360 0.3108484 0.820917251
## X1113 0 0.495127837 0.75995351 1.13147070 -0.1043438 -0.831341597
## X1115 1 0.343414497 0.42867850 1.32482715 0.3108484 -0.005212173
## X1116 0 0.184958063 0.20728011 0.16468846 -0.1043438 -0.005212173
## X1117 0 -0.362866384 -0.30530231 0.16468846 -0.1043438 -0.005212173
## X1119 0 0.729152370 -0.40240913 0.16468846 0.3108484 -0.005212173
## X1120 0 1.457427050 1.99292450 -0.60873734 -0.1043438 1.647046674
## X1121 0 1.086675495 1.16359252 0.55140136 0.3108484 1.647046674
## X1122 0 1.525264217 2.03269881 -0.41538089 -0.1043438 2.473176098
## X1124 0 -0.092028152 -0.12219740 0.55140136 -0.9347280 1.647046674
## X1125 0 0.083816857 -2.10721958 -1.18880668 -0.9347280 -0.831341597
## X1126 0 -0.421224013 -1.22934392 -0.02866799 -0.9347280 -0.831341597
## X1127 0 -0.875243942 -0.30530231 -0.02866799 -0.9347280 -0.831341597
## X1128 0 0.361087352 -0.40240913 0.16468846 -0.5195359 -0.005212173
## X1129 0 -0.732339628 -0.83728034 -0.02866799 -0.9347280 -0.831341597
## X1130 0 0.594543822 -0.50369472 0.16468846 -0.1043438 -0.005212173
## X1131 0 -1.581515202 -0.50369472 -1.18880668 -0.9347280 -0.831341597
## X1133 1 0.813999190 0.04803954 0.55140136 -0.5195359 1.647046674
## X1135 0 -0.489295914 0.28325136 -0.99545024 1.9716169 -0.005212173
## X1136 0 -0.105975307 -0.83728034 -0.02866799 -0.9347280 -0.831341597
## X1138 0 2.722777775 3.22789945 0.16468846 0.3108484 4.951564368
## X1139 0 1.445796891 1.91172984 -0.41538089 -0.1043438 2.473176098
## X1141 0 -1.581515202 -0.60958681 -0.99545024 -0.1043438 -0.005212173
## X1142 0 -0.421224013 -1.22934392 -0.02866799 -0.9347280 -0.831341597
## X1143 1 1.213307444 1.31981693 1.71154005 1.1412327 1.647046674
## X1144 0 0.959436086 1.31981693 0.16468846 -0.9347280 -0.005212173
## X1145 0 0.991282387 0.56629095 0.55140136 -0.1043438 1.647046674
## X1146 0 -0.078774283 0.49840233 -0.99545024 2.3868091 -0.005212173
## X1147 0 0.254569455 0.69697444 -0.99545024 1.9716169 -0.005212173
## X1149 0 0.357292051 0.20728011 0.16468846 0.3108484 -0.005212173
## X1150 0 -0.090698960 0.56629095 -0.99545024 2.3868091 -0.005212173
## X1151 0 0.373978500 0.82146772 -0.99545024 0.7260405 -0.005212173
## X1152 0 0.959436086 1.21665476 0.55140136 0.3108484 1.647046674
## X1153 0 2.401813942 -1.53694587 -0.22202444 -0.9347280 -0.831341597
## X1156 0 0.072232210 0.75995351 -0.99545024 2.8020012 -0.005212173
## X1158 0 0.980480348 0.82146772 1.32482715 -0.5195359 -0.005212173
## X1159 0 0.381694291 0.20728011 1.13147070 -0.5195359 0.820917251
## X1160 0 1.705409579 1.56220886 2.09825295 1.1412327 3.299305521
## NumCarbon NumNitrogen NumOxygen NumSulfer NumChlorine NumHalogen
## X661 0.85821946 1.0008314 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X662 1.80408084 1.8438701 -0.3320280 1.7123815 -0.3972472 -0.4741055
## X663 0.70131917 -0.6852460 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X665 0.18177643 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X668 -0.01199386 3.5299475 -0.9103405 -0.3360145 0.3168966 0.2049221
## X669 0.18177643 0.1577927 -0.3320280 1.7123815 1.0310404 0.8839497
## X670 1.29203392 2.6869088 -0.9103405 -0.3360145 1.0310404 0.8839497
## X671 0.53699786 -0.6852460 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X672 1.92274051 -0.6852460 1.4029096 -0.3360145 -0.3972472 0.2049221
## X673 0.85821946 1.0008314 -0.3320280 -0.3360145 -0.3972472 -0.4741055
## X674 0.85821946 -0.6852460 0.8245970 -0.3360145 -0.3972472 -0.4741055
## X676 1.55615914 -0.6852460 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X677 0.53699786 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X678 0.18177643 -0.6852460 -0.9103405 -0.3360145 0.3168966 0.2049221
## X679 0.36423857 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X682 0.85821946 -0.6852460 0.8245970 -0.3360145 -0.3972472 -0.4741055
## X683 0.70131917 2.6869088 0.8245970 1.7123815 -0.3972472 -0.4741055
## X684 1.80408084 1.8438701 -0.3320280 1.7123815 0.3168966 0.2049221
## X685 1.55615914 -0.6852460 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X686 0.53699786 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X688 1.00853037 -0.6852460 0.8245970 -0.3360145 0.3168966 0.2049221
## X689 1.55615914 1.0008314 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X690 1.29203392 0.1577927 0.2462845 -0.3360145 0.3168966 0.2049221
## X691 0.18177643 2.6869088 0.2462845 -0.3360145 3.8876154 3.6000599
## X692 0.85821946 0.1577927 1.4029096 5.8091734 -0.3972472 -0.4741055
## X693 0.85821946 1.0008314 0.8245970 1.7123815 -0.3972472 -0.4741055
## X695 1.55615914 1.0008314 -0.3320280 1.7123815 -0.3972472 -0.4741055
## X696 0.70131917 1.0008314 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X698 1.15294194 0.1577927 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X699 -0.44251753 0.1577927 -0.9103405 -0.3360145 1.0310404 0.8839497
## X700 -0.01199386 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X702 -0.44251753 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X703 -0.21915966 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X704 0.53699786 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X706 1.00853037 -0.6852460 0.8245970 -0.3360145 -0.3972472 -0.4741055
## X708 0.53699786 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X709 -0.21915966 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X711 2.15069776 -0.6852460 1.9812221 -0.3360145 -0.3972472 -0.4741055
## X712 1.42629884 -0.6852460 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X713 0.85821946 0.1577927 0.2462845 -0.3360145 -0.3972472 1.5629772
## X714 2.03820634 -0.6852460 2.5595346 -0.3360145 -0.3972472 -0.4741055
## X715 0.36423857 0.1577927 0.2462845 -0.3360145 1.0310404 0.8839497
## X717 0.18177643 -0.6852460 -0.9103405 -0.3360145 -0.3972472 0.2049221
## X718 1.68198027 1.8438701 -0.9103405 1.7123815 0.3168966 0.2049221
## X721 -0.01199386 3.5299475 -0.9103405 -0.3360145 0.3168966 0.2049221
## X722 1.55615914 0.1577927 -0.3320280 -0.3360145 -0.3972472 1.5629772
## X723 -0.21915966 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X724 0.53699786 1.0008314 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X726 0.53699786 -0.6852460 0.2462845 -0.3360145 1.7451841 1.5629772
## X728 1.00853037 -0.6852460 0.2462845 -0.3360145 -0.3972472 0.2049221
## X729 -0.68595798 -0.6852460 -0.9103405 -0.3360145 -0.3972472 1.5629772
## X731 -0.44251753 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X732 0.53699786 -0.6852460 -0.9103405 -0.3360145 0.3168966 0.2049221
## X733 -0.44251753 3.5299475 -0.9103405 -0.3360145 0.3168966 0.2049221
## X734 -0.68595798 -0.6852460 -0.9103405 -0.3360145 2.4593279 2.2420048
## X735 1.68198027 -0.6852460 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X736 0.85821946 0.1577927 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X737 0.36423857 0.1577927 -0.9103405 1.7123815 -0.3972472 -0.4741055
## X739 1.29203392 -0.6852460 2.5595346 -0.3360145 0.3168966 0.2049221
## X740 1.55615914 0.1577927 1.4029096 -0.3360145 0.3168966 0.2049221
## X741 0.53699786 -0.6852460 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X742 0.36423857 -0.6852460 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X743 -0.68595798 -0.6852460 -0.9103405 -0.3360145 2.4593279 2.2420048
## X744 0.53699786 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X746 1.15294194 -0.6852460 1.4029096 -0.3360145 -0.3972472 -0.4741055
## X747 0.53699786 -0.6852460 -0.3320280 -0.3360145 -0.3972472 -0.4741055
## X749 2.03820634 1.8438701 0.2462845 1.7123815 0.3168966 0.2049221
## X752 2.47218708 -0.6852460 2.5595346 -0.3360145 -0.3972472 0.2049221
## X753 -0.21915966 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X754 1.55615914 1.0008314 -0.9103405 1.7123815 -0.3972472 -0.4741055
## X755 0.53699786 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X757 -0.44251753 -0.6852460 -0.9103405 -0.3360145 -0.3972472 0.2049221
## X758 0.85821946 -0.6852460 -0.3320280 -0.3360145 -0.3972472 -0.4741055
## X759 0.18177643 1.0008314 -0.9103405 7.8575693 -0.3972472 -0.4741055
## X760 0.53699786 -0.6852460 -0.9103405 -0.3360145 0.3168966 0.2049221
## X761 2.15069776 -0.6852460 2.5595346 -0.3360145 -0.3972472 0.2049221
## X762 0.70131917 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X763 0.53699786 1.0008314 -0.9103405 -0.3360145 1.0310404 0.8839497
## X764 0.70131917 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X765 1.29203392 -0.6852460 0.8245970 -0.3360145 -0.3972472 0.8839497
## X767 2.03820634 -0.6852460 1.4029096 -0.3360145 0.3168966 0.2049221
## X768 0.53699786 0.1577927 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X770 1.29203392 1.0008314 -0.9103405 1.7123815 0.3168966 0.2049221
## X771 0.53699786 0.1577927 0.8245970 -0.3360145 1.7451841 1.5629772
## X772 -0.68595798 -0.6852460 -0.9103405 -0.3360145 -0.3972472 1.5629772
## X773 -0.01199386 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X774 -0.21915966 -0.6852460 -0.9103405 -0.3360145 -0.3972472 0.2049221
## X775 1.15294194 -0.6852460 0.8245970 -0.3360145 -0.3972472 -0.4741055
## X776 2.03820634 1.8438701 1.9812221 1.7123815 0.3168966 0.2049221
## X777 0.53699786 -0.6852460 -0.3320280 5.8091734 -0.3972472 -0.4741055
## X778 2.36752103 0.1577927 2.5595346 -0.3360145 -0.3972472 -0.4741055
## X779 0.85821946 0.1577927 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X780 -0.95516548 -0.6852460 -0.9103405 -0.3360145 3.8876154 3.6000599
## X781 1.55615914 -0.6852460 0.8245970 -0.3360145 -0.3972472 -0.4741055
## X782 0.85821946 -0.6852460 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X784 1.00853037 0.1577927 1.4029096 -0.3360145 -0.3972472 1.5629772
## X786 -0.21915966 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X787 0.53699786 -0.6852460 -0.9103405 -0.3360145 1.0310404 0.8839497
## X788 2.03820634 -0.6852460 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X789 0.53699786 -0.6852460 -0.9103405 -0.3360145 1.0310404 0.8839497
## X791 0.53699786 -0.6852460 -0.9103405 -0.3360145 1.0310404 0.8839497
## X792 1.42629884 1.0008314 -0.9103405 1.7123815 -0.3972472 1.5629772
## X794 0.85821946 -0.6852460 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X798 1.42629884 1.0008314 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X799 0.18177643 0.1577927 0.2462845 1.7123815 2.4593279 2.2420048
## X800 1.55615914 -0.6852460 -0.3320280 1.7123815 -0.3972472 -0.4741055
## X804 1.55615914 1.8438701 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X805 2.47218708 -0.6852460 2.5595346 -0.3360145 -0.3972472 -0.4741055
## X807 -0.01199386 -0.6852460 1.4029096 7.8575693 -0.3972472 -0.4741055
## X808 1.80408084 0.1577927 1.4029096 -0.3360145 -0.3972472 -0.4741055
## X809 1.55615914 -0.6852460 1.4029096 -0.3360145 -0.3972472 -0.4741055
## X810 0.18177643 -0.6852460 -0.9103405 -0.3360145 3.8876154 3.6000599
## X813 1.42629884 -0.6852460 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X814 1.00853037 1.0008314 0.8245970 -0.3360145 1.0310404 0.8839497
## X818 0.53699786 -0.6852460 -0.9103405 -0.3360145 1.7451841 1.5629772
## X819 0.85821946 1.0008314 0.2462845 -0.3360145 0.3168966 1.5629772
## X820 0.85821946 -0.6852460 -0.3320280 -0.3360145 -0.3972472 -0.4741055
## X821 0.53699786 -0.6852460 -0.9103405 -0.3360145 1.7451841 1.5629772
## X822 1.15294194 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X823 1.42629884 0.1577927 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X827 0.53699786 -0.6852460 -0.3320280 -0.3360145 3.8876154 3.6000599
## X828 0.53699786 -0.6852460 -0.9103405 -0.3360145 1.7451841 1.5629772
## X829 0.85821946 0.1577927 1.4029096 3.7607774 0.3168966 0.2049221
## X831 0.85821946 -0.6852460 -0.9103405 -0.3360145 2.4593279 2.2420048
## X832 0.53699786 -0.6852460 -0.9103405 -0.3360145 1.0310404 0.8839497
## X833 0.53699786 -0.6852460 -0.9103405 -0.3360145 2.4593279 2.2420048
## X834 0.85821946 -0.6852460 -0.9103405 -0.3360145 2.4593279 2.2420048
## X835 0.53699786 -0.6852460 -0.9103405 -0.3360145 1.0310404 0.8839497
## X836 0.53699786 -0.6852460 -0.9103405 -0.3360145 2.4593279 2.2420048
## X839 1.29203392 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X840 1.42629884 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X841 0.53699786 -0.6852460 -0.9103405 -0.3360145 2.4593279 2.2420048
## X842 1.15294194 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X843 0.85821946 -0.6852460 -0.9103405 -0.3360145 2.4593279 2.2420048
## X846 1.42629884 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X848 0.53699786 -0.6852460 -0.9103405 -0.3360145 3.1734717 2.9210324
## X849 0.53699786 -0.6852460 -0.9103405 -0.3360145 2.4593279 2.2420048
## X851 2.47218708 -0.6852460 0.8245970 -0.3360145 -0.3972472 -0.4741055
## X854 0.53699786 -0.6852460 -0.9103405 -0.3360145 2.4593279 2.2420048
## X855 1.68198027 0.1577927 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X856 0.53699786 -0.6852460 -0.9103405 -0.3360145 3.8876154 3.6000599
## X857 0.53699786 -0.6852460 -0.9103405 -0.3360145 3.1734717 2.9210324
## X858 0.53699786 -0.6852460 -0.9103405 -0.3360145 3.8876154 3.6000599
## X859 0.53699786 -0.6852460 -0.9103405 -0.3360145 3.8876154 3.6000599
## X860 0.53699786 -0.6852460 -0.9103405 -0.3360145 2.4593279 2.2420048
## X862 0.53699786 -0.6852460 -0.9103405 -0.3360145 3.1734717 2.9210324
## X863 0.53699786 -0.6852460 -0.9103405 -0.3360145 4.6017592 4.2790875
## X864 1.80408084 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X865 1.68198027 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X866 0.53699786 -0.6852460 -0.9103405 -0.3360145 3.8876154 3.6000599
## X867 1.68198027 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X869 1.92274051 1.8438701 -0.9103405 -0.3360145 -0.3972472 1.5629772
## X870 0.53699786 -0.6852460 -0.9103405 -0.3360145 3.8876154 3.6000599
## X871 0.53699786 -0.6852460 -0.9103405 -0.3360145 3.8876154 3.6000599
## X872 0.53699786 -0.6852460 -0.9103405 -0.3360145 3.8876154 3.6000599
## X873 1.68198027 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X875 0.53699786 -0.6852460 -0.9103405 -0.3360145 5.3159030 4.9581151
## X876 0.53699786 -0.6852460 -0.9103405 -0.3360145 5.3159030 4.9581151
## X877 0.53699786 -0.6852460 -0.9103405 -0.3360145 6.7441905 6.3161702
## X1190 0.53699786 -0.6852460 -0.3320280 -0.3360145 -0.3972472 -0.4741055
## X1191 -0.44251753 -0.6852460 -0.9103405 -0.3360145 0.3168966 0.2049221
## X1192 1.68198027 -0.6852460 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X1193 0.36423857 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X1194 2.03820634 -0.6852460 2.5595346 -0.3360145 -0.3972472 -0.4741055
## X1195 -0.68595798 -0.6852460 -0.9103405 -0.3360145 1.7451841 1.5629772
## X1197 0.18177643 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X1198 -0.68595798 -0.6852460 -0.9103405 -0.3360145 -0.3972472 0.8839497
## X1199 0.18177643 3.5299475 -0.9103405 1.7123815 -0.3972472 -0.4741055
## X1200 -0.44251753 -0.6852460 0.2462845 5.8091734 -0.3972472 -0.4741055
## X1201 1.80408084 0.1577927 2.5595346 -0.3360145 -0.3972472 -0.4741055
## X1202 2.26041072 -0.6852460 3.7161597 -0.3360145 -0.3972472 0.2049221
## X1203 -0.21915966 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X1204 1.00853037 1.8438701 1.4029096 1.7123815 -0.3972472 -0.4741055
## X1205 0.70131917 1.0008314 0.2462845 -0.3360145 -0.3972472 1.5629772
## X1206 -1.25901822 -0.6852460 -0.9103405 -0.3360145 3.1734717 2.9210324
## X1207 1.29203392 1.0008314 -0.9103405 1.7123815 -0.3972472 -0.4741055
## X1208 2.15069776 -0.6852460 1.4029096 1.7123815 -0.3972472 -0.4741055
## X1209 -0.68595798 -0.6852460 -0.3320280 -0.3360145 3.1734717 2.9210324
## X1210 2.15069776 -0.6852460 1.4029096 -0.3360145 -0.3972472 -0.4741055
## X1212 1.68198027 -0.6852460 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X1213 1.29203392 1.0008314 -0.9103405 1.7123815 -0.3972472 -0.4741055
## X1215 2.15069776 -0.6852460 2.5595346 -0.3360145 -0.3972472 0.2049221
## X1216 0.53699786 -0.6852460 -0.9103405 1.7123815 -0.3972472 -0.4741055
## X1217 1.29203392 1.0008314 -0.3320280 -0.3360145 1.0310404 0.8839497
## X1219 1.42629884 -0.6852460 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X1220 1.80408084 0.1577927 0.2462845 -0.3360145 0.3168966 0.8839497
## X1221 -0.44251753 -0.6852460 -0.9103405 -0.3360145 -0.3972472 0.2049221
## X1222 1.68198027 0.1577927 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X1226 1.80408084 1.8438701 -0.9103405 1.7123815 -0.3972472 1.5629772
## X1228 0.18177643 -0.6852460 0.8245970 3.7607774 -0.3972472 -0.4741055
## X1229 2.36752103 -0.6852460 2.5595346 -0.3360145 -0.3972472 -0.4741055
## X1230 0.85821946 0.1577927 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X1231 0.85821946 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X1233 1.80408084 -0.6852460 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X1234 0.53699786 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X1236 1.92274051 -0.6852460 0.8245970 -0.3360145 -0.3972472 -0.4741055
## X1237 -0.44251753 0.1577927 0.8245970 1.7123815 1.7451841 1.5629772
## X1239 0.18177643 0.1577927 -0.3320280 1.7123815 1.7451841 1.5629772
## X1242 -1.25901822 -0.6852460 -0.9103405 -0.3360145 3.8876154 3.6000599
## X1244 0.53699786 -0.6852460 -0.9103405 -0.3360145 0.3168966 0.2049221
## X1245 0.53699786 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X1246 1.42629884 -0.6852460 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X1247 2.03820634 -0.6852460 0.8245970 -0.3360145 -0.3972472 -0.4741055
## X1249 0.85821946 -0.6852460 1.9812221 1.7123815 0.3168966 0.2049221
## X1250 0.18177643 -0.6852460 -0.3320280 -0.3360145 3.8876154 3.6000599
## X1251 -0.21915966 1.0008314 -0.9103405 -0.3360145 2.4593279 2.2420048
## X1253 0.36423857 -0.6852460 0.2462845 5.8091734 0.3168966 0.2049221
## X1254 0.53699786 -0.6852460 -0.9103405 -0.3360145 1.0310404 0.8839497
## X1255 1.00853037 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X1256 1.15294194 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X1257 0.53699786 -0.6852460 -0.9103405 -0.3360145 1.7451841 1.5629772
## X1259 0.53699786 -0.6852460 -0.3320280 -0.3360145 3.8876154 3.6000599
## X1260 0.53699786 -0.6852460 -0.9103405 -0.3360145 1.7451841 1.5629772
## X1262 1.80408084 -0.6852460 0.8245970 -0.3360145 1.0310404 0.8839497
## X1264 0.18177643 -0.6852460 -0.9103405 -0.3360145 4.6017592 4.2790875
## X1265 0.53699786 -0.6852460 -0.9103405 -0.3360145 2.4593279 2.2420048
## X1266 0.85821946 -0.6852460 -0.9103405 -0.3360145 3.1734717 2.9210324
## X1267 1.80408084 -0.6852460 3.1378471 -0.3360145 -0.3972472 -0.4741055
## X1268 1.15294194 -0.6852460 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X1273 0.53699786 -0.6852460 -0.9103405 -0.3360145 2.4593279 2.2420048
## X1274 1.15294194 -0.6852460 -0.3320280 -0.3360145 -0.3972472 -0.4741055
## X1275 0.53699786 -0.6852460 -0.9103405 -0.3360145 3.8876154 3.6000599
## X1276 1.68198027 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X1277 0.53699786 -0.6852460 -0.9103405 -0.3360145 3.1734717 2.9210324
## X1278 1.29203392 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X1279 1.42629884 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X1281 0.53699786 -0.6852460 -0.9103405 -0.3360145 3.8876154 3.6000599
## X1282 0.53699786 -0.6852460 -0.9103405 -0.3360145 3.8876154 3.6000599
## X1283 1.68198027 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X1284 1.42629884 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X1285 0.53699786 -0.6852460 -0.9103405 -0.3360145 3.8876154 3.6000599
## X1288 0.53699786 -0.6852460 -0.9103405 -0.3360145 6.0300467 5.6371426
## X1299 1.00853037 1.0008314 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X1301 1.55615914 -0.6852460 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X1302 -0.68595798 -0.6852460 -0.9103405 -0.3360145 3.8876154 3.6000599
## X1307 -0.01199386 0.1577927 0.8245970 1.7123815 1.7451841 1.5629772
## X1309 0.85821946 -0.6852460 -0.9103405 -0.3360145 3.1734717 2.9210324
## X1310 0.18177643 -0.6852460 -0.9103405 -0.3360145 5.3159030 4.9581151
## X447 -0.21915966 -0.6852460 0.8245970 -0.3360145 1.0310404 0.8839497
## X448 1.80408084 1.0008314 3.7161597 -0.3360145 0.3168966 0.2049221
## X451 -0.95516548 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X452 -0.44251753 -0.6852460 -0.9103405 -0.3360145 0.3168966 0.8839497
## X453 -0.01199386 0.1577927 -0.3320280 -0.3360145 -0.3972472 -0.4741055
## X454 0.53699786 2.6869088 0.8245970 1.7123815 -0.3972472 -0.4741055
## X455 0.18177643 -0.6852460 0.8245970 -0.3360145 0.3168966 0.2049221
## X456 0.70131917 0.1577927 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X458 0.36423857 2.6869088 0.8245970 1.7123815 -0.3972472 -0.4741055
## X459 -0.01199386 -0.6852460 -0.3320280 -0.3360145 -0.3972472 -0.4741055
## X460 -0.68595798 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X461 -0.44251753 -0.6852460 0.2462845 -0.3360145 0.3168966 0.2049221
## X462 -0.68595798 -0.6852460 -0.9103405 1.7123815 -0.3972472 -0.4741055
## X463 1.29203392 1.8438701 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X464 -2.04708364 -0.6852460 -0.9103405 -0.3360145 3.1734717 2.9210324
## X465 1.00853037 1.0008314 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X466 -0.01199386 0.1577927 0.8245970 1.7123815 0.3168966 0.2049221
## X468 -0.21915966 0.1577927 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X471 -0.01199386 0.1577927 -0.3320280 -0.3360145 -0.3972472 -0.4741055
## X472 -0.95516548 -0.6852460 -0.9103405 -0.3360145 0.3168966 0.2049221
## X473 -0.95516548 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X476 0.53699786 -0.6852460 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X477 0.18177643 1.0008314 0.8245970 1.7123815 -0.3972472 -0.4741055
## X478 -0.68595798 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X479 -0.95516548 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X480 0.53699786 1.0008314 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X482 -0.95516548 -0.6852460 -0.9103405 -0.3360145 1.0310404 0.8839497
## X483 -1.25901822 -0.6852460 -0.9103405 -0.3360145 1.0310404 0.8839497
## X484 0.53699786 1.0008314 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X486 -0.01199386 -0.6852460 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X487 1.00853037 0.1577927 0.8245970 -0.3360145 -0.3972472 -0.4741055
## X488 0.36423857 -0.6852460 0.8245970 -0.3360145 -0.3972472 -0.4741055
## X489 -0.44251753 -0.6852460 0.2462845 -0.3360145 -0.3972472 0.2049221
## X490 1.00853037 0.1577927 0.2462845 -0.3360145 0.3168966 0.2049221
## X491 -0.95516548 -0.6852460 -0.9103405 -0.3360145 0.3168966 0.2049221
## X492 0.53699786 1.0008314 0.8245970 -0.3360145 -0.3972472 -0.4741055
## X493 -0.01199386 -0.6852460 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X494 -0.68595798 1.0008314 0.2462845 -0.3360145 1.7451841 1.5629772
## X495 1.68198027 1.0008314 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X496 -0.68595798 2.6869088 -0.9103405 1.7123815 -0.3972472 -0.4741055
## X497 0.70131917 0.1577927 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X498 -0.21915966 -0.6852460 -0.3320280 -0.3360145 0.3168966 0.2049221
## X499 -0.21915966 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X501 -0.01199386 1.0008314 0.8245970 -0.3360145 1.0310404 0.8839497
## X502 -0.21915966 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X503 1.68198027 1.0008314 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X505 -0.21915966 0.1577927 -0.3320280 -0.3360145 0.3168966 0.2049221
## X506 0.36423857 2.6869088 0.2462845 1.7123815 -0.3972472 -0.4741055
## X507 0.85821946 2.6869088 0.8245970 -0.3360145 -0.3972472 -0.4741055
## X508 -0.01199386 0.1577927 0.8245970 -0.3360145 -0.3972472 0.8839497
## X509 1.92274051 1.0008314 3.7161597 -0.3360145 -0.3972472 -0.4741055
## X510 0.18177643 1.8438701 -0.3320280 -0.3360145 0.3168966 0.2049221
## X513 -0.95516548 -0.6852460 -0.9103405 -0.3360145 -0.3972472 0.2049221
## X514 0.36423857 1.8438701 0.8245970 1.7123815 -0.3972472 -0.4741055
## X515 0.18177643 -0.6852460 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X516 0.18177643 -0.6852460 -0.3320280 -0.3360145 -0.3972472 -0.4741055
## X518 0.85821946 1.8438701 0.8245970 -0.3360145 -0.3972472 -0.4741055
## X521 0.53699786 2.6869088 1.4029096 1.7123815 -0.3972472 -0.4741055
## X523 0.36423857 -0.6852460 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X524 -0.01199386 0.1577927 -0.3320280 -0.3360145 1.0310404 0.8839497
## X525 0.70131917 1.0008314 0.8245970 -0.3360145 -0.3972472 -0.4741055
## X526 -0.01199386 -0.6852460 -0.3320280 -0.3360145 -0.3972472 -0.4741055
## X530 0.18177643 0.1577927 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X531 0.70131917 0.1577927 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X532 -0.01199386 3.5299475 -0.9103405 1.7123815 -0.3972472 -0.4741055
## X533 -0.44251753 1.8438701 1.4029096 3.7607774 0.3168966 0.2049221
## X534 0.36423857 1.0008314 0.8245970 1.7123815 -0.3972472 -0.4741055
## X535 -0.68595798 -0.6852460 -0.9103405 -0.3360145 1.0310404 0.8839497
## X536 1.55615914 1.0008314 -0.3320280 -0.3360145 -0.3972472 -0.4741055
## X538 1.00853037 -0.6852460 3.1378471 -0.3360145 -0.3972472 -0.4741055
## X539 1.55615914 1.0008314 -0.3320280 -0.3360145 -0.3972472 -0.4741055
## X542 1.80408084 -0.6852460 1.9812221 -0.3360145 -0.3972472 -0.4741055
## X543 -0.68595798 -0.6852460 -0.9103405 -0.3360145 0.3168966 0.2049221
## X544 1.92274051 1.0008314 3.7161597 -0.3360145 -0.3972472 -0.4741055
## X545 0.53699786 0.1577927 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X546 -2.04708364 -0.6852460 -0.9103405 -0.3360145 1.0310404 3.6000599
## X548 0.18177643 -0.6852460 -0.3320280 -0.3360145 -0.3972472 -0.4741055
## X549 -0.68595798 -0.6852460 -0.9103405 -0.3360145 -0.3972472 0.8839497
## X551 -2.64432555 -0.6852460 -0.9103405 -0.3360145 -0.3972472 2.2420048
## X552 1.92274051 0.1577927 3.1378471 -0.3360145 -0.3972472 -0.4741055
## X553 0.53699786 0.1577927 0.2462845 1.7123815 -0.3972472 -0.4741055
## X554 -0.01199386 4.3729862 -0.9103405 -0.3360145 0.3168966 0.2049221
## X556 0.70131917 -0.6852460 0.8245970 -0.3360145 -0.3972472 -0.4741055
## X557 0.85821946 1.8438701 0.2462845 -0.3360145 0.3168966 0.2049221
## X558 -0.44251753 0.1577927 -0.9103405 3.7607774 -0.3972472 -0.4741055
## X559 -0.95516548 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X560 -0.01199386 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X561 -0.68595798 -0.6852460 -0.9103405 -0.3360145 0.3168966 0.8839497
## X562 -0.01199386 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X563 0.85821946 -0.6852460 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X565 -0.68595798 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X566 -0.68595798 0.1577927 -0.9103405 -0.3360145 1.0310404 0.8839497
## X567 0.36423857 1.0008314 0.8245970 1.7123815 -0.3972472 1.5629772
## X568 -0.21915966 0.1577927 -0.3320280 -0.3360145 -0.3972472 0.2049221
## X569 0.85821946 0.1577927 0.2462845 -0.3360145 0.3168966 0.2049221
## X571 -0.21915966 0.1577927 0.2462845 -0.3360145 1.0310404 0.8839497
## X572 0.85821946 1.0008314 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X574 -0.44251753 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X576 0.36423857 2.6869088 0.8245970 1.7123815 -0.3972472 -0.4741055
## X577 0.53699786 0.1577927 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X579 0.53699786 0.1577927 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X580 -0.44251753 -0.6852460 0.8245970 -0.3360145 -0.3972472 0.8839497
## X582 0.18177643 -0.6852460 -0.3320280 -0.3360145 -0.3972472 -0.4741055
## X583 -0.01199386 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X584 1.80408084 1.0008314 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X586 0.53699786 0.1577927 1.4029096 1.7123815 -0.3972472 -0.4741055
## X587 0.70131917 0.1577927 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X588 0.36423857 1.0008314 0.2462845 1.7123815 -0.3972472 -0.4741055
## X589 2.15069776 -0.6852460 1.9812221 -0.3360145 -0.3972472 -0.4741055
## X591 1.68198027 1.0008314 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X592 -0.01199386 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X593 1.15294194 1.8438701 -0.3320280 -0.3360145 -0.3972472 0.8839497
## X594 -0.01199386 -0.6852460 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X595 -0.21915966 0.1577927 -0.9103405 3.7607774 0.3168966 0.2049221
## X596 0.53699786 1.0008314 0.8245970 1.7123815 -0.3972472 -0.4741055
## X597 1.55615914 0.1577927 -0.3320280 -0.3360145 -0.3972472 -0.4741055
## X598 0.36423857 -0.6852460 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X599 -0.01199386 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X600 0.70131917 -0.6852460 1.9812221 1.7123815 -0.3972472 -0.4741055
## X603 0.18177643 -0.6852460 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X604 0.53699786 1.0008314 0.2462845 1.7123815 -0.3972472 -0.4741055
## X605 1.55615914 -0.6852460 0.8245970 -0.3360145 -0.3972472 -0.4741055
## X606 0.36423857 -0.6852460 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X608 -0.68595798 -0.6852460 -0.9103405 -0.3360145 -0.3972472 0.8839497
## X609 0.18177643 2.6869088 0.2462845 1.7123815 -0.3972472 -0.4741055
## X611 -0.44251753 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X612 -0.01199386 1.0008314 0.2462845 -0.3360145 1.0310404 0.8839497
## X613 -0.44251753 -0.6852460 -0.9103405 -0.3360145 -0.3972472 0.2049221
## X614 -0.44251753 -0.6852460 -0.9103405 -0.3360145 0.3168966 0.2049221
## X616 -0.68595798 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X617 1.29203392 0.1577927 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X619 1.00853037 1.8438701 1.4029096 3.7607774 -0.3972472 1.5629772
## X620 -0.68595798 -0.6852460 -0.9103405 -0.3360145 1.7451841 1.5629772
## X621 0.70131917 0.1577927 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X622 0.18177643 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X623 1.00853037 1.0008314 0.2462845 -0.3360145 1.0310404 0.8839497
## X625 0.85821946 1.8438701 0.2462845 -0.3360145 0.3168966 0.2049221
## X628 1.92274051 -0.6852460 1.9812221 -0.3360145 -0.3972472 0.2049221
## X629 2.15069776 -0.6852460 1.4029096 -0.3360145 -0.3972472 -0.4741055
## X630 1.42629884 1.0008314 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X631 -0.21915966 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X632 -2.04708364 -0.6852460 -0.9103405 -0.3360145 3.8876154 3.6000599
## X633 0.18177643 -0.6852460 0.8245970 -0.3360145 1.0310404 0.8839497
## X635 0.85821946 1.8438701 0.8245970 1.7123815 -0.3972472 -0.4741055
## X636 1.80408084 -0.6852460 2.5595346 -0.3360145 -0.3972472 0.2049221
## X637 1.55615914 -0.6852460 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X638 1.15294194 -0.6852460 0.8245970 -0.3360145 -0.3972472 -0.4741055
## X639 0.18177643 2.6869088 0.2462845 1.7123815 -0.3972472 -0.4741055
## X641 1.55615914 1.0008314 0.8245970 -0.3360145 -0.3972472 -0.4741055
## X648 1.00853037 1.0008314 1.4029096 1.7123815 0.3168966 0.2049221
## X650 -0.01199386 1.0008314 0.8245970 3.7607774 -0.3972472 -0.4741055
## X651 1.55615914 1.0008314 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X653 2.15069776 -0.6852460 1.4029096 -0.3360145 -0.3972472 -0.4741055
## X654 1.29203392 0.1577927 0.8245970 -0.3360145 -0.3972472 -0.4741055
## X655 0.18177643 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X656 0.18177643 -0.6852460 -0.9103405 -0.3360145 0.3168966 0.2049221
## X657 0.70131917 0.1577927 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X1082 -0.95516548 -0.6852460 -0.9103405 -0.3360145 0.3168966 0.2049221
## X1083 0.85821946 -0.6852460 -0.3320280 -0.3360145 -0.3972472 -0.4741055
## X1084 0.18177643 -0.6852460 -0.3320280 -0.3360145 -0.3972472 -0.4741055
## X1086 -0.68595798 -0.6852460 -0.9103405 -0.3360145 -0.3972472 0.2049221
## X1088 -0.01199386 1.0008314 0.2462845 -0.3360145 0.3168966 0.2049221
## X1089 0.53699786 1.0008314 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X1090 -0.01199386 0.1577927 0.8245970 -0.3360145 -0.3972472 -0.4741055
## X1091 0.53699786 -0.6852460 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X1092 -0.01199386 -0.6852460 -0.3320280 -0.3360145 -0.3972472 -0.4741055
## X1093 -0.95516548 1.0008314 0.2462845 -0.3360145 1.0310404 0.8839497
## X1094 -0.21915966 -0.6852460 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X1095 -0.21915966 0.1577927 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X1097 -0.95516548 -0.6852460 -0.9103405 -0.3360145 0.3168966 0.2049221
## X1098 0.85821946 1.0008314 0.8245970 -0.3360145 -0.3972472 -0.4741055
## X1101 -0.21915966 1.8438701 1.4029096 3.7607774 1.7451841 1.5629772
## X1103 1.15294194 -0.6852460 2.5595346 -0.3360145 -0.3972472 -0.4741055
## X1104 0.36423857 1.8438701 0.2462845 1.7123815 -0.3972472 -0.4741055
## X1105 -0.68595798 2.6869088 -0.9103405 1.7123815 -0.3972472 -0.4741055
## X1106 -0.21915966 0.1577927 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X1108 -0.21915966 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X1110 -0.68595798 -0.6852460 -0.9103405 -0.3360145 -0.3972472 0.2049221
## X1112 0.36423857 2.6869088 0.2462845 1.7123815 -0.3972472 -0.4741055
## X1113 1.00853037 -0.6852460 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X1115 0.85821946 -0.6852460 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X1116 0.18177643 1.0008314 -0.9103405 -0.3360145 0.3168966 0.2049221
## X1117 -0.21915966 0.1577927 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X1119 -0.21915966 -0.6852460 0.8245970 -0.3360145 1.7451841 1.5629772
## X1120 1.80408084 -0.6852460 1.9812221 -0.3360145 -0.3972472 -0.4741055
## X1121 0.85821946 3.5299475 0.8245970 -0.3360145 -0.3972472 -0.4741055
## X1122 1.92274051 -0.6852460 1.9812221 -0.3360145 -0.3972472 -0.4741055
## X1124 0.36423857 -0.6852460 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X1125 -2.04708364 -0.6852460 -0.9103405 -0.3360145 1.7451841 3.6000599
## X1126 -0.68595798 -0.6852460 -0.9103405 -0.3360145 1.0310404 0.8839497
## X1127 -0.01199386 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X1128 -0.21915966 0.1577927 -0.3320280 -0.3360145 -0.3972472 0.2049221
## X1129 -0.44251753 -0.6852460 -0.9103405 -0.3360145 0.3168966 0.2049221
## X1130 -0.21915966 -0.6852460 0.2462845 -0.3360145 1.7451841 1.5629772
## X1131 -0.68595798 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X1133 0.18177643 1.8438701 -0.3320280 -0.3360145 -0.3972472 0.2049221
## X1135 -0.01199386 -0.6852460 -0.3320280 -0.3360145 -0.3972472 -0.4741055
## X1136 -0.44251753 -0.6852460 -0.9103405 -0.3360145 -0.3972472 0.2049221
## X1138 3.05604172 0.1577927 6.6077223 -0.3360145 -0.3972472 -0.4741055
## X1139 1.80408084 -0.6852460 1.9812221 -0.3360145 -0.3972472 -0.4741055
## X1141 -0.68595798 -0.6852460 -0.9103405 -0.3360145 -0.3972472 -0.4741055
## X1142 -0.68595798 -0.6852460 -0.9103405 -0.3360145 1.0310404 0.8839497
## X1143 1.55615914 1.0008314 0.8245970 -0.3360145 -0.3972472 -0.4741055
## X1144 1.29203392 0.1577927 0.8245970 -0.3360145 -0.3972472 -0.4741055
## X1145 0.18177643 1.8438701 0.8245970 1.7123815 0.3168966 0.2049221
## X1146 -0.01199386 0.1577927 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X1147 0.18177643 0.1577927 -0.3320280 1.7123815 -0.3972472 -0.4741055
## X1149 0.18177643 0.1577927 0.2462845 -0.3360145 0.3168966 0.2049221
## X1150 0.18177643 -0.6852460 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X1151 0.36423857 0.1577927 -0.3320280 1.7123815 -0.3972472 -0.4741055
## X1152 1.29203392 0.1577927 0.8245970 -0.3360145 -0.3972472 -0.4741055
## X1153 -1.25901822 0.1577927 -0.9103405 -0.3360145 -0.3972472 2.2420048
## X1156 0.36423857 -0.6852460 0.2462845 -0.3360145 -0.3972472 -0.4741055
## X1158 1.00853037 -0.6852460 2.5595346 -0.3360145 -0.3972472 -0.4741055
## X1159 0.53699786 -0.6852460 1.4029096 -0.3360145 -0.3972472 -0.4741055
## X1160 1.92274051 -0.6852460 3.7161597 -0.3360145 -0.3972472 -0.4741055
## NumRings HydrophilicFactor SurfaceArea1 SurfaceArea2
## X661 1.2306033 -0.741919037 -0.302617991 -0.379138448
## X662 2.0005400 -0.310306393 0.445784255 1.054350614
## X663 -0.3092700 -0.274782719 0.023833878 -0.076964725
## X665 -0.3092700 -0.834280591 -1.033167401 -1.055357076
## X668 -0.3092700 -0.042990743 0.495375467 0.359508432
## X669 -1.0792067 -0.559860206 -0.457625954 0.141009550
## X670 2.0005400 -0.629131371 0.187343191 0.074384441
## X671 -1.0792067 -0.723269108 -0.287882317 -0.365498662
## X672 2.0005400 0.190577416 1.080835157 0.901427627
## X673 0.4606666 0.331784022 0.132367790 0.023497546
## X674 0.4606666 -0.698402536 0.418013175 0.287899555
## X676 2.0005400 -0.365368089 0.023833878 -0.076964725
## X677 0.4606666 -0.842273418 -1.033167401 -1.055357076
## X678 0.4606666 -0.760568966 -1.033167401 -1.055357076
## X679 -0.3092700 -0.838721050 -1.033167401 -1.055357076
## X682 0.4606666 -0.260573249 0.285392103 0.165141479
## X683 -0.3092700 -0.115814276 1.359112705 1.378820142
## X684 2.0005400 -0.288992189 -0.136558273 0.515316758
## X685 2.0005400 -0.365368089 0.023833878 -0.076964725
## X686 0.4606666 -0.842273418 -1.033167401 -1.055357076
## X688 1.2306033 -0.249028055 0.285392103 0.165141479
## X689 1.2306033 -0.773002252 -0.849538224 -0.885384357
## X690 -0.3092700 -0.689521618 -0.196067728 -0.280512302
## X691 -0.3092700 0.566240273 0.799723825 0.641222476
## X692 -0.3092700 -0.119366643 0.798306933 2.622401413
## X693 0.4606666 0.382405258 1.099821507 1.138812367
## X695 1.2306033 -0.705507271 -0.540089056 0.141796461
## X696 1.2306033 0.343329216 0.069457794 -0.034733848
## X698 -0.3092700 -0.295208832 0.053021849 -0.049947456
## X699 -0.3092700 -0.578510135 -0.359010285 -0.431336861
## X700 -1.0792067 -0.828952040 -1.033167401 -1.055357076
## X702 -1.0792067 -0.812966386 -1.033167401 -1.055357076
## X703 -0.3092700 -0.821847305 -1.033167401 -1.055357076
## X704 0.4606666 -0.842273418 -1.033167401 -1.055357076
## X706 0.4606666 -0.708171547 0.084476847 -0.020831759
## X708 0.4606666 -0.842273418 -1.033167401 -1.055357076
## X709 -0.3092700 -0.821847305 -1.033167401 -1.055357076
## X711 2.0005400 1.404598989 1.743657139 1.514955700
## X712 0.4606666 0.207451161 0.113381439 0.005923206
## X713 0.4606666 0.382405258 0.364738044 0.238586482
## X714 2.0005400 0.190577416 1.826120241 1.591286041
## X715 -0.3092700 -0.130911837 0.053021849 -0.049947456
## X717 0.4606666 -0.760568966 -1.033167401 -1.055357076
## X718 2.0005400 -0.683304975 -0.709832693 -0.015323383
## X721 -0.3092700 0.574233100 0.744465045 0.590073278
## X722 1.2306033 -0.676200240 -0.409735011 -0.478289201
## X723 -1.0792067 -0.821847305 -1.033167401 -1.055357076
## X724 0.4606666 -0.723269108 -0.332656097 -0.406942628
## X726 0.4606666 -0.157554593 -0.198334755 -0.282610731
## X728 0.4606666 -0.278335086 0.023833878 -0.076964725
## X729 -0.3092700 -0.546538828 -1.033167401 -1.055357076
## X731 -1.0792067 -0.812966386 -1.033167401 -1.055357076
## X732 0.4606666 -0.778330804 -1.033167401 -1.055357076
## X733 -0.3092700 0.687908858 0.744465045 0.590073278
## X734 -0.3092700 -0.493253316 -1.033167401 -1.055357076
## X735 2.0005400 -0.376025191 0.023833878 -0.076964725
## X736 -0.3092700 0.331784022 0.449468173 0.317015252
## X737 0.4606666 -0.711723914 -0.682911749 0.110582335
## X739 1.2306033 -0.602488615 0.980519218 0.808572160
## X740 1.2306033 -0.263237525 0.908824493 0.742209354
## X741 -1.0792067 -0.252580422 0.023833878 -0.076964725
## X742 -1.0792067 -0.711723914 -0.287882317 -0.365498662
## X743 -0.3092700 -0.493253316 -1.033167401 -1.055357076
## X744 1.2306033 -0.842273418 -1.033167401 -1.055357076
## X746 -0.3092700 -0.680640699 0.457402767 0.324359752
## X747 -1.0792067 -0.294320740 -0.459892981 -0.524716935
## X749 2.0005400 -0.655774127 0.035452391 0.674535031
## X752 2.0005400 0.148837099 1.826120241 1.591286041
## X753 -0.3092700 -0.821847305 -1.033167401 -1.055357076
## X754 2.0005400 -0.737478578 -0.801647282 -0.100309743
## X755 0.4606666 -0.842273418 -1.033167401 -1.055357076
## X757 -1.0792067 -0.717052465 -1.033167401 -1.055357076
## X758 0.4606666 -0.791652182 -0.771609176 -0.813250873
## X759 -1.0792067 -0.525224623 -0.849538224 2.125336130
## X760 0.4606666 -0.778330804 -1.033167401 -1.055357076
## X761 2.0005400 0.189689324 1.826120241 1.591286041
## X762 1.2306033 -0.844937693 -1.033167401 -1.055357076
## X763 0.4606666 1.916139901 0.441533579 0.309670752
## X764 0.4606666 -0.844937693 -1.033167401 -1.055357076
## X765 0.4606666 -0.257020882 0.285392103 0.165141479
## X767 2.0005400 -0.703731087 0.679571401 0.530005758
## X768 1.2306033 -0.294320740 -0.585712972 -0.641179724
## X770 1.2306033 -0.689521618 -0.801647282 -0.100309743
## X771 0.4606666 -0.111373817 0.758917341 0.603450761
## X772 -0.3092700 -0.546538828 -1.033167401 -1.055357076
## X773 -1.0792067 -0.828952040 -1.033167401 -1.055357076
## X774 -1.0792067 -0.734814302 -1.033167401 -1.055357076
## X775 0.4606666 -0.295208832 0.507560737 0.370787486
## X776 1.2306033 0.810465534 2.186010757 2.144221987
## X777 -1.0792067 -0.596271972 -0.549440542 1.640599114
## X778 2.0005400 2.044025128 2.568288163 2.278259116
## X779 1.2306033 0.285603245 -0.295816911 -0.372843162
## X780 -0.3092700 -0.371584732 -1.033167401 -1.055357076
## X781 -1.0792067 -0.737478578 -0.026324091 -0.123392458
## X782 1.2306033 -0.741919037 -0.065713683 -0.159852656
## X784 0.4606666 1.712766865 1.596017014 1.378295535
## X786 -1.0792067 -0.821847305 -1.033167401 -1.055357076
## X787 0.4606666 -0.723269108 -1.033167401 -1.055357076
## X788 2.0005400 -0.788987906 -0.065713683 -0.159852656
## X789 0.4606666 -0.723269108 -1.033167401 -1.055357076
## X791 0.4606666 -0.723269108 -1.033167401 -1.055357076
## X792 1.2306033 -0.638900382 -0.801647282 -0.100309743
## X794 -1.0792067 -0.294320740 0.023833878 -0.076964725
## X798 2.0005400 -0.768561793 -0.302617991 -0.379138448
## X799 0.4606666 -0.465722469 0.026100905 0.588761760
## X800 2.7704767 -0.365368089 -0.459892981 0.138911121
## X804 0.4606666 -0.737478578 -0.240841509 -0.321956268
## X805 2.0005400 0.135515721 1.826120241 1.591286041
## X807 -1.0792067 -0.395563212 0.013065500 3.438427849
## X808 1.2306033 -0.310306393 0.908824493 0.742209354
## X809 0.4606666 -0.705507271 0.457402767 0.324359752
## X810 1.2306033 -0.525224623 -1.033167401 -1.055357076
## X813 -1.0792067 -0.353822894 0.023833878 -0.076964725
## X814 0.4606666 -0.578510135 0.589457083 0.446593220
## X818 0.4606666 -0.675312148 -1.033167401 -1.055357076
## X819 0.4606666 0.395726636 0.616094648 0.471249757
## X820 -1.0792067 -0.332508690 -0.459892981 -0.524716935
## X821 0.4606666 -0.675312148 -1.033167401 -1.055357076
## X822 2.0005400 -0.851154336 -1.033167401 -1.055357076
## X823 2.0005400 0.183472681 -0.295816911 -0.372843162
## X827 2.7704767 -0.533217450 -0.678094317 -0.726690691
## X828 0.4606666 -0.675312148 -1.033167401 -1.055357076
## X829 0.4606666 -0.515455613 0.597108298 2.216355472
## X831 0.4606666 -0.659326494 -1.033167401 -1.055357076
## X832 0.4606666 -0.723269108 -1.033167401 -1.055357076
## X833 0.4606666 -0.633571830 -1.033167401 -1.055357076
## X834 0.4606666 -0.659326494 -1.033167401 -1.055357076
## X835 0.4606666 -0.723269108 -1.033167401 -1.055357076
## X836 0.4606666 -0.633571830 -1.033167401 -1.055357076
## X839 2.0005400 -0.852042428 -1.033167401 -1.055357076
## X840 2.0005400 -0.853818612 -1.033167401 -1.055357076
## X841 0.4606666 -0.633571830 -1.033167401 -1.055357076
## X842 1.2306033 -0.851154336 -1.033167401 -1.055357076
## X843 0.4606666 -0.659326494 -1.033167401 -1.055357076
## X846 1.2306033 -0.853818612 -1.033167401 -1.055357076
## X848 0.4606666 -0.596271972 -1.033167401 -1.055357076
## X849 0.4606666 -0.633571830 -1.033167401 -1.055357076
## X851 3.5404134 -0.408884590 0.063223470 -0.040504527
## X854 0.4606666 -0.633571830 -1.033167401 -1.055357076
## X855 2.7704767 -0.407108406 -0.585712972 -0.641179724
## X856 0.4606666 -0.562524482 -1.033167401 -1.055357076
## X857 0.4606666 -0.596271972 -1.033167401 -1.055357076
## X858 0.4606666 -0.562524482 -1.033167401 -1.055357076
## X859 0.4606666 -0.562524482 -1.033167401 -1.055357076
## X860 0.4606666 -0.633571830 -1.033167401 -1.055357076
## X862 0.4606666 -0.596271972 -1.033167401 -1.055357076
## X863 0.4606666 -0.533217450 -1.033167401 -1.055357076
## X864 2.7704767 -0.856482887 -1.033167401 -1.055357076
## X865 2.7704767 -0.855594796 -1.033167401 -1.055357076
## X866 0.4606666 -0.562524482 -1.033167401 -1.055357076
## X867 2.7704767 -0.855594796 -1.033167401 -1.055357076
## X869 2.0005400 -0.672647872 -0.162912460 -0.249822784
## X870 0.4606666 -0.562524482 -1.033167401 -1.055357076
## X871 0.4606666 -0.562524482 -1.033167401 -1.055357076
## X872 0.4606666 -0.562524482 -1.033167401 -1.055357076
## X873 2.7704767 -0.855594796 -1.033167401 -1.055357076
## X875 0.4606666 -0.505686603 -1.033167401 -1.055357076
## X876 0.4606666 -0.505686603 -1.033167401 -1.055357076
## X877 0.4606666 -0.459505826 -1.033167401 -1.055357076
## X1190 0.4606666 -0.778330804 -0.771609176 -0.813250873
## X1191 -1.0792067 -0.717052465 -1.033167401 -1.055357076
## X1192 2.0005400 -0.376025191 0.023833878 -0.076964725
## X1193 -0.3092700 -0.838721050 -1.033167401 -1.055357076
## X1194 2.0005400 -0.311194485 1.736572680 1.508398110
## X1195 -0.3092700 -0.546538828 -1.033167401 -1.055357076
## X1197 -0.3092700 -0.834280591 -1.033167401 -1.055357076
## X1198 -0.3092700 -0.612257626 -1.033167401 -1.055357076
## X1199 -0.3092700 0.527164231 0.744465045 1.253701335
## X1200 -1.0792067 -0.446184448 -0.510050950 1.855163443
## X1201 2.7704767 -0.640676565 0.850165173 0.687912513
## X1202 2.0005400 0.201234518 2.571405325 2.281144456
## X1203 -0.3092700 -0.821847305 -1.033167401 -1.055357076
## X1204 1.2306033 0.379740982 1.789281054 1.776996976
## X1205 0.4606666 0.425921759 0.730012749 0.576695796
## X1206 -1.0792067 -0.358263354 -1.033167401 -1.055357076
## X1207 1.2306033 -0.724157200 -0.801647282 -0.100309743
## X1208 2.7704767 -0.709059639 0.679571401 1.193633815
## X1209 -0.3092700 0.088446852 -0.459892981 -0.524716935
## X1210 2.0005400 0.738530094 1.170382718 0.984315558
## X1212 2.0005400 0.168375119 0.113381439 0.005923206
## X1213 1.2306033 -0.724157200 -0.801647282 -0.100309743
## X1215 2.7704767 0.189689324 1.603951608 1.385640035
## X1216 1.2306033 -0.778330804 -1.033167401 -0.314611768
## X1217 1.2306033 -0.257020882 0.270656429 0.151501693
## X1219 0.4606666 0.207451161 0.113381439 0.005923206
## X1220 1.2306033 -0.310306393 0.115648466 0.008021635
## X1221 -1.0792067 -0.717052465 -1.033167401 -1.055357076
## X1222 1.2306033 -0.814742570 -0.941352813 -0.970370717
## X1226 2.0005400 -0.640676565 -0.709832693 -0.015323383
## X1228 -0.3092700 -0.525224623 -0.248492725 1.433641590
## X1229 2.0005400 0.147949007 1.826120241 1.591286041
## X1230 1.2306033 -0.698402536 0.188193326 0.075171351
## X1231 0.4606666 -0.847601969 -1.033167401 -1.055357076
## X1233 2.0005400 -0.385794201 0.023833878 -0.076964725
## X1234 0.4606666 -0.842273418 -1.033167401 -1.055357076
## X1236 2.0005400 -0.753464232 0.195844542 0.082253548
## X1237 -0.3092700 -0.361815721 0.116781980 1.108122848
## X1239 -1.0792067 -0.525224623 -0.457625954 0.141009550
## X1242 -1.0792067 -0.322739679 -1.033167401 -1.055357076
## X1244 0.4606666 -0.778330804 -1.033167401 -1.055357076
## X1245 -0.3092700 -0.842273418 -1.033167401 -1.055357076
## X1246 2.0005400 -0.353822894 0.023833878 -0.076964725
## X1247 1.2306033 -0.757904691 -0.026324091 -0.123392458
## X1249 0.4606666 -0.538546001 0.607593298 1.562432648
## X1250 1.2306033 -0.055424029 -0.459892981 -0.524716935
## X1251 -0.3092700 -0.476379571 0.315146831 0.192683355
## X1253 -0.3092700 -0.514567521 -0.510050950 1.855163443
## X1254 0.4606666 -0.723269108 -1.033167401 -1.055357076
## X1255 1.2306033 -0.849378152 -1.033167401 -1.055357076
## X1256 2.0005400 -0.851154336 -1.033167401 -1.055357076
## X1257 0.4606666 -0.675312148 -1.033167401 -1.055357076
## X1259 2.7704767 -0.533217450 -0.678094317 -0.726690691
## X1260 0.4606666 -0.675312148 -1.033167401 -1.055357076
## X1262 1.2306033 -0.690409709 -0.026324091 -0.123392458
## X1264 1.2306033 -0.494141408 -1.033167401 -1.055357076
## X1265 0.4606666 -0.633571830 -1.033167401 -1.055357076
## X1266 0.4606666 -0.624690912 -1.033167401 -1.055357076
## X1267 1.2306033 0.840660658 1.955057394 1.967953982
## X1268 -1.0792067 -0.327180139 0.023833878 -0.076964725
## X1273 0.4606666 -0.633571830 -1.033167401 -1.055357076
## X1274 -1.0792067 -0.362703813 -0.459892981 -0.524716935
## X1275 2.0005400 -0.562524482 -1.033167401 -1.055357076
## X1276 2.7704767 -0.855594796 -1.033167401 -1.055357076
## X1277 0.4606666 -0.596271972 -1.033167401 -1.055357076
## X1278 2.0005400 -0.852042428 -1.033167401 -1.055357076
## X1279 2.0005400 -0.853818612 -1.033167401 -1.055357076
## X1281 0.4606666 -0.562524482 -1.033167401 -1.055357076
## X1282 0.4606666 -0.562524482 -1.033167401 -1.055357076
## X1283 2.7704767 -0.855594796 -1.033167401 -1.055357076
## X1284 2.0005400 -0.853818612 -1.033167401 -1.055357076
## X1285 0.4606666 -0.562524482 -1.033167401 -1.055357076
## X1288 0.4606666 -0.481708122 -1.033167401 -1.055357076
## X1299 1.2306033 0.321126919 0.616094648 0.471249757
## X1301 2.0005400 -0.365368089 0.023833878 -0.076964725
## X1302 -0.3092700 -0.411548865 -1.033167401 -1.055357076
## X1307 -0.3092700 -0.417765508 0.116781980 1.108122848
## X1309 0.4606666 -0.624690912 -1.033167401 -1.055357076
## X1310 1.2306033 -0.465722469 -1.033167401 -1.055357076
## X447 -0.3092700 -0.028781274 0.285392103 0.165141479
## X448 2.0005400 3.680778427 4.113550354 3.708600536
## X451 -1.0792067 -0.779218896 -1.033167401 -1.055357076
## X452 -0.3092700 -0.640676565 -1.033167401 -1.055357076
## X453 0.4606666 -0.164659328 -0.094618276 -0.186607621
## X454 0.4606666 1.129290512 2.004648607 1.976347696
## X455 -0.3092700 -0.129135654 0.285392103 0.165141479
## X456 0.4606666 -0.240147136 0.053021849 -0.049947456
## X458 0.4606666 1.175471289 2.004648607 1.976347696
## X459 -1.0792067 -0.749023772 -0.549440542 -0.607604866
## X460 -0.3092700 -0.799645008 -1.033167401 -1.055357076
## X461 -0.3092700 -0.039438376 0.023833878 -0.076964725
## X462 -0.3092700 -0.693962077 -1.033167401 -0.314611768
## X463 1.2306033 -0.310306393 -0.250192995 -0.330612286
## X464 -1.0792067 -0.218832932 -1.033167401 -1.055357076
## X465 1.2306033 -0.249028055 0.532214654 0.393607897
## X466 0.4606666 -0.042990743 0.647266268 1.240848459
## X468 -1.0792067 0.604428223 0.449468173 0.317015252
## X471 -0.3092700 0.527164231 0.187909948 0.074909048
## X472 -1.0792067 -0.662878862 -1.033167401 -1.055357076
## X473 -0.3092700 -0.779218896 -1.033167401 -1.055357076
## X476 0.4606666 -0.252580422 0.023833878 -0.076964725
## X477 0.4606666 -0.076738234 0.850731929 0.908247520
## X478 -1.0792067 -0.799645008 -1.033167401 -1.055357076
## X479 -1.0792067 -0.779218896 -1.033167401 -1.055357076
## X480 1.2306033 -0.723269108 -0.302617991 -0.379138448
## X482 -1.0792067 -0.574957768 -1.033167401 -1.055357076
## X483 -1.0792067 -0.527000807 -1.033167401 -1.055357076
## X484 0.4606666 1.948111208 0.441533579 0.309670752
## X486 -1.0792067 -0.683304975 -0.287882317 -0.365498662
## X487 -0.3092700 -0.670871689 0.065490497 -0.038406098
## X488 -0.3092700 -0.190413992 0.285392103 0.165141479
## X489 -0.3092700 -0.039438376 0.023833878 -0.076964725
## X490 -0.3092700 -0.670871689 -0.196067728 -0.280512302
## X491 -1.0792067 -0.662878862 -1.033167401 -1.055357076
## X492 0.4606666 -0.157554593 0.850731929 0.688437121
## X493 -1.0792067 -0.164659328 0.023833878 -0.076964725
## X494 -0.3092700 1.517386655 1.126459073 0.943658503
## X495 2.0005400 -0.321851587 0.258754538 0.140484943
## X496 0.4606666 0.068908831 0.510111142 1.214880405
## X497 1.2306033 -0.785435539 -0.667892696 -0.717247762
## X498 -0.3092700 -0.124695194 -0.459892981 -0.524716935
## X499 -0.3092700 -0.821847305 -1.033167401 -1.055357076
## X501 0.4606666 -0.470162928 0.586056542 0.443445577
## X502 -0.3092700 -0.821847305 -1.033167401 -1.055357076
## X503 3.5404134 0.208339253 0.297010616 0.175895926
## X505 -0.3092700 -0.087395336 -0.208536376 -0.292053660
## X506 0.4606666 1.178135565 1.743090382 1.734241492
## X507 0.4606666 1.766052376 1.956757664 1.712207992
## X508 -0.3092700 2.105303467 1.334458788 1.136189331
## X509 2.0005400 3.653247579 4.113550354 3.708600536
## X510 0.4606666 0.516507129 0.692890184 0.542334027
## X513 -1.0792067 -0.662878862 -1.033167401 -1.055357076
## X514 0.4606666 1.178135565 1.750174841 1.740799082
## X515 0.4606666 0.470326352 0.113381439 0.005923206
## X516 -0.3092700 -0.760568966 -0.771609176 -0.813250873
## X518 -0.3092700 0.382405258 0.969467462 0.798342320
## X521 0.4606666 1.128402420 2.266206832 2.218453900
## X523 -0.3092700 -0.711723914 -0.287882317 -0.365498662
## X524 -0.3092700 -0.094500071 -0.208536376 -0.292053660
## X525 0.4606666 0.399279003 1.099821507 0.919001967
## X526 -1.0792067 -0.209952013 -0.459892981 -0.524716935
## X530 -0.3092700 -0.760568966 -0.941352813 -0.970370717
## X531 -0.3092700 0.364643421 0.364738044 0.238586482
## X532 -0.3092700 0.574233100 0.744465045 1.253701335
## X533 0.4606666 1.385060968 2.330250342 2.497544909
## X534 -0.3092700 0.485423914 1.099821507 1.138812367
## X535 -0.3092700 -0.612257626 -1.033167401 -1.055357076
## X536 2.0005400 -0.336061057 -0.002803688 -0.101621261
## X538 1.2306033 2.486294875 2.689290722 2.390262745
## X539 2.0005400 -0.336061057 -0.002803688 -0.101621261
## X542 2.0005400 0.207451161 1.564562016 1.349179838
## X543 -1.0792067 -0.693962077 -1.033167401 -1.055357076
## X544 2.0005400 3.653247579 4.113550354 3.708600536
## X545 -1.0792067 -0.778330804 -0.941352813 -0.970370717
## X546 -1.0792067 -0.192190176 -1.033167401 -1.055357076
## X548 -0.3092700 -0.760568966 -0.771609176 -0.813250873
## X549 -0.3092700 -0.612257626 -1.033167401 -1.055357076
## X551 -1.0792067 -0.141568940 -1.033167401 -1.055357076
## X552 2.7704767 -0.626467096 1.111723398 0.930018717
## X553 0.4606666 -0.185085441 0.053021849 0.613680600
## X554 -0.3092700 0.581337835 1.418622161 1.214093494
## X556 0.4606666 -0.240147136 0.285392103 0.165141479
## X557 -0.3092700 1.041369418 0.882186927 0.717552818
## X558 0.4606666 -0.039438376 -0.667892696 1.041235435
## X559 -1.0792067 -0.779218896 -1.033167401 -1.055357076
## X560 -0.3092700 -0.828952040 -1.033167401 -1.055357076
## X561 -0.3092700 -0.612257626 -1.033167401 -1.055357076
## X562 -0.3092700 -0.828952040 -1.033167401 -1.055357076
## X563 0.4606666 -0.294320740 0.023833878 -0.076964725
## X565 -1.0792067 -0.799645008 -1.033167401 -1.055357076
## X566 -0.3092700 0.766949033 -0.295816911 -0.372843162
## X567 -0.3092700 0.512954761 1.099821507 1.138812367
## X568 -0.3092700 -0.087395336 -0.208536376 -0.292053660
## X569 -0.3092700 -0.659326494 -0.196067728 -0.280512302
## X571 -0.3092700 0.621301968 0.449468173 0.317015252
## X572 -0.3092700 1.032488500 0.790372339 0.632566458
## X574 -0.3092700 -0.812966386 -1.033167401 -1.055357076
## X576 0.4606666 1.175471289 2.004648607 1.976347696
## X577 0.4606666 -0.217056748 0.053021849 -0.049947456
## X579 0.4606666 -0.217056748 0.163822787 0.052613244
## X580 -0.3092700 0.686132674 0.597108298 0.453675417
## X582 -1.0792067 -0.760568966 -0.549440542 -0.607604866
## X583 -0.3092700 -0.828952040 -1.033167401 -1.055357076
## X584 4.3103501 -0.718828649 -0.104253140 -0.195525943
## X586 0.4606666 -0.533217450 0.597108298 1.552727415
## X587 1.2306033 -0.785435539 -0.667892696 -0.717247762
## X588 -0.3092700 0.472990628 0.616094648 1.312981944
## X589 2.0005400 1.404598989 1.743657139 1.514955700
## X591 2.0005400 -0.321851587 0.258754538 0.140484943
## X592 -0.3092700 -0.828952040 -1.033167401 -1.055357076
## X593 1.2306033 -0.217056748 0.410361960 0.280817358
## X594 -1.0792067 -0.683304975 -0.287882317 -0.365498662
## X595 -1.0792067 -0.555419747 -0.941352813 0.534989527
## X596 -0.3092700 0.447235964 1.099821507 1.138812367
## X597 1.2306033 -0.773002252 -0.679794587 -0.728264513
## X598 -1.0792067 -0.227713850 0.023833878 -0.076964725
## X599 -0.3092700 -0.828952040 -1.033167401 -1.055357076
## X600 0.4606666 -0.578510135 0.718960993 0.786276356
## X603 -1.0792067 -0.198406819 0.023833878 -0.076964725
## X604 -0.3092700 0.433914586 0.616094648 1.312981944
## X605 2.0005400 -0.737478578 0.418013175 0.287899555
## X606 -0.3092700 -0.711723914 -0.287882317 -0.365498662
## X608 -0.3092700 -0.612257626 -1.033167401 -1.055357076
## X609 0.4606666 1.231421076 1.743090382 1.734241492
## X611 -0.3092700 -0.812966386 -1.033167401 -1.055357076
## X612 -0.3092700 -0.042990743 0.144836437 0.035038904
## X613 -0.3092700 -0.717052465 -1.033167401 -1.055357076
## X614 -0.3092700 -0.717052465 -1.033167401 -1.055357076
## X616 -1.0792067 -0.799645008 -1.033167401 -1.055357076
## X617 0.4606666 -0.724157200 -0.196067728 -0.280512302
## X619 1.2306033 1.688788384 2.320898856 2.488888891
## X620 -0.3092700 -0.546538828 -1.033167401 -1.055357076
## X621 0.4606666 0.364643421 0.364738044 0.238586482
## X622 0.4606666 -0.834280591 -1.033167401 -1.055357076
## X623 1.2306033 0.353986318 0.714993696 0.562793706
## X625 0.4606666 -0.593607697 0.582372624 0.440035631
## X628 2.0005400 0.801584616 1.654109577 1.432067769
## X629 2.0005400 0.738530094 1.170382718 0.984315558
## X630 1.2306033 -0.353822894 -0.600448647 -0.654819510
## X631 -1.0792067 -0.821847305 -1.033167401 -1.055357076
## X632 -1.0792067 -0.192190176 -1.033167401 -1.055357076
## X633 -0.3092700 -0.100716714 0.285392103 0.165141479
## X635 0.4606666 0.395726636 1.191636095 1.223798726
## X636 2.0005400 1.494296267 2.227383997 1.962707910
## X637 2.0005400 -0.773002252 -0.065713683 -0.159852656
## X638 0.4606666 -0.295208832 0.507560737 0.370787486
## X639 0.4606666 1.231421076 1.743090382 1.734241492
## X641 1.2306033 -0.285439821 0.691189913 0.540760205
## X648 0.4606666 1.712766865 2.069542251 2.036415216
## X650 0.4606666 0.581337835 1.298469737 2.063432485
## X651 1.2306033 -0.705507271 0.117915493 0.010120064
## X653 2.0005400 0.738530094 1.170382718 0.984315558
## X654 -0.3092700 -0.689521618 0.065490497 -0.038406098
## X655 -0.3092700 -0.834280591 -1.033167401 -1.055357076
## X656 0.4606666 -0.760568966 -1.033167401 -1.055357076
## X657 -0.3092700 0.364643421 0.449468173 0.317015252
## X1082 -1.0792067 -0.662878862 -1.033167401 -1.055357076
## X1083 0.4606666 -0.332508690 -0.459892981 -0.524716935
## X1084 -0.3092700 -0.242811412 -0.459892981 -0.524716935
## X1086 -0.3092700 -0.693962077 -1.033167401 -1.055357076
## X1088 -0.3092700 -0.066969224 0.144836437 0.035038904
## X1089 0.4606666 1.123073869 0.151637518 0.041334190
## X1090 -0.3092700 2.164805621 1.334458788 1.136189331
## X1091 -0.3092700 0.380629074 0.113381439 0.005923206
## X1092 -1.0792067 -0.749023772 -0.549440542 -0.607604866
## X1093 -0.3092700 -0.371584732 0.117915493 0.010120064
## X1094 -0.3092700 -0.124695194 0.023833878 -0.076964725
## X1095 0.4606666 -0.087395336 0.381740745 0.254324696
## X1097 -1.0792067 -0.662878862 -1.033167401 -1.055357076
## X1098 1.2306033 0.367307696 1.099821507 0.919001967
## X1101 0.4606666 2.036032302 2.320898856 2.488888891
## X1103 2.0005400 1.679019374 2.005215364 1.757061904
## X1104 0.4606666 1.180799840 1.377815677 1.396132178
## X1105 0.4606666 0.068908831 0.510111142 1.214880405
## X1106 -1.0792067 0.577785467 -0.295816911 -0.372843162
## X1108 -0.3092700 -0.821847305 -1.033167401 -1.055357076
## X1110 -0.3092700 -0.693962077 -1.033167401 -1.055357076
## X1112 0.4606666 1.178135565 1.743090382 1.734241492
## X1113 0.4606666 0.280274694 0.113381439 0.005923206
## X1115 0.4606666 -0.294320740 0.023833878 -0.076964725
## X1116 -0.3092700 -0.646005116 -0.591097161 -0.646163492
## X1117 -0.3092700 0.604428223 0.364738044 0.238586482
## X1119 -0.3092700 -0.005690885 0.285392103 0.165141479
## X1120 2.0005400 0.815794086 1.654109577 1.432067769
## X1121 1.2306033 0.407271830 1.810534431 1.576859345
## X1122 2.0005400 0.792703697 1.654109577 1.432067769
## X1124 0.4606666 -0.711723914 -0.065713683 -0.159852656
## X1125 -1.0792067 -0.192190176 -1.033167401 -1.055357076
## X1126 -0.3092700 -0.612257626 -1.033167401 -1.055357076
## X1127 0.4606666 -0.828952040 -1.033167401 -1.055357076
## X1128 -0.3092700 -0.087395336 -0.208536376 -0.292053660
## X1129 -0.3092700 -0.717052465 -1.033167401 -1.055357076
## X1130 -0.3092700 -0.028781274 0.023833878 -0.076964725
## X1131 -0.3092700 -0.799645008 -1.033167401 -1.055357076
## X1133 0.4606666 0.516507129 0.692890184 0.542334027
## X1135 -1.0792067 -0.749023772 -0.549440542 -0.607604866
## X1136 -0.3092700 -0.717052465 -1.033167401 -1.055357076
## X1138 2.0005400 3.944541710 5.512589313 5.003593308
## X1139 2.0005400 0.815794086 1.654109577 1.432067769
## X1141 -1.0792067 -0.799645008 -1.033167401 -1.055357076
## X1142 -0.3092700 -0.612257626 -1.033167401 -1.055357076
## X1143 1.2306033 -0.676200240 0.601642352 0.457872274
## X1144 2.7704767 0.270505683 0.466754253 0.333015770
## X1145 0.4606666 1.984522974 1.837171997 1.821326281
## X1146 -1.0792067 0.542261793 0.449468173 0.317015252
## X1147 -1.0792067 -0.646005116 -0.457625954 0.141009550
## X1149 -0.3092700 -0.129135654 0.053021849 -0.049947456
## X1150 -1.0792067 -0.698402536 -0.287882317 -0.365498662
## X1151 -0.3092700 -0.661990770 -0.457625954 0.141009550
## X1152 1.2306033 -0.689521618 0.065490497 -0.038406098
## X1153 -0.3092700 0.205674978 -0.585712972 -0.641179724
## X1156 -1.0792067 -0.227713850 0.023833878 -0.076964725
## X1158 1.2306033 1.724312059 2.005215364 1.757061904
## X1159 1.2306033 -0.633571830 0.456836011 0.323835145
## X1160 2.0005400 0.234093917 2.570838568 2.280619849
## [ reached 'max' / getOption("max.print") -- omitted 497 rows ]
##
## $usekernel
## [1] FALSE
##
## $varnames
## [1] "FP001" "FP002" "FP003"
## [4] "FP004" "FP005" "FP006"
## [7] "FP007" "FP008" "FP009"
## [10] "FP010" "FP011" "FP012"
## [13] "FP013" "FP014" "FP015"
## [16] "FP016" "FP017" "FP018"
## [19] "FP019" "FP020" "FP021"
## [22] "FP022" "FP023" "FP024"
## [25] "FP025" "FP026" "FP027"
## [28] "FP028" "FP029" "FP030"
## [31] "FP031" "FP032" "FP033"
## [34] "FP034" "FP035" "FP036"
## [37] "FP037" "FP038" "FP039"
## [40] "FP040" "FP041" "FP042"
## [43] "FP043" "FP044" "FP045"
## [46] "FP046" "FP047" "FP048"
## [49] "FP049" "FP050" "FP051"
## [52] "FP052" "FP053" "FP054"
## [55] "FP055" "FP056" "FP057"
## [58] "FP058" "FP059" "FP060"
## [61] "FP061" "FP062" "FP063"
## [64] "FP064" "FP065" "FP066"
## [67] "FP067" "FP068" "FP069"
## [70] "FP070" "FP071" "FP072"
## [73] "FP073" "FP074" "FP075"
## [76] "FP076" "FP077" "FP078"
## [79] "FP079" "FP080" "FP081"
## [82] "FP082" "FP083" "FP084"
## [85] "FP085" "FP086" "FP087"
## [88] "FP088" "FP089" "FP090"
## [91] "FP091" "FP092" "FP093"
## [94] "FP094" "FP095" "FP096"
## [97] "FP097" "FP098" "FP099"
## [100] "FP100" "FP101" "FP102"
## [103] "FP103" "FP104" "FP105"
## [106] "FP106" "FP107" "FP108"
## [109] "FP109" "FP110" "FP111"
## [112] "FP112" "FP113" "FP114"
## [115] "FP115" "FP116" "FP117"
## [118] "FP118" "FP119" "FP120"
## [121] "FP121" "FP122" "FP123"
## [124] "FP124" "FP125" "FP126"
## [127] "FP127" "FP128" "FP129"
## [130] "FP130" "FP131" "FP132"
## [133] "FP133" "FP134" "FP135"
## [136] "FP136" "FP137" "FP138"
## [139] "FP139" "FP140" "FP141"
## [142] "FP142" "FP143" "FP144"
## [145] "FP145" "FP146" "FP147"
## [148] "FP148" "FP149" "FP150"
## [151] "FP151" "FP152" "FP153"
## [154] "FP155" "FP156" "FP157"
## [157] "FP158" "FP159" "FP160"
## [160] "FP161" "FP162" "FP163"
## [163] "FP164" "FP165" "FP166"
## [166] "FP167" "FP168" "FP169"
## [169] "FP170" "FP171" "FP172"
## [172] "FP173" "FP174" "FP175"
## [175] "FP176" "FP177" "FP178"
## [178] "FP179" "FP180" "FP181"
## [181] "FP182" "FP183" "FP184"
## [184] "FP185" "FP186" "FP187"
## [187] "FP188" "FP189" "FP190"
## [190] "FP191" "FP192" "FP193"
## [193] "FP194" "FP195" "FP196"
## [196] "FP197" "FP198" "FP201"
## [199] "FP202" "FP203" "FP204"
## [202] "FP205" "FP206" "FP207"
## [205] "FP208" "MolWeight" "NumBonds"
## [208] "NumMultBonds" "NumRotBonds" "NumDblBonds"
## [211] "NumCarbon" "NumNitrogen" "NumOxygen"
## [214] "NumSulfer" "NumChlorine" "NumHalogen"
## [217] "NumRings" "HydrophilicFactor" "SurfaceArea1"
## [220] "SurfaceArea2"
##
## $xNames
## [1] "FP001" "FP002" "FP003"
## [4] "FP004" "FP005" "FP006"
## [7] "FP007" "FP008" "FP009"
## [10] "FP010" "FP011" "FP012"
## [13] "FP013" "FP014" "FP015"
## [16] "FP016" "FP017" "FP018"
## [19] "FP019" "FP020" "FP021"
## [22] "FP022" "FP023" "FP024"
## [25] "FP025" "FP026" "FP027"
## [28] "FP028" "FP029" "FP030"
## [31] "FP031" "FP032" "FP033"
## [34] "FP034" "FP035" "FP036"
## [37] "FP037" "FP038" "FP039"
## [40] "FP040" "FP041" "FP042"
## [43] "FP043" "FP044" "FP045"
## [46] "FP046" "FP047" "FP048"
## [49] "FP049" "FP050" "FP051"
## [52] "FP052" "FP053" "FP054"
## [55] "FP055" "FP056" "FP057"
## [58] "FP058" "FP059" "FP060"
## [61] "FP061" "FP062" "FP063"
## [64] "FP064" "FP065" "FP066"
## [67] "FP067" "FP068" "FP069"
## [70] "FP070" "FP071" "FP072"
## [73] "FP073" "FP074" "FP075"
## [76] "FP076" "FP077" "FP078"
## [79] "FP079" "FP080" "FP081"
## [82] "FP082" "FP083" "FP084"
## [85] "FP085" "FP086" "FP087"
## [88] "FP088" "FP089" "FP090"
## [91] "FP091" "FP092" "FP093"
## [94] "FP094" "FP095" "FP096"
## [97] "FP097" "FP098" "FP099"
## [100] "FP100" "FP101" "FP102"
## [103] "FP103" "FP104" "FP105"
## [106] "FP106" "FP107" "FP108"
## [109] "FP109" "FP110" "FP111"
## [112] "FP112" "FP113" "FP114"
## [115] "FP115" "FP116" "FP117"
## [118] "FP118" "FP119" "FP120"
## [121] "FP121" "FP122" "FP123"
## [124] "FP124" "FP125" "FP126"
## [127] "FP127" "FP128" "FP129"
## [130] "FP130" "FP131" "FP132"
## [133] "FP133" "FP134" "FP135"
## [136] "FP136" "FP137" "FP138"
## [139] "FP139" "FP140" "FP141"
## [142] "FP142" "FP143" "FP144"
## [145] "FP145" "FP146" "FP147"
## [148] "FP148" "FP149" "FP150"
## [151] "FP151" "FP152" "FP153"
## [154] "FP155" "FP156" "FP157"
## [157] "FP158" "FP159" "FP160"
## [160] "FP161" "FP162" "FP163"
## [163] "FP164" "FP165" "FP166"
## [166] "FP167" "FP168" "FP169"
## [169] "FP170" "FP171" "FP172"
## [172] "FP173" "FP174" "FP175"
## [175] "FP176" "FP177" "FP178"
## [178] "FP179" "FP180" "FP181"
## [181] "FP182" "FP183" "FP184"
## [184] "FP185" "FP186" "FP187"
## [187] "FP188" "FP189" "FP190"
## [190] "FP191" "FP192" "FP193"
## [193] "FP194" "FP195" "FP196"
## [196] "FP197" "FP198" "FP201"
## [199] "FP202" "FP203" "FP204"
## [202] "FP205" "FP206" "FP207"
## [205] "FP208" "MolWeight" "NumBonds"
## [208] "NumMultBonds" "NumRotBonds" "NumDblBonds"
## [211] "NumCarbon" "NumNitrogen" "NumOxygen"
## [214] "NumSulfer" "NumChlorine" "NumHalogen"
## [217] "NumRings" "HydrophilicFactor" "SurfaceArea1"
## [220] "SurfaceArea2"
##
## $problemType
## [1] "Classification"
##
## $tuneValue
## fL usekernel adjust
## 1 2 FALSE FALSE
##
## $obsLevels
## [1] "Low" "High"
## attr(,"ordered")
## [1] FALSE
##
## $param
## list()
##
## attr(,"class")
## [1] "NaiveBayes"NB_Tune$results## usekernel fL adjust ROC Sens Spec ROCSD SensSD
## 1 FALSE 2 FALSE 0.8818276 0.7772979 0.8072932 0.03408364 0.07087909
## 2 TRUE 2 FALSE NaN NaN NaN NA NA
## SpecSD
## 1 0.05222652
## 2 NA(NB_Train_ROCCurveAUC <- NB_Tune$results[NB_Tune$results$usekernel==NB_Tune$bestTune$usekernel &
NB_Tune$results$adjust==NB_Tune$bestTune$adjust,
c("ROC")])## [1] 0.8818276##################################
# Identifying and plotting the
# best model predictors
##################################
# model does not support variable importance measurement
##################################
# Independently evaluating the model
# on the test set
##################################
NB_Test <- data.frame(NB_Observed = PMA_PreModelling_Test_NB$Log_Solubility_Class,
NB_Predicted = predict(NB_Tune,
PMA_PreModelling_Test_NB[,!names(PMA_PreModelling_Test_NB) %in% c("Log_Solubility_Class")],
type = "prob"))
NB_Test## NB_Observed NB_Predicted.Low NB_Predicted.High
## 20 High 4.364662e-14 1.000000e+00
## 21 High 6.410958e-17 1.000000e+00
## 23 High 9.534226e-07 9.999990e-01
## 25 High 1.062868e-11 1.000000e+00
## 28 High 1.381006e-09 1.000000e+00
## 31 High 2.725477e-15 1.000000e+00
## 32 High 1.009329e-13 1.000000e+00
## 33 High 1.297622e-11 1.000000e+00
## 34 High 1.203507e-13 1.000000e+00
## 37 High 2.708885e-05 9.999729e-01
## 38 High 1.943691e-06 9.999981e-01
## 42 High 2.701061e-01 7.298939e-01
## 49 High 1.085724e-12 1.000000e+00
## 54 High 2.898243e-12 1.000000e+00
## 55 High 1.529527e-07 9.999998e-01
## 58 High 8.528585e-04 9.991471e-01
## 60 High 1.095641e-07 9.999999e-01
## 61 High 2.858235e-13 1.000000e+00
## 65 High 7.180941e-09 1.000000e+00
## 69 High 2.153357e-03 9.978466e-01
## 73 High 3.393127e-14 1.000000e+00
## 86 High 9.586947e-11 1.000000e+00
## 90 High 2.238680e-11 1.000000e+00
## 91 High 3.952971e-10 1.000000e+00
## 93 High 1.501086e-12 1.000000e+00
## 96 High 7.496453e-09 1.000000e+00
## 98 High 2.756200e-09 1.000000e+00
## 100 High 1.725896e-09 1.000000e+00
## 104 High 9.999626e-01 3.736998e-05
## 112 High 1.850118e-07 9.999998e-01
## 115 High 9.998048e-01 1.951718e-04
## 119 High 1.378442e-12 1.000000e+00
## 128 High 1.535482e-12 1.000000e+00
## 130 High 3.513718e-09 1.000000e+00
## 139 High 2.255600e-10 1.000000e+00
## 143 High 1.081262e-12 1.000000e+00
## 145 High 1.811821e-10 1.000000e+00
## 146 High 2.569698e-12 1.000000e+00
## 149 High 1.219667e-08 1.000000e+00
## 150 High 3.245685e-11 1.000000e+00
## 152 High 5.352517e-13 1.000000e+00
## 157 High 9.942953e-01 5.704656e-03
## 161 High 1.791776e-06 9.999982e-01
## 162 High 1.513519e-18 1.000000e+00
## 166 High 3.097081e-08 1.000000e+00
## 167 High 2.157478e-11 1.000000e+00
## 173 High 2.952122e-11 1.000000e+00
## 176 High 8.962827e-13 1.000000e+00
## 182 High 9.808933e-12 1.000000e+00
## 187 High 3.182456e-09 1.000000e+00
## 190 High 9.002230e-13 1.000000e+00
## 194 High 1.288191e-04 9.998712e-01
## 195 High 9.278369e-05 9.999072e-01
## 201 High 1.408298e-11 1.000000e+00
## 207 High 7.382190e-10 1.000000e+00
## 208 High 8.630909e-06 9.999914e-01
## 215 High 1.642038e-09 1.000000e+00
## 222 High 3.797564e-06 9.999962e-01
## 224 High 6.287627e-07 9.999994e-01
## 231 High 3.707866e-01 6.292134e-01
## 236 High 1.076599e-07 9.999999e-01
## 237 High 1.507970e-10 1.000000e+00
## 240 High 2.850582e-03 9.971494e-01
## 243 High 3.503573e-10 1.000000e+00
## 248 High 1.472072e-04 9.998528e-01
## 251 High 9.999890e-01 1.099658e-05
## 256 High 3.554193e-03 9.964458e-01
## 258 High 9.985646e-01 1.435368e-03
## 262 High 5.275795e-04 9.994724e-01
## 266 High 8.308258e-01 1.691742e-01
## 272 High 1.030189e-02 9.896981e-01
## 280 High 1.463723e-03 9.985363e-01
## 283 High 1.398582e-07 9.999999e-01
## 286 High 9.999986e-01 1.353171e-06
## 287 High 1.549529e-05 9.999845e-01
## 289 High 1.097015e-01 8.902985e-01
## 290 High 4.551853e-05 9.999545e-01
## 298 High 3.961289e-09 1.000000e+00
## 305 High 2.366783e-07 9.999998e-01
## 306 High 3.248590e-05 9.999675e-01
## 312 High 1.741562e-06 9.999983e-01
## 320 High 2.448799e-05 9.999755e-01
## 325 High 2.115973e-07 9.999998e-01
## 332 High 9.961767e-11 1.000000e+00
## 333 High 8.326838e-03 9.916732e-01
## 335 High 1.065318e-10 1.000000e+00
## 339 High 9.908988e-01 9.101184e-03
## 346 High 5.895639e-01 4.104361e-01
## 347 High 2.839264e-03 9.971607e-01
## 350 High 1.158072e-07 9.999999e-01
## 353 High 4.901773e-04 9.995098e-01
## 358 High 5.884228e-04 9.994116e-01
## 365 High 9.999931e-01 6.894831e-06
## 367 High 2.135277e-04 9.997865e-01
## 370 High 9.414952e-07 9.999991e-01
## 379 High 8.673552e-08 9.999999e-01
## 386 High 1.668272e-05 9.999833e-01
## 394 High 4.911945e-02 9.508805e-01
## 396 High 3.811223e-08 1.000000e+00
## 400 High 3.421792e-10 1.000000e+00
## 404 High 9.963372e-01 3.662832e-03
## 405 High 3.084035e-05 9.999692e-01
## 413 High 1.741976e-02 9.825802e-01
## 415 High 9.648352e-07 9.999990e-01
## 417 High 1.202736e-09 1.000000e+00
## 418 High 1.996106e-06 9.999980e-01
## 423 High 9.993650e-01 6.349562e-04
## 434 High 5.324453e-01 4.675547e-01
## 437 High 9.999992e-01 7.983086e-07
## 440 High 9.996967e-01 3.033301e-04
## 449 High 9.715650e-04 9.990284e-01
## 450 High 9.998962e-01 1.038334e-04
## 457 High 3.368502e-04 9.996631e-01
## 467 High 9.992981e-01 7.018652e-04
## 469 High 1.000000e+00 2.525893e-14
## 474 High 9.999930e-01 6.995108e-06
## 475 High 9.999980e-01 2.014157e-06
## 485 High 1.164597e-08 1.000000e+00
## 504 Low 9.822745e-01 1.772553e-02
## 511 Low 1.000000e+00 1.815732e-14
## 512 Low 9.998762e-01 1.237755e-04
## 517 Low 4.116534e-08 1.000000e+00
## 519 Low 9.997131e-01 2.869350e-04
## 520 Low 1.519122e-08 1.000000e+00
## 522 Low 9.905422e-01 9.457770e-03
## 527 Low 5.537178e-02 9.446282e-01
## 528 Low 3.473163e-08 1.000000e+00
## 529 Low 1.508821e-03 9.984912e-01
## 537 Low 1.696684e-07 9.999998e-01
## 540 Low 1.000000e+00 6.348742e-09
## 541 Low 2.095219e-04 9.997905e-01
## 547 Low 9.972504e-01 2.749566e-03
## 550 Low 9.999977e-01 2.289149e-06
## 555 Low 1.091912e-01 8.908088e-01
## 564 Low 4.763308e-09 1.000000e+00
## 570 Low 1.431011e-02 9.856899e-01
## 573 Low 9.679719e-01 3.202806e-02
## 575 Low 2.517162e-04 9.997483e-01
## 578 Low 5.846899e-07 9.999994e-01
## 581 Low 9.937508e-01 6.249203e-03
## 585 Low 8.739457e-01 1.260543e-01
## 590 Low 9.999837e-01 1.630388e-05
## 601 Low 1.000000e+00 7.824787e-13
## 602 Low 9.966568e-01 3.343166e-03
## 607 Low 8.879842e-01 1.120158e-01
## 610 Low 8.482429e-01 1.517571e-01
## 618 Low 9.999992e-01 7.774012e-07
## 624 Low 9.548460e-01 4.515403e-02
## 626 Low 8.951432e-07 9.999991e-01
## 627 Low 9.999958e-01 4.178262e-06
## 634 Low 9.680823e-01 3.191774e-02
## 640 Low 1.000000e+00 7.032587e-14
## 642 Low 1.382852e-09 1.000000e+00
## 643 Low 3.033635e-04 9.996966e-01
## 644 Low 9.988343e-01 1.165673e-03
## 645 Low 1.000000e+00 3.962132e-08
## 646 Low 9.992822e-01 7.178371e-04
## 647 Low 1.000000e+00 2.977842e-20
## 652 Low 1.381426e-06 9.999986e-01
## 658 Low 1.000000e+00 1.969600e-11
## 659 Low 9.998991e-01 1.009193e-04
## 660 Low 1.000000e+00 4.116921e-11
## 664 Low 1.806239e-01 8.193761e-01
## 666 Low 1.000000e+00 2.145719e-12
## 667 Low 1.000000e+00 1.268306e-14
## 675 Low 4.539644e-03 9.954604e-01
## 680 Low 1.000000e+00 1.301625e-18
## 681 Low 9.622303e-01 3.776968e-02
## 687 Low 8.802245e-01 1.197755e-01
## 694 Low 9.999997e-01 3.043066e-07
## 697 Low 1.000000e+00 1.741707e-14
## 701 Low 3.682376e-05 9.999632e-01
## 705 Low 1.000000e+00 7.111946e-13
## 707 Low 2.250327e-01 7.749673e-01
## 710 Low 1.000000e+00 2.909279e-08
## 716 Low 9.999999e-01 1.183748e-07
## 719 Low 9.999650e-01 3.502423e-05
## 720 Low 1.000000e+00 2.878200e-12
## 725 Low 1.000000e+00 2.736921e-12
## 727 Low 8.048301e-06 9.999920e-01
## 730 Low 1.000000e+00 5.518936e-25
## 738 Low 9.996194e-01 3.805966e-04
## 745 Low 5.152225e-01 4.847775e-01
## 748 Low 1.349340e-02 9.865066e-01
## 751 Low 1.000000e+00 3.215821e-11
## 756 Low 1.000000e+00 8.871037e-11
## 766 Low 9.979852e-01 2.014818e-03
## 769 Low 1.000000e+00 3.821915e-16
## 783 Low 1.000000e+00 3.950841e-15
## 785 Low 1.000000e+00 1.822996e-08
## 790 Low 1.000000e+00 1.764736e-13
## 793 Low 9.980992e-01 1.900826e-03
## 795 Low 1.000000e+00 1.730572e-14
## 796 Low 1.000000e+00 7.804220e-13
## 797 Low 9.820198e-01 1.798018e-02
## 801 Low 1.000000e+00 4.135155e-18
## 811 Low 1.000000e+00 6.317191e-24
## 812 Low 1.000000e+00 5.366420e-11
## 815 Low 1.000000e+00 2.314690e-09
## 816 Low 1.000000e+00 8.814549e-16
## 817 Low 1.000000e+00 9.133178e-12
## 824 Low 1.000000e+00 1.996744e-21
## 825 Low 1.000000e+00 8.201293e-22
## 826 Low 1.000000e+00 1.170412e-19
## 830 Low 9.999966e-01 3.448913e-06
## 837 Low 9.999995e-01 5.441761e-07
## 838 Low 1.000000e+00 6.678992e-14
## 844 Low 9.999993e-01 6.850550e-07
## 845 Low 1.000000e+00 1.967339e-10
## 847 Low 1.000000e+00 2.967574e-22
## 850 Low 1.000000e+00 7.031151e-26
## 852 Low 1.000000e+00 5.197849e-34
## 853 Low 1.000000e+00 1.285701e-32
## 861 Low 1.000000e+00 2.652783e-41
## 868 Low 1.000000e+00 1.919862e-16
## 874 Low 1.000000e+00 1.327751e-53
## 879 High 2.956321e-10 1.000000e+00
## 895 High 1.470326e-14 1.000000e+00
## 899 High 3.385981e-21 1.000000e+00
## 903 High 7.518799e-14 1.000000e+00
## 917 High 1.712196e-09 1.000000e+00
## 927 High 6.248833e-14 1.000000e+00
## 929 High 3.451424e-12 1.000000e+00
## 931 High 4.725543e-12 1.000000e+00
## 933 High 9.097195e-01 9.028051e-02
## 944 High 1.846048e-04 9.998154e-01
## 947 High 1.690710e-11 1.000000e+00
## 949 High 2.315612e-07 9.999998e-01
## 953 High 7.734168e-14 1.000000e+00
## 958 High 3.199961e-01 6.800039e-01
## 961 High 1.932456e-10 1.000000e+00
## 963 High 1.668592e-07 9.999998e-01
## 964 High 9.024263e-11 1.000000e+00
## 973 High 9.911857e-07 9.999990e-01
## 976 High 1.528087e-08 1.000000e+00
## 977 High 3.583251e-04 9.996417e-01
## 980 High 1.320632e-01 8.679368e-01
## 983 High 8.106142e-02 9.189386e-01
## 984 High 9.278369e-05 9.999072e-01
## 986 High 2.337792e-08 1.000000e+00
## 989 High 1.004199e-11 1.000000e+00
## 991 High 8.467073e-11 1.000000e+00
## 996 High 1.027637e-10 1.000000e+00
## 997 High 8.473551e-01 1.526449e-01
## 999 High 9.987976e-01 1.202435e-03
## 1000 High 4.480506e-08 1.000000e+00
## 1003 High 1.751854e-10 1.000000e+00
## 1008 High 1.829140e-07 9.999998e-01
## 1009 High 4.481990e-09 1.000000e+00
## 1014 High 1.374653e-08 1.000000e+00
## 1015 High 8.448272e-05 9.999155e-01
## 1040 High 4.688915e-05 9.999531e-01
## 1042 High 2.821302e-04 9.997179e-01
## 1043 High 9.999978e-01 2.168049e-06
## 1050 High 1.806202e-06 9.999982e-01
## 1052 High 1.651919e-01 8.348081e-01
## 1056 High 5.730803e-07 9.999994e-01
## 1070 High 7.173292e-02 9.282671e-01
## 1073 High 9.999956e-01 4.405921e-06
## 1074 High 3.598259e-06 9.999964e-01
## 1079 High 3.207395e-08 1.000000e+00
## 1080 High 8.409607e-04 9.991590e-01
## 1085 High 9.996070e-01 3.930446e-04
## 1087 High 1.460034e-01 8.539966e-01
## 1096 High 1.000000e+00 6.411628e-09
## 1099 High 6.012363e-01 3.987637e-01
## 1100 High 1.811717e-04 9.998188e-01
## 1102 High 1.829295e-11 1.000000e+00
## 1107 Low 6.548054e-05 9.999345e-01
## 1109 Low 9.996320e-01 3.679754e-04
## 1114 Low 2.276602e-04 9.997723e-01
## 1118 Low 8.925095e-01 1.074905e-01
## 1123 Low 1.000000e+00 6.204119e-09
## 1132 Low 4.821842e-01 5.178158e-01
## 1134 Low 9.112545e-03 9.908875e-01
## 1137 Low 9.999991e-01 8.593389e-07
## 1154 Low 9.999425e-01 5.749553e-05
## 1155 Low 3.591183e-04 9.996409e-01
## 1157 Low 9.999999e-01 1.207967e-07
## 1162 Low 6.090085e-03 9.939099e-01
## 1164 Low 2.940110e-10 1.000000e+00
## 1171 Low 1.000000e+00 7.521191e-11
## 1172 Low 1.000000e+00 4.427012e-14
## 1175 Low 9.807048e-01 1.929515e-02
## 1177 Low 1.424471e-04 9.998576e-01
## 1179 Low 1.000000e+00 7.221229e-21
## 1183 Low 1.894181e-05 9.999811e-01
## 1185 Low 1.000000e+00 3.476284e-10
## 1189 Low 9.999975e-01 2.496675e-06
## 1211 Low 9.996911e-01 3.088793e-04
## 1218 Low 1.000000e+00 3.348881e-15
## 1224 Low 1.000000e+00 5.537053e-10
## 1225 Low 2.729124e-03 9.972709e-01
## 1227 Low 1.000000e+00 2.185986e-13
## 1232 Low 1.000000e+00 1.750445e-13
## 1235 Low 9.999437e-01 5.632486e-05
## 1238 Low 1.000000e+00 5.638167e-10
## 1240 Low 1.000000e+00 5.460272e-10
## 1241 Low 9.982659e-01 1.734119e-03
## 1248 Low 9.999829e-01 1.706585e-05
## 1258 Low 1.000000e+00 1.058522e-13
## 1261 Low 1.000000e+00 1.176989e-44
## 1263 Low 1.000000e+00 3.209935e-19
## 1269 Low 1.000000e+00 4.191854e-12
## 1270 Low 1.000000e+00 1.776959e-14
## 1271 Low 1.000000e+00 1.524365e-27
## 1272 Low 1.000000e+00 5.280803e-33
## 1280 Low 1.000000e+00 1.491056e-51
## 1286 Low 1.000000e+00 2.499037e-14
## 1287 Low 1.000000e+00 7.501795e-16
## 1289 Low 1.000000e+00 1.073174e-74
## 1290 Low 1.000000e+00 1.144887e-34
## 1291 High 6.868184e-07 9.999993e-01
## 1294 High 9.974144e-01 2.585565e-03
## 1305 Low 1.000000e+00 5.562553e-10
## 1308 High 9.999936e-01 6.369129e-06##################################
# Reporting the independent evaluation results
# for the test set
##################################
NB_Test_ROC <- roc(response = NB_Test$NB_Observed,
predictor = NB_Test$NB_Predicted.High,
levels = rev(levels(NB_Test$NB_Observed)))
(NB_Test_ROCCurveAUC <- auc(NB_Test_ROC)[1])## [1] 0.88560571.5.6 Nearest Shrunken Centroids (NSC)
[A] The nearest shrunken centroids model from the pamr package was implemented through the caret package.
[B] The model contains 1 hyperparameter:
[B.1] threshold = shrinkage threshold made to vary across a range of values equal to 0 to 25
[C] The cross-validated model performance of the final model is summarized as follows:
[C.1] Final model configuration involves threshold=0
[C.2] ROC Curve AUC = 0.86622
[D] The model allows for ranking of predictors in terms of variable importance. The top-performing predictors in the model are as follows:
[D.1] MolWeight variable (numeric)
[D.2] NumCarbon variable (numeric)
[D.3] NumBonds variable (numeric)
[D.4] FP076 variable (factor)
[D.5] NumRings variable (numeric)
[E] The independent test model performance of the final model is summarized as follows:
[E.1] ROC Curve AUC = 0.88771
##################################
# Transforming factor predictors
# as required by the nature of the model
##################################
# Creating a local object
# for the train and test sets
##################################
PMA_PreModelling_Train_NSC <- as.data.frame(lapply(PMA_PreModelling_Train[,!names(PMA_PreModelling_Train) %in%
c("Log_Solubility_Class")],
function(x) as.numeric(as.character(x))))
PMA_PreModelling_Train_NSC$Log_Solubility_Class <- PMA_PreModelling_Train$Log_Solubility_Class
dim(PMA_PreModelling_Train_NSC)## [1] 951 221PMA_PreModelling_Test_NSC <- as.data.frame(lapply(PMA_PreModelling_Test[,!names(PMA_PreModelling_Test) %in%
c("Log_Solubility_Class")],
function(x) as.numeric(as.character(x))))
PMA_PreModelling_Test_NSC$Log_Solubility_Class <- PMA_PreModelling_Test$Log_Solubility_Class
dim(PMA_PreModelling_Test_NSC)## [1] 316 221##################################
# Creating consistent fold assignments
# for the 10-Fold Cross Validation process
##################################
set.seed(12345678)
KFold_Indices <- createFolds(PMA_PreModelling_Train_NSC$Log_Solubility_Class,
k = 10,
returnTrain=TRUE)
KFold_Control <- trainControl(method="cv",
index=KFold_Indices,
summaryFunction = twoClassSummary,
classProbs = TRUE)
##################################
# Setting the conditions
# for hyperparameter tuning
##################################
NSC_Grid = data.frame(threshold = seq(0, 8, length = 9))
##################################
# Running the nearest shrunken centroids model
# by setting the caret method to 'pam'
##################################
set.seed(12345678)
NSC_Tune <- train(x = PMA_PreModelling_Train_NSC[,!names(PMA_PreModelling_Train_NSC) %in% c("Log_Solubility_Class")],
y = PMA_PreModelling_Train_NSC$Log_Solubility_Class,
method = "pam",
tuneGrid = NSC_Grid,
metric = "ROC",
preProc = c("center", "scale"),
trControl = KFold_Control)## 11111111111##################################
# Reporting the cross-validation results
# for the train set
##################################
NSC_Tune## Nearest Shrunken Centroids
##
## 951 samples
## 220 predictors
## 2 classes: 'Low', 'High'
##
## Pre-processing: centered (220), scaled (220)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 857, 855, 857, 855, 856, 856, ...
## Resampling results across tuning parameters:
##
## threshold ROC Sens Spec
## 0 0.8662268 0.73289037 0.8111756
## 1 0.8506061 0.75874862 0.7864296
## 2 0.8423625 0.75642303 0.7920900
## 3 0.8452235 0.74939092 0.7977141
## 4 0.8496146 0.69335548 0.8473149
## 5 0.8482607 0.63283499 0.8854499
## 6 0.8523256 0.51306755 0.9160377
## 7 0.8567815 0.25027685 0.9770682
## 8 0.8600584 0.01168328 0.9961901
##
## ROC was used to select the optimal model using the largest value.
## The final value used for the model was threshold = 0.NSC_Tune$finalModel## Call:
## pamr::pamr.train(data = list(x = t(x), y = y), threshold = param$threshold)
## threshold nonzero errors
## 1 0 220 202NSC_Tune$results## threshold ROC Sens Spec ROCSD SensSD SpecSD
## 1 0 0.8662268 0.73289037 0.8111756 0.04304383 0.07762574 0.058680015
## 2 1 0.8506061 0.75874862 0.7864296 0.04510309 0.06988456 0.061942549
## 3 2 0.8423625 0.75642303 0.7920900 0.04603917 0.06821025 0.057910338
## 4 3 0.8452235 0.74939092 0.7977141 0.04694042 0.07866890 0.051514933
## 5 4 0.8496146 0.69335548 0.8473149 0.04925590 0.07823711 0.059665077
## 6 5 0.8482607 0.63283499 0.8854499 0.04933820 0.08297623 0.060328817
## 7 6 0.8523256 0.51306755 0.9160377 0.04688017 0.07061927 0.055446607
## 8 7 0.8567815 0.25027685 0.9770682 0.04392608 0.09298992 0.029762016
## 9 8 0.8600584 0.01168328 0.9961901 0.04172407 0.01648872 0.008032365(NSC_Train_ROCCurveAUC <- NSC_Tune$results[NSC_Tune$results$threshold==NSC_Tune$bestTune$threshold,
c("ROC")])## [1] 0.8662268##################################
# Identifying and plotting the
# best model predictors
##################################
NSC_VarImp <- varImp(NSC_Tune, scale = TRUE)
plot(NSC_VarImp,
top=25,
scales=list(y=list(cex = .95)),
main="Ranked Variable Importance : Nearest Shrunken Centroids",
xlab="Scaled Variable Importance Metrics",
ylab="Predictors",
cex=2,
origin=0,
alpha=0.45)
##################################
# Independently evaluating the model
# on the test set
##################################
NSC_Test <- data.frame(NSC_Observed = PMA_PreModelling_Test_NSC$Log_Solubility_Class,
NSC_Predicted = predict(NSC_Tune,
PMA_PreModelling_Test_NSC[,!names(PMA_PreModelling_Test_NSC) %in% c("Log_Solubility_Class")],
type = "prob"))
NSC_Test## NSC_Observed NSC_Predicted.Low NSC_Predicted.High
## 1 High 0.0006451421 9.993549e-01
## 2 High 0.0002155134 9.997845e-01
## 3 High 0.0604052901 9.395947e-01
## 4 High 0.0036516100 9.963484e-01
## 5 High 0.0127876960 9.872123e-01
## 6 High 0.0003903184 9.996097e-01
## 7 High 0.0009972407 9.990028e-01
## 8 High 0.0033402920 9.966597e-01
## 9 High 0.0010627698 9.989372e-01
## 10 High 0.1138515825 8.861484e-01
## 11 High 0.0610720674 9.389279e-01
## 12 High 0.4255360697 5.744639e-01
## 13 High 0.0017229985 9.982770e-01
## 14 High 0.0020473609 9.979526e-01
## 15 High 0.0663941770 9.336058e-01
## 16 High 0.1786758840 8.213241e-01
## 17 High 0.0317688876 9.682311e-01
## 18 High 0.0013350406 9.986650e-01
## 19 High 0.0165625828 9.834374e-01
## 20 High 0.2110285968 7.889714e-01
## 21 High 0.0049303783 9.950696e-01
## 22 High 0.0041076900 9.958923e-01
## 23 High 0.0033128336 9.966872e-01
## 24 High 0.0349658408 9.650342e-01
## 25 High 0.0016530272 9.983470e-01
## 26 High 0.0740667283 9.259333e-01
## 27 High 0.0117268171 9.882732e-01
## 28 High 0.0114968940 9.885031e-01
## 29 High 0.8444140973 1.555859e-01
## 30 High 0.0362966029 9.637034e-01
## 31 High 0.9177869219 8.221308e-02
## 32 High 0.0018008068 9.981992e-01
## 33 High 0.0018414958 9.981585e-01
## 34 High 0.0262377857 9.737622e-01
## 35 High 0.0126567263 9.873433e-01
## 36 High 0.0018063539 9.981936e-01
## 37 High 0.0072185822 9.927814e-01
## 38 High 0.0020931449 9.979069e-01
## 39 High 0.0187987024 9.812013e-01
## 40 High 0.0042009170 9.957991e-01
## 41 High 0.0015451771 9.984548e-01
## 42 High 0.7900253745 2.099746e-01
## 43 High 0.0623805741 9.376194e-01
## 44 High 0.0001318583 9.998681e-01
## 45 High 0.0094873913 9.905126e-01
## 46 High 0.0039090942 9.960909e-01
## 47 High 0.0037091520 9.962908e-01
## 48 High 0.0016046890 9.983953e-01
## 49 High 0.0022270332 9.977730e-01
## 50 High 0.0208788218 9.791212e-01
## 51 High 0.0029586276 9.970414e-01
## 52 High 0.0051965990 9.948034e-01
## 53 High 0.1412080677 8.587919e-01
## 54 High 0.0027853958 9.972146e-01
## 55 High 0.0072298168 9.927702e-01
## 56 High 0.0943990696 9.056009e-01
## 57 High 0.0046030522 9.953969e-01
## 58 High 0.0705826967 9.294173e-01
## 59 High 0.0378928514 9.621071e-01
## 60 High 0.5375022873 4.624977e-01
## 61 High 0.0141514443 9.858486e-01
## 62 High 0.0044352392 9.955648e-01
## 63 High 0.0452858623 9.547141e-01
## 64 High 0.0060561748 9.939438e-01
## 65 High 0.1568926225 8.431074e-01
## 66 High 0.9603224703 3.967753e-02
## 67 High 0.2848295126 7.151705e-01
## 68 High 0.8740413066 1.259587e-01
## 69 High 0.2092377088 7.907623e-01
## 70 High 0.4545052487 5.454948e-01
## 71 High 0.1044235855 8.955764e-01
## 72 High 0.1855730399 8.144270e-01
## 73 High 0.0330928020 9.669072e-01
## 74 High 0.9306661556 6.933384e-02
## 75 High 0.0994052177 9.005948e-01
## 76 High 0.0146100639 9.853899e-01
## 77 High 0.0766221354 9.233779e-01
## 78 High 0.0104427733 9.895572e-01
## 79 High 0.0346527577 9.653472e-01
## 80 High 0.1009499622 8.990500e-01
## 81 High 0.0654556273 9.345444e-01
## 82 High 0.1117124831 8.882875e-01
## 83 High 0.0119600012 9.880400e-01
## 84 High 0.0038588189 9.961412e-01
## 85 High 0.3558402137 6.441598e-01
## 86 High 0.0045565456 9.954435e-01
## 87 High 0.8136371244 1.863629e-01
## 88 High 0.6218632759 3.781367e-01
## 89 High 0.0122704930 9.877295e-01
## 90 High 0.0243772968 9.756227e-01
## 91 High 0.1983860000 8.016140e-01
## 92 High 0.2027821824 7.972178e-01
## 93 High 0.9056529367 9.434706e-02
## 94 High 0.1587829028 8.412171e-01
## 95 High 0.0624728156 9.375272e-01
## 96 High 0.0384895305 9.615105e-01
## 97 High 0.1057861890 8.942138e-01
## 98 High 0.3845721632 6.154278e-01
## 99 High 0.0270587001 9.729413e-01
## 100 High 0.0052493149 9.947507e-01
## 101 High 0.0106982381 9.893018e-01
## 102 High 0.1165548893 8.834451e-01
## 103 High 0.3981173362 6.018827e-01
## 104 High 0.0457464643 9.542535e-01
## 105 High 0.0099848730 9.900151e-01
## 106 High 0.0504588490 9.495412e-01
## 107 High 0.9010348692 9.896513e-02
## 108 High 0.5953615657 4.046384e-01
## 109 High 0.4940206315 5.059794e-01
## 110 High 0.7847934712 2.152065e-01
## 111 High 0.1614638537 8.385361e-01
## 112 High 0.8241775179 1.758225e-01
## 113 High 0.1280848277 8.719152e-01
## 114 High 0.7593350386 2.406650e-01
## 115 High 0.9873332495 1.266675e-02
## 116 High 0.9318522720 6.814773e-02
## 117 High 0.8966058414 1.033942e-01
## 118 High 0.0044359562 9.955640e-01
## 119 Low 0.7059862458 2.940138e-01
## 120 Low 0.9992039934 7.960066e-04
## 121 Low 0.9254749153 7.452508e-02
## 122 Low 0.0614419655 9.385580e-01
## 123 Low 0.8216358132 1.783642e-01
## 124 Low 0.0145674300 9.854326e-01
## 125 Low 0.7790689837 2.209310e-01
## 126 Low 0.3265989491 6.734011e-01
## 127 Low 0.0216945436 9.783055e-01
## 128 Low 0.1944302765 8.055697e-01
## 129 Low 0.0282641441 9.717359e-01
## 130 Low 0.9870327120 1.296729e-02
## 131 Low 0.1769263234 8.230737e-01
## 132 Low 0.6147460621 3.852539e-01
## 133 Low 0.9670585597 3.294144e-02
## 134 Low 0.4175143677 5.824856e-01
## 135 Low 0.0060725476 9.939275e-01
## 136 Low 0.2789407323 7.210593e-01
## 137 Low 0.7864057952 2.135942e-01
## 138 Low 0.1817168682 8.182831e-01
## 139 Low 0.0458896309 9.541104e-01
## 140 Low 0.8360770959 1.639229e-01
## 141 Low 0.6099989237 3.900011e-01
## 142 Low 0.9408002570 5.919974e-02
## 143 Low 0.9971660007 2.833999e-03
## 144 Low 0.6743596806 3.256403e-01
## 145 Low 0.6514118409 3.485882e-01
## 146 Low 0.6576481694 3.423518e-01
## 147 Low 0.8914030599 1.085969e-01
## 148 Low 0.6621449861 3.378550e-01
## 149 Low 0.0177509658 9.822490e-01
## 150 Low 0.9491547834 5.084522e-02
## 151 Low 0.5203157974 4.796842e-01
## 152 Low 0.9961080716 3.891928e-03
## 153 Low 0.0095049175 9.904951e-01
## 154 Low 0.1853892874 8.146107e-01
## 155 Low 0.8740987088 1.259013e-01
## 156 Low 0.9674183514 3.258165e-02
## 157 Low 0.8946839739 1.053160e-01
## 158 Low 0.9999337235 6.627646e-05
## 159 Low 0.0447853229 9.552147e-01
## 160 Low 0.9939275185 6.072482e-03
## 161 Low 0.9129391235 8.706088e-02
## 162 Low 0.9957596197 4.240380e-03
## 163 Low 0.2242162462 7.757838e-01
## 164 Low 0.7539654647 2.460345e-01
## 165 Low 0.9966972430 3.302757e-03
## 166 Low 0.3112479576 6.887520e-01
## 167 Low 0.9991233346 8.766654e-04
## 168 Low 0.6520699832 3.479300e-01
## 169 Low 0.6785401780 3.214598e-01
## 170 Low 0.9785772776 2.142272e-02
## 171 Low 0.1502065053 8.497935e-01
## 172 Low 0.1152558521 8.847441e-01
## 173 Low 0.9943281827 5.671817e-03
## 174 Low 0.0549368462 9.450632e-01
## 175 Low 0.9896569892 1.034301e-02
## 176 Low 0.9642378155 3.576218e-02
## 177 Low 0.7790371001 2.209629e-01
## 178 Low 0.9972559255 2.744074e-03
## 179 Low 0.9971255101 2.874490e-03
## 180 Low 0.0767808327 9.232192e-01
## 181 Low 0.4301839881 5.698160e-01
## 182 Low 0.8580215080 1.419785e-01
## 183 Low 0.6163950576 3.836049e-01
## 184 Low 0.0692678605 9.307321e-01
## 185 Low 0.9942257577 5.774242e-03
## 186 Low 0.9919312293 8.068771e-03
## 187 Low 0.8021939594 1.978060e-01
## 188 Low 0.9940449615 5.955038e-03
## 189 Low 0.9992009255 7.990745e-04
## 190 Low 0.9858106244 1.418938e-02
## 191 Low 0.9988732188 1.126781e-03
## 192 Low 0.8293315437 1.706685e-01
## 193 Low 0.9982746009 1.725399e-03
## 194 Low 0.9977498074 2.250193e-03
## 195 Low 0.5610525943 4.389474e-01
## 196 Low 0.9847347160 1.526528e-02
## 197 Low 0.9795852037 2.041480e-02
## 198 Low 0.9945028341 5.497166e-03
## 199 Low 0.9874691327 1.253087e-02
## 200 Low 0.9927605623 7.239438e-03
## 201 Low 0.9938890399 6.110960e-03
## 202 Low 0.9998255334 1.744666e-04
## 203 Low 0.9998620929 1.379071e-04
## 204 Low 0.9995375420 4.624580e-04
## 205 Low 0.9428008480 5.719915e-02
## 206 Low 0.9604329765 3.956702e-02
## 207 Low 0.9933658354 6.634165e-03
## 208 Low 0.9596194312 4.038057e-02
## 209 Low 0.9833061545 1.669385e-02
## 210 Low 0.9982821586 1.717841e-03
## 211 Low 0.9997679953 2.320047e-04
## 212 Low 0.9999084539 9.154606e-05
## 213 Low 0.9997814480 2.185520e-04
## 214 Low 0.9998359264 1.640736e-04
## 215 Low 0.9983247200 1.675280e-03
## 216 Low 0.9999608221 3.917790e-05
## 217 High 0.0074646417 9.925354e-01
## 218 High 0.0005760025 9.994240e-01
## 219 High 0.0002649070 9.997351e-01
## 220 High 0.0008848922 9.991151e-01
## 221 High 0.0187393374 9.812607e-01
## 222 High 0.0007936273 9.992064e-01
## 223 High 0.0021676805 9.978323e-01
## 224 High 0.0023409681 9.976590e-01
## 225 High 0.7194570709 2.805429e-01
## 226 High 0.1901781286 8.098219e-01
## 227 High 0.0030597464 9.969403e-01
## 228 High 0.0356846918 9.643153e-01
## 229 High 0.0010122283 9.989878e-01
## 230 High 0.5725853361 4.274147e-01
## 231 High 0.0062145433 9.937855e-01
## 232 High 0.0090779468 9.909221e-01
## 233 High 0.0044657553 9.955342e-01
## 234 High 0.0553769178 9.446231e-01
## 235 High 0.0045671499 9.954329e-01
## 236 High 0.1905650501 8.094349e-01
## 237 High 0.1689928956 8.310071e-01
## 238 High 0.4297281313 5.702719e-01
## 239 High 0.1412080677 8.587919e-01
## 240 High 0.0227777896 9.772222e-01
## 241 High 0.0030204347 9.969796e-01
## 242 High 0.0024685397 9.975315e-01
## 243 High 0.0043818648 9.956181e-01
## 244 High 0.4988962890 5.011037e-01
## 245 High 0.8989197706 1.010802e-01
## 246 High 0.0245100099 9.754900e-01
## 247 High 0.0047309052 9.952691e-01
## 248 High 0.0393670009 9.606330e-01
## 249 High 0.0120412984 9.879587e-01
## 250 High 0.0137409392 9.862591e-01
## 251 High 0.0918186102 9.081814e-01
## 252 High 0.1189486505 8.810513e-01
## 253 High 0.0846307230 9.153693e-01
## 254 High 0.9048304888 9.516951e-02
## 255 High 0.0240351907 9.759648e-01
## 256 High 0.4969369759 5.030630e-01
## 257 High 0.0298939066 9.701061e-01
## 258 High 0.4463491338 5.536509e-01
## 259 High 0.7813977296 2.186023e-01
## 260 High 0.0335418128 9.664582e-01
## 261 High 0.0145031733 9.854968e-01
## 262 High 0.2216389279 7.783611e-01
## 263 High 0.0209186265 9.790814e-01
## 264 High 0.4445345695 5.554654e-01
## 265 High 0.9826378538 1.736215e-02
## 266 High 0.6162120467 3.837880e-01
## 267 High 0.1556435022 8.443565e-01
## 268 High 0.0041259382 9.958741e-01
## 269 Low 0.1455014205 8.544986e-01
## 270 Low 0.8193065276 1.806935e-01
## 271 Low 0.1894942278 8.105058e-01
## 272 Low 0.6812582118 3.187418e-01
## 273 Low 0.9760506062 2.394939e-02
## 274 Low 0.5606332084 4.393668e-01
## 275 Low 0.2634212741 7.365787e-01
## 276 Low 0.9661276096 3.387239e-02
## 277 Low 0.9173573191 8.264268e-02
## 278 Low 0.1691964809 8.308035e-01
## 279 Low 0.9620030679 3.799693e-02
## 280 Low 0.3233319475 6.766681e-01
## 281 Low 0.0064495468 9.935505e-01
## 282 Low 0.9929135607 7.086439e-03
## 283 Low 0.8862071821 1.137928e-01
## 284 Low 0.7476439656 2.523560e-01
## 285 Low 0.0496836908 9.503163e-01
## 286 Low 0.9969648465 3.035153e-03
## 287 Low 0.0985066882 9.014933e-01
## 288 Low 0.9891470074 1.085299e-02
## 289 Low 0.8991985373 1.008015e-01
## 290 Low 0.9142758333 8.572417e-02
## 291 Low 0.9980491267 1.950873e-03
## 292 Low 0.9279022519 7.209775e-02
## 293 Low 0.2618544740 7.381455e-01
## 294 Low 0.9967399616 3.260038e-03
## 295 Low 0.9975933704 2.406630e-03
## 296 Low 0.8878077878 1.121922e-01
## 297 Low 0.9916684411 8.331559e-03
## 298 Low 0.9940168300 5.983170e-03
## 299 Low 0.8658837237 1.341163e-01
## 300 Low 0.9169678611 8.303214e-02
## 301 Low 0.9927222315 7.277768e-03
## 302 Low 0.9913736647 8.626335e-03
## 303 Low 0.9994443946 5.556054e-04
## 304 Low 0.9664330235 3.356698e-02
## 305 Low 0.9688445020 3.115550e-02
## 306 Low 0.9999072373 9.276269e-05
## 307 Low 0.9998272440 1.727560e-04
## 308 Low 0.9998760262 1.239738e-04
## 309 Low 0.9928194694 7.180531e-03
## 310 Low 0.9923710166 7.628983e-03
## 311 Low 0.9997797378 2.202622e-04
## 312 Low 0.9999309292 6.907076e-05
## 313 High 0.0487302695 9.512697e-01
## 314 High 0.8691458723 1.308541e-01
## 315 Low 0.9791566576 2.084334e-02
## 316 High 0.5663955060 4.336045e-01##################################
# Reporting the independent evaluation results
# for the test set
##################################
NSC_Test_ROC <- roc(response = NSC_Test$NSC_Observed,
predictor = NSC_Test$NSC_Predicted.High,
levels = rev(levels(NSC_Test$NSC_Observed)))
(NSC_Test_ROCCurveAUC <- auc(NSC_Test_ROC)[1])## [1] 0.88770771.5.7 Averaged Neural Network (AVNN)
[A] The averaged neural network model from the nnet package was implemented through the caret package.
[B] The model contains 3 hyperparameters:
[B.1] size = number of hidden units made to vary across a range of values equal to 1 to 13
[B.2] decay = weight decay made to vary across a range of values equal to 0.00 to 0.10
[B.3] bag = bagging held constant at a value of FALSE
[C] The cross-validated model performance of the final model is summarized as follows:
[C.1] Final model configuration involves size=13, decay=0 and bag=FALSE
[C.2] ROC Curve AUC = 0.91577
[D] The model does not allow for ranking of predictors in terms of variable importance.
[E] The independent test model performance of the final model is summarized as follows:
[E.1] ROC Curve AUC = 0.91891
##################################
# Transforming factor predictors
# as required by the nature of the model
##################################
# Creating a local object
# for the train and test sets
##################################
PMA_PreModelling_Train_AVNN <- as.data.frame(lapply(PMA_PreModelling_Train[,!names(PMA_PreModelling_Train) %in%
c("Log_Solubility_Class")],
function(x) as.numeric(as.character(x))))
PMA_PreModelling_Train_AVNN$Log_Solubility_Class <- PMA_PreModelling_Train$Log_Solubility_Class
dim(PMA_PreModelling_Train_AVNN)## [1] 951 221PMA_PreModelling_Test_AVNN <- as.data.frame(lapply(PMA_PreModelling_Test[,!names(PMA_PreModelling_Test) %in%
c("Log_Solubility_Class")],
function(x) as.numeric(as.character(x))))
PMA_PreModelling_Test_AVNN$Log_Solubility_Class <- PMA_PreModelling_Test$Log_Solubility_Class
dim(PMA_PreModelling_Test_AVNN)## [1] 316 221##################################
# Creating consistent fold assignments
# for the 10-Fold Cross Validation process
##################################
set.seed(12345678)
KFold_Indices <- createFolds(PMA_PreModelling_Train_AVNN$Log_Solubility_Class,
k = 10,
returnTrain=TRUE)
KFold_Control <- trainControl(method="cv",
index=KFold_Indices,
summaryFunction = twoClassSummary,
classProbs = TRUE)
##################################
# Setting the conditions
# for hyperparameter tuning
##################################
AVNN_Grid = expand.grid(decay = c(0.00, 0.01, 0.10),
size = c(1, 5, 9, 13),
bag = FALSE)
maxSize <- max(AVNN_Grid$size)
##################################
# Running the averaged neural network model
# by setting the caret method to 'avNNet'
##################################
set.seed(12345678)
AVNN_Tune <- train(x = PMA_PreModelling_Train_AVNN[,!names(PMA_PreModelling_Train_AVNN) %in% c("Log_Solubility_Class")],
y = PMA_PreModelling_Train_AVNN$Log_Solubility_Class,
method = "avNNet",
tuneGrid = AVNN_Grid,
metric = "ROC",
preProc = c("center", "scale"),
trControl = KFold_Control,
maxit = 5,
repeats = 10,
allowParallel = FALSE,
MaxNWts = 10*(maxSize * (length(PMA_PreModelling_Train_AVNN) + 1) + maxSize + 1),
trace = FALSE)
##################################
# Reporting the cross-validation results
# for the train set
##################################
AVNN_Tune## Model Averaged Neural Network
##
## 951 samples
## 220 predictors
## 2 classes: 'Low', 'High'
##
## Pre-processing: centered (220), scaled (220)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 857, 855, 857, 855, 856, 856, ...
## Resampling results across tuning parameters:
##
## decay size ROC Sens Spec
## 0.00 1 0.8825921 0.7633444 0.8016691
## 0.00 5 0.9031602 0.8055371 0.8283019
## 0.00 9 0.9038488 0.8431340 0.8189405
## 0.00 13 0.9157703 0.8431340 0.8130987
## 0.01 1 0.8954928 0.7797342 0.8264514
## 0.01 5 0.9082890 0.8125692 0.8398766
## 0.01 9 0.9109317 0.8101883 0.8304790
## 0.01 13 0.9143824 0.8314507 0.8208999
## 0.10 1 0.8898842 0.7727575 0.8169811
## 0.10 5 0.9112202 0.8055925 0.8302975
## 0.10 9 0.9151277 0.8335548 0.8169448
## 0.10 13 0.9100212 0.8361573 0.8132075
##
## Tuning parameter 'bag' was held constant at a value of FALSE
## ROC was used to select the optimal model using the largest value.
## The final values used for the model were size = 13, decay = 0 and bag = FALSE.AVNN_Tune$finalModel## Model Averaged Neural Network with 10 Repeats
##
## a 220-13-2 network with 2901 weights
## options were -AVNN_Tune$results## decay size bag ROC Sens Spec ROCSD SensSD
## 1 0.00 1 FALSE 0.8825921 0.7633444 0.8016691 0.04823911 0.08305738
## 5 0.01 1 FALSE 0.8954928 0.7797342 0.8264514 0.03014815 0.05618559
## 9 0.10 1 FALSE 0.8898842 0.7727575 0.8169811 0.03692104 0.06246770
## 2 0.00 5 FALSE 0.9031602 0.8055371 0.8283019 0.03633354 0.06987663
## 6 0.01 5 FALSE 0.9082890 0.8125692 0.8398766 0.03021656 0.05753685
## 10 0.10 5 FALSE 0.9112202 0.8055925 0.8302975 0.02411834 0.06593744
## 3 0.00 9 FALSE 0.9038488 0.8431340 0.8189405 0.03203737 0.02884734
## 7 0.01 9 FALSE 0.9109317 0.8101883 0.8304790 0.02572001 0.06094991
## 11 0.10 9 FALSE 0.9151277 0.8335548 0.8169448 0.02549665 0.04102289
## 4 0.00 13 FALSE 0.9157703 0.8431340 0.8130987 0.02920262 0.04522834
## 8 0.01 13 FALSE 0.9143824 0.8314507 0.8208999 0.02699052 0.05335330
## 12 0.10 13 FALSE 0.9100212 0.8361573 0.8132075 0.02657216 0.06021816
## SpecSD
## 1 0.05745084
## 5 0.04742283
## 9 0.06285986
## 2 0.04474555
## 6 0.06106486
## 10 0.05037463
## 3 0.06463390
## 7 0.05517753
## 11 0.06163075
## 4 0.05019146
## 8 0.05725751
## 12 0.05339363(AVNN_Train_ROCCurveAUC <- AVNN_Tune$results[AVNN_Tune$results$decay==AVNN_Tune$bestTune$decay &
AVNN_Tune$results$size==AVNN_Tune$bestTune$size,
c("ROC")])## [1] 0.9157703##################################
# Identifying and plotting the
# best model predictors
##################################
# model does not support variable importance measurement
##################################
# Independently evaluating the model
# on the test set
##################################
AVNN_Test <- data.frame(AVNN_Observed = PMA_PreModelling_Test_AVNN$Log_Solubility_Class,
AVNN_Predicted = predict(AVNN_Tune,
PMA_PreModelling_Test_AVNN[,!names(PMA_PreModelling_Test_AVNN) %in% c("Log_Solubility_Class")],
type = "prob"))
AVNN_Test## AVNN_Observed AVNN_Predicted.Low AVNN_Predicted.High
## 1 High 0.009075436 0.990924564
## 2 High 0.002944622 0.997055378
## 3 High 0.120949889 0.879050111
## 4 High 0.004360401 0.995639599
## 5 High 0.002530240 0.997469760
## 6 High 0.007328969 0.992671031
## 7 High 0.006755470 0.993244530
## 8 High 0.013689319 0.986310681
## 9 High 0.006965524 0.993034476
## 10 High 0.174618767 0.825381233
## 11 High 0.097733727 0.902266273
## 12 High 0.059870171 0.940129829
## 13 High 0.003443345 0.996556655
## 14 High 0.004401860 0.995598140
## 15 High 0.004528048 0.995471952
## 16 High 0.106837453 0.893162547
## 17 High 0.009407477 0.990592523
## 18 High 0.006085903 0.993914097
## 19 High 0.011945235 0.988054765
## 20 High 0.148692361 0.851307639
## 21 High 0.004952876 0.995047124
## 22 High 0.007359064 0.992640936
## 23 High 0.005392134 0.994607866
## 24 High 0.006147565 0.993852435
## 25 High 0.004287563 0.995712437
## 26 High 0.103695157 0.896304843
## 27 High 0.014464923 0.985535077
## 28 High 0.003150246 0.996849754
## 29 High 0.336209602 0.663790398
## 30 High 0.103845044 0.896154956
## 31 High 0.766407311 0.233592689
## 32 High 0.007338751 0.992661249
## 33 High 0.009850246 0.990149754
## 34 High 0.006757652 0.993242348
## 35 High 0.006119217 0.993880783
## 36 High 0.003803251 0.996196749
## 37 High 0.001946729 0.998053271
## 38 High 0.008730696 0.991269304
## 39 High 0.003916729 0.996083271
## 40 High 0.138297066 0.861702934
## 41 High 0.007588491 0.992411509
## 42 High 0.537740645 0.462259355
## 43 High 0.005859229 0.994140771
## 44 High 0.003143247 0.996856753
## 45 High 0.022090133 0.977909867
## 46 High 0.007417016 0.992582984
## 47 High 0.143086112 0.856913888
## 48 High 0.007486543 0.992513457
## 49 High 0.004759311 0.995240689
## 50 High 0.005310054 0.994689946
## 51 High 0.003430125 0.996569875
## 52 High 0.097227199 0.902772801
## 53 High 0.175058016 0.824941984
## 54 High 0.002699461 0.997300539
## 55 High 0.005105070 0.994894930
## 56 High 0.096284498 0.903715502
## 57 High 0.007098666 0.992901334
## 58 High 0.017945253 0.982054747
## 59 High 0.004957684 0.995042316
## 60 High 0.264928660 0.735071340
## 61 High 0.004058279 0.995941721
## 62 High 0.007466087 0.992533913
## 63 High 0.266659463 0.733340537
## 64 High 0.079682139 0.920317861
## 65 High 0.186007170 0.813992830
## 66 High 0.813179759 0.186820241
## 67 High 0.141694451 0.858305549
## 68 High 0.698236559 0.301763441
## 69 High 0.113000750 0.886999250
## 70 High 0.417179252 0.582820748
## 71 High 0.337626196 0.662373804
## 72 High 0.568569667 0.431430333
## 73 High 0.170029205 0.829970795
## 74 High 0.686700275 0.313299725
## 75 High 0.013092929 0.986907071
## 76 High 0.106731512 0.893268488
## 77 High 0.093654862 0.906345138
## 78 High 0.344117963 0.655882037
## 79 High 0.002205824 0.997794176
## 80 High 0.029881152 0.970118848
## 81 High 0.098471764 0.901528236
## 82 High 0.394384227 0.605615773
## 83 High 0.141720266 0.858279734
## 84 High 0.223804977 0.776195023
## 85 High 0.249279133 0.750720867
## 86 High 0.010527973 0.989472027
## 87 High 0.810175908 0.189824092
## 88 High 0.552555425 0.447444575
## 89 High 0.107618410 0.892381590
## 90 High 0.598790410 0.401209590
## 91 High 0.200249679 0.799750321
## 92 High 0.282986054 0.717013946
## 93 High 0.822438938 0.177561062
## 94 High 0.010938512 0.989061488
## 95 High 0.002820357 0.997179643
## 96 High 0.007690156 0.992309844
## 97 High 0.208094813 0.791905187
## 98 High 0.719580524 0.280419476
## 99 High 0.012585343 0.987414657
## 100 High 0.008075974 0.991924026
## 101 High 0.103288044 0.896711956
## 102 High 0.020032298 0.979967702
## 103 High 0.632304782 0.367695218
## 104 High 0.004501042 0.995498958
## 105 High 0.313829024 0.686170976
## 106 High 0.296321202 0.703678798
## 107 High 0.822085490 0.177914510
## 108 High 0.549958394 0.450041606
## 109 High 0.336331608 0.663668392
## 110 High 0.523107591 0.476892409
## 111 High 0.381149366 0.618850634
## 112 High 0.479999448 0.520000552
## 113 High 0.189134163 0.810865837
## 114 High 0.483475421 0.516524579
## 115 High 0.950883244 0.049116756
## 116 High 0.954042752 0.045957248
## 117 High 0.866967004 0.133032996
## 118 High 0.035026921 0.964973079
## 119 Low 0.569080628 0.430919372
## 120 Low 0.991079622 0.008920378
## 121 Low 0.801670314 0.198329686
## 122 Low 0.005837367 0.994162633
## 123 Low 0.297516821 0.702483179
## 124 Low 0.359954354 0.640045646
## 125 Low 0.865007196 0.134992804
## 126 Low 0.552498446 0.447501554
## 127 Low 0.630630401 0.369369599
## 128 Low 0.710578213 0.289421787
## 129 Low 0.664424133 0.335575867
## 130 Low 0.895714354 0.104285646
## 131 Low 0.705155838 0.294844162
## 132 Low 0.615764404 0.384235596
## 133 Low 0.398149695 0.601850305
## 134 Low 0.326874324 0.673125676
## 135 Low 0.096484781 0.903515219
## 136 Low 0.650125491 0.349874509
## 137 Low 0.415013242 0.584986758
## 138 Low 0.256066779 0.743933221
## 139 Low 0.373451165 0.626548835
## 140 Low 0.588616318 0.411383682
## 141 Low 0.367825448 0.632174552
## 142 Low 0.816695293 0.183304707
## 143 Low 0.900477008 0.099522992
## 144 Low 0.615471125 0.384528875
## 145 Low 0.310983064 0.689016936
## 146 Low 0.471079329 0.528920671
## 147 Low 0.683190008 0.316809992
## 148 Low 0.398246317 0.601753683
## 149 Low 0.561994019 0.438005981
## 150 Low 0.867969902 0.132030098
## 151 Low 0.139592417 0.860407583
## 152 Low 0.897505020 0.102494980
## 153 Low 0.222542930 0.777457070
## 154 Low 0.652124075 0.347875925
## 155 Low 0.763285255 0.236714745
## 156 Low 0.852191101 0.147808899
## 157 Low 0.979114971 0.020885029
## 158 Low 0.980680743 0.019319257
## 159 Low 0.682693263 0.317306737
## 160 Low 0.934434448 0.065565552
## 161 Low 0.988813155 0.011186845
## 162 Low 0.985170236 0.014829764
## 163 Low 0.561722689 0.438277311
## 164 Low 0.529687344 0.470312656
## 165 Low 0.880466244 0.119533756
## 166 Low 0.557602714 0.442397286
## 167 Low 0.990018944 0.009981056
## 168 Low 0.255264410 0.744735590
## 169 Low 0.755008957 0.244991043
## 170 Low 0.887894984 0.112105016
## 171 Low 0.674465565 0.325534435
## 172 Low 0.744033065 0.255966935
## 173 Low 0.897913791 0.102086209
## 174 Low 0.717913850 0.282086150
## 175 Low 0.996303935 0.003696065
## 176 Low 0.887444283 0.112555717
## 177 Low 0.939322895 0.060677105
## 178 Low 0.989788417 0.010211583
## 179 Low 0.897013874 0.102986126
## 180 Low 0.384885532 0.615114468
## 181 Low 0.731574430 0.268425570
## 182 Low 0.778395662 0.221604338
## 183 Low 0.894815890 0.105184110
## 184 Low 0.701334314 0.298665686
## 185 Low 0.899067018 0.100932982
## 186 Low 0.989790504 0.010209496
## 187 Low 0.824883585 0.175116415
## 188 Low 0.986866571 0.013133429
## 189 Low 0.994913828 0.005086172
## 190 Low 0.993800770 0.006199230
## 191 Low 0.987219387 0.012780613
## 192 Low 0.507825554 0.492174446
## 193 Low 0.899939225 0.100060775
## 194 Low 0.899326361 0.100673639
## 195 Low 0.874349477 0.125650523
## 196 Low 0.973386424 0.026613576
## 197 Low 0.911455492 0.088544508
## 198 Low 0.895363619 0.104636381
## 199 Low 0.990973339 0.009026661
## 200 Low 0.985734911 0.014265089
## 201 Low 0.995881769 0.004118231
## 202 Low 0.995914764 0.004085236
## 203 Low 0.995940958 0.004059042
## 204 Low 0.993390192 0.006609808
## 205 Low 0.983421801 0.016578199
## 206 Low 0.994878465 0.005121535
## 207 Low 0.985656058 0.014343942
## 208 Low 0.994716193 0.005283807
## 209 Low 0.994681182 0.005318818
## 210 Low 0.995647095 0.004352905
## 211 Low 0.995819938 0.004180062
## 212 Low 0.995290402 0.004709598
## 213 Low 0.995391222 0.004608778
## 214 Low 0.995480922 0.004519078
## 215 Low 0.995537067 0.004462933
## 216 Low 0.995869516 0.004130484
## 217 High 0.006026996 0.993973004
## 218 High 0.004411564 0.995588436
## 219 High 0.002139601 0.997860399
## 220 High 0.058151022 0.941848978
## 221 High 0.006360488 0.993639512
## 222 High 0.005465205 0.994534795
## 223 High 0.007255526 0.992744474
## 224 High 0.250087404 0.749912596
## 225 High 0.309226197 0.690773803
## 226 High 0.204247726 0.795752274
## 227 High 0.159565110 0.840434890
## 228 High 0.004113367 0.995886633
## 229 High 0.003679028 0.996320972
## 230 High 0.790100572 0.209899428
## 231 High 0.407797303 0.592202697
## 232 High 0.038174772 0.961825228
## 233 High 0.002674115 0.997325885
## 234 High 0.005153756 0.994846244
## 235 High 0.095573250 0.904426750
## 236 High 0.198286647 0.801713353
## 237 High 0.329173015 0.670826985
## 238 High 0.121933600 0.878066400
## 239 High 0.175058016 0.824941984
## 240 High 0.002645853 0.997354147
## 241 High 0.007852475 0.992147525
## 242 High 0.044277316 0.955722684
## 243 High 0.006166807 0.993833193
## 244 High 0.341122006 0.658877994
## 245 High 0.673324477 0.326675523
## 246 High 0.004352136 0.995647864
## 247 High 0.004933736 0.995066264
## 248 High 0.006821772 0.993178228
## 249 High 0.005675419 0.994324581
## 250 High 0.485817279 0.514182721
## 251 High 0.012741559 0.987258441
## 252 High 0.006290356 0.993709644
## 253 High 0.008985404 0.991014596
## 254 High 0.911929061 0.088070939
## 255 High 0.026033341 0.973966659
## 256 High 0.280310993 0.719689007
## 257 High 0.004463459 0.995536541
## 258 High 0.232723781 0.767276219
## 259 High 0.874515083 0.125484917
## 260 High 0.050109251 0.949890749
## 261 High 0.529592219 0.470407781
## 262 High 0.487200246 0.512799754
## 263 High 0.103041452 0.896958548
## 264 High 0.336990809 0.663009191
## 265 High 0.890062718 0.109937282
## 266 High 0.279658013 0.720341987
## 267 High 0.223686714 0.776313286
## 268 High 0.006605181 0.993394819
## 269 Low 0.246234335 0.753765665
## 270 Low 0.347222737 0.652777263
## 271 Low 0.228226898 0.771773102
## 272 Low 0.449215912 0.550784088
## 273 Low 0.989648820 0.010351180
## 274 Low 0.465773474 0.534226526
## 275 Low 0.068267004 0.931732996
## 276 Low 0.881949821 0.118050179
## 277 Low 0.882361787 0.117638213
## 278 Low 0.074214663 0.925785337
## 279 Low 0.804232169 0.195767831
## 280 Low 0.518691729 0.481308271
## 281 Low 0.063739985 0.936260015
## 282 Low 0.823653944 0.176346056
## 283 Low 0.815584437 0.184415563
## 284 Low 0.795450584 0.204549416
## 285 Low 0.718046669 0.281953331
## 286 Low 0.892604378 0.107395622
## 287 Low 0.682328014 0.317671986
## 288 Low 0.831105136 0.168894864
## 289 Low 0.885485881 0.114514119
## 290 Low 0.990790735 0.009209265
## 291 Low 0.894011737 0.105988263
## 292 Low 0.892802085 0.107197915
## 293 Low 0.674065334 0.325934666
## 294 Low 0.982227171 0.017772829
## 295 Low 0.902003530 0.097996470
## 296 Low 0.708922980 0.291077020
## 297 Low 0.985059570 0.014940430
## 298 Low 0.903843459 0.096156541
## 299 Low 0.971104017 0.028895983
## 300 Low 0.974406933 0.025593067
## 301 Low 0.985666050 0.014333950
## 302 Low 0.994123530 0.005876470
## 303 Low 0.991671889 0.008328111
## 304 Low 0.986853368 0.013146632
## 305 Low 0.887901979 0.112098021
## 306 Low 0.995871839 0.004128161
## 307 Low 0.995850649 0.004149351
## 308 Low 0.995524417 0.004475583
## 309 Low 0.993028443 0.006971557
## 310 Low 0.995483995 0.004516005
## 311 Low 0.992808106 0.007191894
## 312 Low 0.995883893 0.004116107
## 313 High 0.008963637 0.991036363
## 314 High 0.589683065 0.410316935
## 315 Low 0.815388827 0.184611173
## 316 High 0.879467490 0.120532510##################################
# Reporting the independent evaluation results
# for the test set
##################################
AVNN_Test_ROC <- roc(response = AVNN_Test$AVNN_Observed,
predictor = AVNN_Test$AVNN_Predicted.High,
levels = rev(levels(AVNN_Test$AVNN_Observed)))
(AVNN_Test_ROCCurveAUC <- auc(AVNN_Test_ROC)[1])## [1] 0.91891351.5.8 Support Vector Machine - Radial Basis Function Kernel (SVM_R)
[A] The support vector machine (radial basis function kernel) model from the kernlab package was implemented through the caret package.
[B] The model contains 2 hyperparameters:
[B.1] sigma = sigma held constant at a value of 0.00285
[B.2] C = cost made to vary across a range of 14 default values
[C] The cross-validated model performance of the final model is summarized as follows:
[C.1] Final model configuration involves sigma=0.00285 and C=2048
[C.2] ROC Curve AUC = 0.95514
[D] The model does not allow for ranking of predictors in terms of variable importance.
[E] The independent test model performance of the final model is summarized as follows:
[E.1] ROC Curve AUC = 0.95016
##################################
# Transforming factor predictors
# as required by the nature of the model
##################################
# Creating a local object
# for the train and test sets
##################################
PMA_PreModelling_Train_SVM_R <- as.data.frame(lapply(PMA_PreModelling_Train[,!names(PMA_PreModelling_Train) %in%
c("Log_Solubility_Class")],
function(x) as.numeric(as.character(x))))
PMA_PreModelling_Train_SVM_R$Log_Solubility_Class <- PMA_PreModelling_Train$Log_Solubility_Class
dim(PMA_PreModelling_Train_SVM_R)## [1] 951 221PMA_PreModelling_Test_SVM_R <- as.data.frame(lapply(PMA_PreModelling_Test[,!names(PMA_PreModelling_Test) %in%
c("Log_Solubility_Class")],
function(x) as.numeric(as.character(x))))
PMA_PreModelling_Test_SVM_R$Log_Solubility_Class <- PMA_PreModelling_Test$Log_Solubility_Class
dim(PMA_PreModelling_Test_SVM_R)## [1] 316 221##################################
# Creating consistent fold assignments
# for the 10-Fold Cross Validation process
##################################
set.seed(12345678)
KFold_Indices <- createFolds(PMA_PreModelling_Train_SVM_R$Log_Solubility_Class,
k = 10,
returnTrain=TRUE)
KFold_Control <- trainControl(method="cv",
index=KFold_Indices,
summaryFunction = twoClassSummary,
classProbs = TRUE)
##################################
# Setting the conditions
# for hyperparameter tuning
##################################
# used a range of default values
##################################
# Running the support vector machine (radial basis function kernel) model
# by setting the caret method to 'svmRadial'
##################################
set.seed(12345678)
SVM_R_Tune <- train(x = PMA_PreModelling_Train_SVM_R[,!names(PMA_PreModelling_Train_SVM_R) %in% c("Log_Solubility_Class")],
y = PMA_PreModelling_Train_SVM_R$Log_Solubility_Class,
method = "svmRadial",
tuneLength = 14,
metric = "ROC",
preProc = c("center", "scale"),
trControl = KFold_Control)
##################################
# Reporting the cross-validation results
# for the train set
##################################
SVM_R_Tune## Support Vector Machines with Radial Basis Function Kernel
##
## 951 samples
## 220 predictors
## 2 classes: 'Low', 'High'
##
## Pre-processing: centered (220), scaled (220)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 857, 855, 857, 855, 856, 856, ...
## Resampling results across tuning parameters:
##
## C ROC Sens Spec
## 0.25 0.9225768 0.8265227 0.8264151
## 0.50 0.9342063 0.8358250 0.8570029
## 1.00 0.9407996 0.8592470 0.8628084
## 2.00 0.9399949 0.8522148 0.8609216
## 4.00 0.9415450 0.8498893 0.8627358
## 8.00 0.9432946 0.8501107 0.8760522
## 16.00 0.9463556 0.8477298 0.8798621
## 32.00 0.9497924 0.8640642 0.8893324
## 64.00 0.9530000 0.8664452 0.8835631
## 128.00 0.9549537 0.8663344 0.8778665
## 256.00 0.9550376 0.8733666 0.8836720
## 512.00 0.9548026 0.8756921 0.8798258
## 1024.00 0.9550544 0.8638981 0.8874819
## 2048.00 0.9551422 0.8734219 0.8779028
##
## Tuning parameter 'sigma' was held constant at a value of 0.002858301
## ROC was used to select the optimal model using the largest value.
## The final values used for the model were sigma = 0.002858301 and C = 2048.SVM_R_Tune$finalModel## Support Vector Machine object of class "ksvm"
##
## SV type: C-svc (classification)
## parameter : cost C = 2048
##
## Gaussian Radial Basis kernel function.
## Hyperparameter : sigma = 0.00285830098890164
##
## Number of Support Vectors : 291
##
## Objective Function Value : -3693.276
## Training error : 0
## Probability model included.SVM_R_Tune$results## sigma C ROC Sens Spec ROCSD SensSD
## 1 0.002858301 0.25 0.9225768 0.8265227 0.8264151 0.02509293 0.06472858
## 2 0.002858301 0.50 0.9342063 0.8358250 0.8570029 0.02213186 0.07345896
## 3 0.002858301 1.00 0.9407996 0.8592470 0.8628084 0.02005568 0.06645585
## 4 0.002858301 2.00 0.9399949 0.8522148 0.8609216 0.01956500 0.07184322
## 5 0.002858301 4.00 0.9415450 0.8498893 0.8627358 0.01971806 0.07861746
## 6 0.002858301 8.00 0.9432946 0.8501107 0.8760522 0.01940473 0.08869159
## 7 0.002858301 16.00 0.9463556 0.8477298 0.8798621 0.01801010 0.06878890
## 8 0.002858301 32.00 0.9497924 0.8640642 0.8893324 0.01615007 0.06305448
## 9 0.002858301 64.00 0.9530000 0.8664452 0.8835631 0.01542028 0.06220900
## 10 0.002858301 128.00 0.9549537 0.8663344 0.8778665 0.01562122 0.06722412
## 11 0.002858301 256.00 0.9550376 0.8733666 0.8836720 0.01940156 0.05888913
## 12 0.002858301 512.00 0.9548026 0.8756921 0.8798258 0.02017246 0.05878213
## 13 0.002858301 1024.00 0.9550544 0.8638981 0.8874819 0.02025362 0.05562805
## 14 0.002858301 2048.00 0.9551422 0.8734219 0.8779028 0.02019085 0.05097821
## SpecSD
## 1 0.05221581
## 2 0.04712527
## 3 0.05009315
## 4 0.06492702
## 5 0.06183544
## 6 0.06440586
## 7 0.06613147
## 8 0.05976556
## 9 0.07032273
## 10 0.06892971
## 11 0.05927357
## 12 0.06044189
## 13 0.06266413
## 14 0.05850801(SVM_R_Train_ROCCurveAUC <- SVM_R_Tune$results[SVM_R_Tune$results$C==SVM_R_Tune$bestTune$C,
c("ROC")])## [1] 0.9551422##################################
# Identifying and plotting the
# best model predictors
##################################
# model does not support variable importance measurement
##################################
# Independently evaluating the model
# on the test set
##################################
SVM_R_Test <- data.frame(SVM_R_Observed = PMA_PreModelling_Test_SVM_R$Log_Solubility_Class,
SVM_R_Predicted = predict(SVM_R_Tune,
PMA_PreModelling_Test_SVM_R[,!names(PMA_PreModelling_Test_SVM_R) %in% c("Log_Solubility_Class")],
type = "prob"))
SVM_R_Test## SVM_R_Observed SVM_R_Predicted.Low SVM_R_Predicted.High
## 1 High 1.790338e-06 9.999982e-01
## 2 High 1.401401e-06 9.999986e-01
## 3 High 3.070497e-02 9.692950e-01
## 4 High 5.885393e-04 9.994115e-01
## 5 High 1.412513e-03 9.985875e-01
## 6 High 7.891937e-06 9.999921e-01
## 7 High 5.940047e-06 9.999941e-01
## 8 High 1.389587e-05 9.999861e-01
## 9 High 8.417733e-07 9.999992e-01
## 10 High 1.493140e-01 8.506860e-01
## 11 High 1.474211e-01 8.525789e-01
## 12 High 3.703014e-02 9.629699e-01
## 13 High 2.573903e-05 9.999743e-01
## 14 High 7.036197e-04 9.992964e-01
## 15 High 1.214928e-02 9.878507e-01
## 16 High 1.662077e-02 9.833792e-01
## 17 High 9.884031e-04 9.990116e-01
## 18 High 1.720732e-05 9.999828e-01
## 19 High 2.102219e-02 9.789778e-01
## 20 High 7.487314e-02 9.251269e-01
## 21 High 1.165631e-03 9.988344e-01
## 22 High 3.126503e-04 9.996873e-01
## 23 High 7.320716e-03 9.926793e-01
## 24 High 2.565070e-03 9.974349e-01
## 25 High 1.035838e-02 9.896416e-01
## 26 High 3.155826e-03 9.968442e-01
## 27 High 3.672396e-04 9.996328e-01
## 28 High 1.509500e-03 9.984905e-01
## 29 High 5.837291e-01 4.162709e-01
## 30 High 3.113714e-03 9.968863e-01
## 31 High 6.568343e-01 3.431657e-01
## 32 High 5.136522e-05 9.999486e-01
## 33 High 5.469666e-05 9.999453e-01
## 34 High 2.372483e-03 9.976275e-01
## 35 High 3.047678e-03 9.969523e-01
## 36 High 3.782893e-03 9.962171e-01
## 37 High 3.858738e-04 9.996141e-01
## 38 High 6.375107e-04 9.993625e-01
## 39 High 5.176126e-03 9.948239e-01
## 40 High 2.224643e-03 9.977754e-01
## 41 High 3.428776e-05 9.999657e-01
## 42 High 1.469633e-01 8.530367e-01
## 43 High 2.045998e-02 9.795400e-01
## 44 High 3.285844e-05 9.999671e-01
## 45 High 7.503964e-03 9.924960e-01
## 46 High 1.445430e-02 9.855457e-01
## 47 High 1.312678e-03 9.986873e-01
## 48 High 3.354200e-03 9.966458e-01
## 49 High 2.012428e-03 9.979876e-01
## 50 High 7.207037e-03 9.927930e-01
## 51 High 5.629299e-03 9.943707e-01
## 52 High 1.186335e-03 9.988137e-01
## 53 High 1.354083e-01 8.645917e-01
## 54 High 6.490681e-02 9.350932e-01
## 55 High 4.110389e-01 5.889611e-01
## 56 High 2.482932e-02 9.751707e-01
## 57 High 2.696183e-02 9.730382e-01
## 58 High 2.262801e-02 9.773720e-01
## 59 High 1.180406e-01 8.819594e-01
## 60 High 5.495807e-01 4.504193e-01
## 61 High 6.181213e-03 9.938188e-01
## 62 High 2.226954e-03 9.977730e-01
## 63 High 6.181144e-03 9.938189e-01
## 64 High 4.282592e-02 9.571741e-01
## 65 High 1.423609e-01 8.576391e-01
## 66 High 2.901213e-01 7.098787e-01
## 67 High 7.845569e-01 2.154431e-01
## 68 High 5.002754e-01 4.997246e-01
## 69 High 1.712645e-02 9.828735e-01
## 70 High 2.734998e-01 7.265002e-01
## 71 High 2.667845e-02 9.733216e-01
## 72 High 4.552093e-01 5.447907e-01
## 73 High 7.370644e-03 9.926294e-01
## 74 High 8.248607e-01 1.751393e-01
## 75 High 1.765986e-01 8.234014e-01
## 76 High 5.809335e-01 4.190665e-01
## 77 High 3.420526e-01 6.579474e-01
## 78 High 5.830957e-03 9.941690e-01
## 79 High 2.454420e-01 7.545580e-01
## 80 High 1.046818e-01 8.953182e-01
## 81 High 4.644391e-02 9.535561e-01
## 82 High 3.394237e-03 9.966058e-01
## 83 High 9.520226e-01 4.797735e-02
## 84 High 1.310691e-02 9.868931e-01
## 85 High 1.972371e-01 8.027629e-01
## 86 High 1.007943e-02 9.899206e-01
## 87 High 2.598815e-01 7.401185e-01
## 88 High 1.396991e-01 8.603009e-01
## 89 High 2.153017e-01 7.846983e-01
## 90 High 1.127097e-02 9.887290e-01
## 91 High 1.288567e-01 8.711433e-01
## 92 High 2.259480e-01 7.740520e-01
## 93 High 4.598056e-01 5.401944e-01
## 94 High 1.542168e-02 9.845783e-01
## 95 High 1.119608e-01 8.880392e-01
## 96 High 1.133068e-01 8.866932e-01
## 97 High 1.755088e-01 8.244912e-01
## 98 High 5.079078e-01 4.920922e-01
## 99 High 6.382407e-02 9.361759e-01
## 100 High 2.044559e-01 7.955441e-01
## 101 High 1.534375e-01 8.465625e-01
## 102 High 1.909820e-01 8.090180e-01
## 103 High 2.408233e-01 7.591767e-01
## 104 High 1.919181e-01 8.080819e-01
## 105 High 9.432536e-01 5.674637e-02
## 106 High 1.519275e-01 8.480725e-01
## 107 High 6.249051e-02 9.375095e-01
## 108 High 3.791111e-01 6.208889e-01
## 109 High 5.759467e-01 4.240533e-01
## 110 High 5.195252e-01 4.804748e-01
## 111 High 4.072976e-01 5.927024e-01
## 112 High 7.846000e-01 2.154000e-01
## 113 High 5.505469e-01 4.494531e-01
## 114 High 2.022685e-01 7.977315e-01
## 115 High 4.404657e-01 5.595343e-01
## 116 High 8.323968e-01 1.676032e-01
## 117 High 9.436804e-01 5.631956e-02
## 118 High 9.973358e-01 2.664155e-03
## 119 Low 9.801695e-02 9.019830e-01
## 120 Low 3.512521e-01 6.487479e-01
## 121 Low 5.310659e-01 4.689341e-01
## 122 Low 3.819842e-03 9.961802e-01
## 123 Low 9.311898e-01 6.881022e-02
## 124 Low 7.557384e-01 2.442616e-01
## 125 Low 6.633683e-01 3.366317e-01
## 126 Low 1.575591e-01 8.424409e-01
## 127 Low 9.854473e-01 1.455266e-02
## 128 Low 6.756350e-01 3.243650e-01
## 129 Low 9.531411e-01 4.685893e-02
## 130 Low 6.118112e-01 3.881888e-01
## 131 Low 9.203029e-01 7.969712e-02
## 132 Low 8.390386e-01 1.609614e-01
## 133 Low 8.698578e-01 1.301422e-01
## 134 Low 7.382761e-01 2.617239e-01
## 135 Low 8.854991e-01 1.145009e-01
## 136 Low 8.404714e-01 1.595286e-01
## 137 Low 7.676196e-01 2.323804e-01
## 138 Low 5.749218e-01 4.250782e-01
## 139 Low 1.522933e-01 8.477067e-01
## 140 Low 1.652831e-01 8.347169e-01
## 141 Low 5.707049e-01 4.292951e-01
## 142 Low 3.400469e-01 6.599531e-01
## 143 Low 8.855962e-01 1.144038e-01
## 144 Low 6.236945e-01 3.763055e-01
## 145 Low 2.676640e-01 7.323360e-01
## 146 Low 9.112520e-01 8.874796e-02
## 147 Low 7.554873e-01 2.445127e-01
## 148 Low 9.167921e-01 8.320788e-02
## 149 Low 9.943827e-01 5.617252e-03
## 150 Low 9.888923e-01 1.110774e-02
## 151 Low 3.954368e-01 6.045632e-01
## 152 Low 8.746760e-01 1.253240e-01
## 153 Low 5.649685e-01 4.350315e-01
## 154 Low 9.662381e-01 3.376195e-02
## 155 Low 7.507664e-01 2.492336e-01
## 156 Low 9.053074e-01 9.469264e-02
## 157 Low 9.348579e-01 6.514214e-02
## 158 Low 7.233638e-01 2.766362e-01
## 159 Low 9.850379e-01 1.496211e-02
## 160 Low 9.702947e-01 2.970530e-02
## 161 Low 9.598928e-01 4.010719e-02
## 162 Low 8.286756e-01 1.713244e-01
## 163 Low 9.277405e-01 7.225949e-02
## 164 Low 9.710798e-01 2.892019e-02
## 165 Low 9.816962e-01 1.830375e-02
## 166 Low 9.136960e-01 8.630396e-02
## 167 Low 9.604719e-01 3.952811e-02
## 168 Low 7.856736e-01 2.143264e-01
## 169 Low 9.808724e-01 1.912755e-02
## 170 Low 9.962140e-01 3.786004e-03
## 171 Low 9.668576e-01 3.314242e-02
## 172 Low 8.662033e-01 1.337967e-01
## 173 Low 8.591393e-01 1.408607e-01
## 174 Low 1.000000e+00 1.701748e-08
## 175 Low 9.931667e-01 6.833306e-03
## 176 Low 8.667594e-01 1.332406e-01
## 177 Low 9.970895e-01 2.910479e-03
## 178 Low 9.634015e-01 3.659853e-02
## 179 Low 9.035671e-01 9.643287e-02
## 180 Low 6.663630e-01 3.336370e-01
## 181 Low 9.898620e-01 1.013795e-02
## 182 Low 8.492058e-01 1.507942e-01
## 183 Low 9.992972e-01 7.027734e-04
## 184 Low 9.999938e-01 6.206858e-06
## 185 Low 9.048412e-01 9.515877e-02
## 186 Low 9.353290e-01 6.467101e-02
## 187 Low 9.898104e-01 1.018960e-02
## 188 Low 9.499785e-01 5.002154e-02
## 189 Low 9.934254e-01 6.574599e-03
## 190 Low 9.946379e-01 5.362141e-03
## 191 Low 8.283376e-01 1.716624e-01
## 192 Low 9.172226e-01 8.277742e-02
## 193 Low 9.545196e-01 4.548039e-02
## 194 Low 9.365299e-01 6.347006e-02
## 195 Low 9.990063e-01 9.936673e-04
## 196 Low 9.735682e-01 2.643178e-02
## 197 Low 9.944962e-01 5.503830e-03
## 198 Low 9.169390e-01 8.306095e-02
## 199 Low 9.882730e-01 1.172697e-02
## 200 Low 9.761712e-01 2.382880e-02
## 201 Low 9.945772e-01 5.422790e-03
## 202 Low 9.968064e-01 3.193578e-03
## 203 Low 9.975266e-01 2.473415e-03
## 204 Low 9.959668e-01 4.033231e-03
## 205 Low 9.955764e-01 4.423604e-03
## 206 Low 9.983975e-01 1.602542e-03
## 207 Low 9.932358e-01 6.764229e-03
## 208 Low 9.964777e-01 3.522281e-03
## 209 Low 9.997733e-01 2.266951e-04
## 210 Low 9.994946e-01 5.054112e-04
## 211 Low 9.994736e-01 5.263985e-04
## 212 Low 9.994078e-01 5.922449e-04
## 213 Low 9.996607e-01 3.393485e-04
## 214 Low 9.997834e-01 2.165655e-04
## 215 Low 9.990583e-01 9.417223e-04
## 216 Low 9.994917e-01 5.083340e-04
## 217 High 9.024443e-05 9.999098e-01
## 218 High 2.077387e-05 9.999792e-01
## 219 High 1.670286e-05 9.999833e-01
## 220 High 7.767513e-06 9.999922e-01
## 221 High 6.360128e-03 9.936399e-01
## 222 High 1.266297e-03 9.987337e-01
## 223 High 9.996676e-04 9.990003e-01
## 224 High 1.365683e-04 9.998634e-01
## 225 High 6.298133e-01 3.701867e-01
## 226 High 6.133212e-02 9.386679e-01
## 227 High 2.886758e-03 9.971132e-01
## 228 High 2.288440e-02 9.771156e-01
## 229 High 3.374120e-04 9.996626e-01
## 230 High 1.241016e-01 8.758984e-01
## 231 High 1.738117e-02 9.826188e-01
## 232 High 5.011933e-04 9.994988e-01
## 233 High 2.381673e-02 9.761833e-01
## 234 High 3.121007e-02 9.687899e-01
## 235 High 4.899600e-03 9.951004e-01
## 236 High 2.205502e-01 7.794498e-01
## 237 High 6.287177e-01 3.712823e-01
## 238 High 6.888203e-02 9.311180e-01
## 239 High 1.354083e-01 8.645917e-01
## 240 High 4.201538e-02 9.579846e-01
## 241 High 3.538389e-04 9.996462e-01
## 242 High 8.932231e-03 9.910678e-01
## 243 High 1.351940e-02 9.864806e-01
## 244 High 6.953742e-01 3.046258e-01
## 245 High 2.622675e-01 7.377325e-01
## 246 High 8.535310e-03 9.914647e-01
## 247 High 1.852684e-02 9.814732e-01
## 248 High 5.937713e-03 9.940623e-01
## 249 High 3.389732e-02 9.661027e-01
## 250 High 5.870720e-01 4.129280e-01
## 251 High 2.857489e-01 7.142511e-01
## 252 High 3.958410e-01 6.041590e-01
## 253 High 2.283274e-01 7.716726e-01
## 254 High 5.922845e-01 4.077155e-01
## 255 High 1.977961e-01 8.022039e-01
## 256 High 4.194252e-02 9.580575e-01
## 257 High 6.517846e-02 9.348215e-01
## 258 High 2.196883e-01 7.803117e-01
## 259 High 5.748524e-01 4.251476e-01
## 260 High 1.796637e-01 8.203363e-01
## 261 High 5.581556e-02 9.441844e-01
## 262 High 1.692169e-02 9.830783e-01
## 263 High 1.227492e-01 8.772508e-01
## 264 High 4.237459e-01 5.762541e-01
## 265 High 6.514849e-01 3.485151e-01
## 266 High 1.102230e-01 8.897770e-01
## 267 High 4.335721e-01 5.664279e-01
## 268 High 5.075314e-02 9.492469e-01
## 269 Low 2.713865e-01 7.286135e-01
## 270 Low 4.070414e-01 5.929586e-01
## 271 Low 2.570201e-01 7.429799e-01
## 272 Low 8.450425e-01 1.549575e-01
## 273 Low 6.669529e-01 3.330471e-01
## 274 Low 8.724159e-01 1.275841e-01
## 275 Low 6.464582e-01 3.535418e-01
## 276 Low 9.895986e-01 1.040137e-02
## 277 Low 9.922429e-01 7.757131e-03
## 278 Low 4.340324e-01 5.659676e-01
## 279 Low 8.110909e-01 1.889091e-01
## 280 Low 9.160900e-01 8.391003e-02
## 281 Low 6.720414e-01 3.279586e-01
## 282 Low 9.266720e-01 7.332797e-02
## 283 Low 9.591404e-01 4.085962e-02
## 284 Low 9.913447e-01 8.655273e-03
## 285 Low 9.960629e-01 3.937105e-03
## 286 Low 8.083243e-01 1.916757e-01
## 287 Low 6.154333e-01 3.845667e-01
## 288 Low 8.056947e-01 1.943053e-01
## 289 Low 9.569709e-01 4.302908e-02
## 290 Low 9.344964e-01 6.550357e-02
## 291 Low 8.634681e-01 1.365319e-01
## 292 Low 9.300919e-01 6.990814e-02
## 293 Low 7.960571e-01 2.039429e-01
## 294 Low 9.655898e-01 3.441016e-02
## 295 Low 9.345680e-01 6.543200e-02
## 296 Low 7.895110e-01 2.104890e-01
## 297 Low 8.107852e-01 1.892148e-01
## 298 Low 8.799394e-01 1.200606e-01
## 299 Low 9.797631e-01 2.023692e-02
## 300 Low 9.963098e-01 3.690246e-03
## 301 Low 9.883049e-01 1.169515e-02
## 302 Low 9.698623e-01 3.013770e-02
## 303 Low 9.975535e-01 2.446516e-03
## 304 Low 9.920587e-01 7.941265e-03
## 305 Low 9.999988e-01 1.199161e-06
## 306 Low 9.980662e-01 1.933844e-03
## 307 Low 9.997139e-01 2.861156e-04
## 308 Low 9.998400e-01 1.600302e-04
## 309 Low 9.999303e-01 6.968800e-05
## 310 Low 9.999389e-01 6.105678e-05
## 311 Low 9.997990e-01 2.010226e-04
## 312 Low 9.989269e-01 1.073065e-03
## 313 High 3.286538e-02 9.671346e-01
## 314 High 6.398317e-01 3.601683e-01
## 315 Low 9.765166e-01 2.348341e-02
## 316 High 9.994079e-01 5.920987e-04##################################
# Reporting the independent evaluation results
# for the test set
##################################
SVM_R_Test_ROC <- roc(response = SVM_R_Test$SVM_R_Observed,
predictor = SVM_R_Test$SVM_R_Predicted.High,
levels = rev(levels(SVM_R_Test$SVM_R_Observed)))
(SVM_R_Test_ROCCurveAUC <- auc(SVM_R_Test_ROC)[1])## [1] 0.95015971.5.9 Support Vector Machine - Polynomial Kernel (SVM_P)
[A] The support vector machine (polynomial kernel) model from the kernlab package was implemented through the caret package.
[B] The model contains 3 hyperparameters:
[B.1] degree = polynomial degree made to vary across a range of values equal to 1 to 2
[B.2] scale = scale made to vary across a range of values equal to 0.001 to 0.010
[B.3] C = cost made to vary across a range of values equal to 0.25 to 32.00
[C] The cross-validated model performance of the final model is summarized as follows:
[C.1] Final model configuration involves degree=2, scale=0.005 and C=32
[C.2] ROC Curve AUC = 0.95048
[D] The model does not allow for ranking of predictors in terms of variable importance.
[E] The independent test model performance of the final model is summarized as follows:
[E.1] ROC Curve AUC = 0.95011
##################################
# Transforming factor predictors
# as required by the nature of the model
##################################
# Creating a local object
# for the train and test sets
##################################
PMA_PreModelling_Train_SVM_P <- as.data.frame(lapply(PMA_PreModelling_Train[,!names(PMA_PreModelling_Train) %in%
c("Log_Solubility_Class")],
function(x) as.numeric(as.character(x))))
PMA_PreModelling_Train_SVM_P$Log_Solubility_Class <- PMA_PreModelling_Train$Log_Solubility_Class
dim(PMA_PreModelling_Train_SVM_P)## [1] 951 221PMA_PreModelling_Test_SVM_P <- as.data.frame(lapply(PMA_PreModelling_Test[,!names(PMA_PreModelling_Test) %in%
c("Log_Solubility_Class")],
function(x) as.numeric(as.character(x))))
PMA_PreModelling_Test_SVM_P$Log_Solubility_Class <- PMA_PreModelling_Test$Log_Solubility_Class
dim(PMA_PreModelling_Test_SVM_P)## [1] 316 221##################################
# Creating consistent fold assignments
# for the 10-Fold Cross Validation process
##################################
set.seed(12345678)
KFold_Indices <- createFolds(PMA_PreModelling_Train_SVM_P$Log_Solubility_Class,
k = 10,
returnTrain=TRUE)
KFold_Control <- trainControl(method="cv",
index=KFold_Indices,
summaryFunction = twoClassSummary,
classProbs = TRUE)
##################################
# Setting the conditions
# for hyperparameter tuning
##################################
SVM_P_Grid = expand.grid(degree = 1:2,
scale = c(0.01, 0.005, 0.001),
C = 2^(-2:5))
##################################
# Running the support vector machine (polynomial kernel) model
# by setting the caret method to 'svmPoly'
##################################
set.seed(12345678)
SVM_P_Tune <- train(x = PMA_PreModelling_Train_SVM_P[,!names(PMA_PreModelling_Train_SVM_P) %in% c("Log_Solubility_Class")],
y = PMA_PreModelling_Train_SVM_P$Log_Solubility_Class,
method = "svmPoly",
tuneGrid = SVM_P_Grid,
metric = "ROC",
preProc = c("center", "scale"),
trControl = KFold_Control)
##################################
# Reporting the cross-validation results
# for the train set
##################################
SVM_P_Tune## Support Vector Machines with Polynomial Kernel
##
## 951 samples
## 220 predictors
## 2 classes: 'Low', 'High'
##
## Pre-processing: centered (220), scaled (220)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 857, 855, 857, 855, 856, 856, ...
## Resampling results across tuning parameters:
##
## degree scale C ROC Sens Spec
## 1 0.001 0.25 0.8982574 0.7492248 0.8245283
## 1 0.001 0.50 0.9154136 0.8100775 0.8397315
## 1 0.001 1.00 0.9300498 0.8266888 0.8530842
## 1 0.001 2.00 0.9382509 0.8406423 0.8607765
## 1 0.001 4.00 0.9410973 0.8382060 0.8665820
## 1 0.001 8.00 0.9418678 0.8450720 0.8684688
## 1 0.001 16.00 0.9423674 0.8523256 0.8665457
## 1 0.001 32.00 0.9384860 0.8405316 0.8723149
## 1 0.005 0.25 0.9334756 0.8312846 0.8607765
## 1 0.005 0.50 0.9385687 0.8334994 0.8570755
## 1 0.005 1.00 0.9429324 0.8405316 0.8685414
## 1 0.005 2.00 0.9420834 0.8522148 0.8665457
## 1 0.005 4.00 0.9416546 0.8497785 0.8646589
## 1 0.005 8.00 0.9377184 0.8381506 0.8723512
## 1 0.005 16.00 0.9378910 0.8428571 0.8703556
## 1 0.005 32.00 0.9340194 0.8358804 0.8684688
## 1 0.010 0.25 0.9385237 0.8334994 0.8627721
## 1 0.010 0.50 0.9429324 0.8428571 0.8685414
## 1 0.010 1.00 0.9420834 0.8475637 0.8626996
## 1 0.010 2.00 0.9416546 0.8498339 0.8646952
## 1 0.010 4.00 0.9377184 0.8357697 0.8685414
## 1 0.010 8.00 0.9378910 0.8405869 0.8741655
## 1 0.010 16.00 0.9340194 0.8451827 0.8703919
## 1 0.010 32.00 0.9331110 0.8336656 0.8779390
## 2 0.001 0.25 0.9177808 0.8170543 0.8397678
## 2 0.001 0.50 0.9312968 0.8313400 0.8531567
## 2 0.001 1.00 0.9382799 0.8358250 0.8626996
## 2 0.001 2.00 0.9415732 0.8287929 0.8665820
## 2 0.001 4.00 0.9437586 0.8498893 0.8627721
## 2 0.001 8.00 0.9434995 0.8359358 0.8741655
## 2 0.001 16.00 0.9429819 0.8381506 0.8817852
## 2 0.001 32.00 0.9441590 0.8499446 0.8874819
## 2 0.005 0.25 0.9370187 0.8357697 0.8686139
## 2 0.005 0.50 0.9398239 0.8498339 0.8666909
## 2 0.005 1.00 0.9416083 0.8381506 0.8761611
## 2 0.005 2.00 0.9424678 0.8406423 0.8836357
## 2 0.005 4.00 0.9454805 0.8570321 0.8798984
## 2 0.005 8.00 0.9458642 0.8616833 0.8874456
## 2 0.005 16.00 0.9478692 0.8593023 0.8835994
## 2 0.005 32.00 0.9504889 0.8592470 0.8836357
## 2 0.010 0.25 0.9366234 0.8311185 0.8666183
## 2 0.010 0.50 0.9383894 0.8428018 0.8742017
## 2 0.010 1.00 0.9411239 0.8476190 0.8779753
## 2 0.010 2.00 0.9442114 0.8453488 0.8798258
## 2 0.010 4.00 0.9459963 0.8593577 0.8817126
## 2 0.010 8.00 0.9490640 0.8593577 0.8816401
## 2 0.010 16.00 0.9503049 0.8640642 0.8874456
## 2 0.010 32.00 0.9502390 0.8686047 0.8969884
##
## ROC was used to select the optimal model using the largest value.
## The final values used for the model were degree = 2, scale = 0.005 and C = 32.SVM_P_Tune$finalModel## Support Vector Machine object of class "ksvm"
##
## SV type: C-svc (classification)
## parameter : cost C = 32
##
## Polynomial kernel function.
## Hyperparameters : degree = 2 scale = 0.005 offset = 1
##
## Number of Support Vectors : 285
##
## Objective Function Value : -720.9112
## Training error : 0.001052
## Probability model included.SVM_P_Tune$results## degree scale C ROC Sens Spec ROCSD SensSD
## 1 1 0.001 0.25 0.8982574 0.7492248 0.8245283 0.03477994 0.08301318
## 2 1 0.001 0.50 0.9154136 0.8100775 0.8397315 0.02673369 0.06433315
## 3 1 0.001 1.00 0.9300498 0.8266888 0.8530842 0.01945843 0.04928813
## 4 1 0.001 2.00 0.9382509 0.8406423 0.8607765 0.02013177 0.07030579
## 5 1 0.001 4.00 0.9410973 0.8382060 0.8665820 0.02291858 0.04666212
## 6 1 0.001 8.00 0.9418678 0.8450720 0.8684688 0.02336680 0.06725583
## 7 1 0.001 16.00 0.9423674 0.8523256 0.8665457 0.02681344 0.06913274
## 8 1 0.001 32.00 0.9384860 0.8405316 0.8723149 0.02848837 0.07512383
## 9 1 0.005 0.25 0.9334756 0.8312846 0.8607765 0.01917285 0.05493122
## 10 1 0.005 0.50 0.9385687 0.8334994 0.8570755 0.02102400 0.05285153
## 11 1 0.005 1.00 0.9429324 0.8405316 0.8685414 0.02285407 0.06061599
## 12 1 0.005 2.00 0.9420834 0.8522148 0.8665457 0.02476222 0.06766016
## 13 1 0.005 4.00 0.9416546 0.8497785 0.8646589 0.02811772 0.06457630
## 14 1 0.005 8.00 0.9377184 0.8381506 0.8723512 0.02845289 0.06964725
## 15 1 0.005 16.00 0.9378910 0.8428571 0.8703556 0.02897121 0.08340389
## 16 1 0.005 32.00 0.9340194 0.8358804 0.8684688 0.03032960 0.07168265
## 17 1 0.010 0.25 0.9385237 0.8334994 0.8627721 0.02105140 0.05285153
## 18 1 0.010 0.50 0.9429324 0.8428571 0.8685414 0.02285407 0.05576994
## 19 1 0.010 1.00 0.9420834 0.8475637 0.8626996 0.02476222 0.06301168
## 20 1 0.010 2.00 0.9416546 0.8498339 0.8646952 0.02811772 0.05953335
## 21 1 0.010 4.00 0.9377184 0.8357697 0.8685414 0.02845289 0.07385252
## 22 1 0.010 8.00 0.9378910 0.8405869 0.8741655 0.02897121 0.07699485
## 23 1 0.010 16.00 0.9340194 0.8451827 0.8703919 0.03032960 0.07766084
## 24 1 0.010 32.00 0.9331110 0.8336656 0.8779390 0.02558704 0.07420272
## 25 2 0.001 0.25 0.9177808 0.8170543 0.8397678 0.02568345 0.06484486
## 26 2 0.001 0.50 0.9312968 0.8313400 0.8531567 0.01925534 0.04373895
## 27 2 0.001 1.00 0.9382799 0.8358250 0.8626996 0.01959475 0.05989700
## 28 2 0.001 2.00 0.9415732 0.8287929 0.8665820 0.02114134 0.05697014
## 29 2 0.001 4.00 0.9437586 0.8498893 0.8627721 0.02195056 0.06577088
## 30 2 0.001 8.00 0.9434995 0.8359358 0.8741655 0.02354723 0.07322104
## 31 2 0.001 16.00 0.9429819 0.8381506 0.8817852 0.02459237 0.07472236
## 32 2 0.001 32.00 0.9441590 0.8499446 0.8874819 0.02467181 0.07254186
## 33 2 0.005 0.25 0.9370187 0.8357697 0.8686139 0.02074181 0.06804611
## 34 2 0.005 0.50 0.9398239 0.8498339 0.8666909 0.02041487 0.06504293
## 35 2 0.005 1.00 0.9416083 0.8381506 0.8761611 0.02057089 0.07794713
## 36 2 0.005 2.00 0.9424678 0.8406423 0.8836357 0.02092003 0.07609199
## 37 2 0.005 4.00 0.9454805 0.8570321 0.8798984 0.01889337 0.07496758
## 38 2 0.005 8.00 0.9458642 0.8616833 0.8874456 0.01805740 0.06284101
## 39 2 0.005 16.00 0.9478692 0.8593023 0.8835994 0.01863617 0.06446458
## 40 2 0.005 32.00 0.9504889 0.8592470 0.8836357 0.01783922 0.06915726
## 41 2 0.010 0.25 0.9366234 0.8311185 0.8666183 0.01843902 0.06917656
## 42 2 0.010 0.50 0.9383894 0.8428018 0.8742017 0.01888776 0.08914918
## 43 2 0.010 1.00 0.9411239 0.8476190 0.8779753 0.01918473 0.09028992
## 44 2 0.010 2.00 0.9442114 0.8453488 0.8798258 0.01847995 0.07938012
## 45 2 0.010 4.00 0.9459963 0.8593577 0.8817126 0.01723191 0.06519004
## 46 2 0.010 8.00 0.9490640 0.8593577 0.8816401 0.01633029 0.06331960
## 47 2 0.010 16.00 0.9503049 0.8640642 0.8874456 0.01766674 0.06400041
## 48 2 0.010 32.00 0.9502390 0.8686047 0.8969884 0.02003144 0.05015350
## SpecSD
## 1 0.05243415
## 2 0.04911453
## 3 0.04009336
## 4 0.04718750
## 5 0.03636061
## 6 0.05098173
## 7 0.05156079
## 8 0.06350242
## 9 0.04456743
## 10 0.04940893
## 11 0.04551867
## 12 0.05381308
## 13 0.05260650
## 14 0.07070969
## 15 0.06155613
## 16 0.06118457
## 17 0.04404403
## 18 0.04551867
## 19 0.04978374
## 20 0.05550653
## 21 0.07266464
## 22 0.06045496
## 23 0.06204463
## 24 0.05504359
## 25 0.04730489
## 26 0.04631419
## 27 0.04616555
## 28 0.04708384
## 29 0.05575721
## 30 0.05339856
## 31 0.05535593
## 32 0.05939838
## 33 0.06308339
## 34 0.06227535
## 35 0.06073578
## 36 0.05812064
## 37 0.06301275
## 38 0.06342667
## 39 0.06911211
## 40 0.06145433
## 41 0.05847149
## 42 0.06778133
## 43 0.06180610
## 44 0.07050687
## 45 0.07207114
## 46 0.07219441
## 47 0.05936077
## 48 0.05190848(SVM_P_Train_ROCCurveAUC <- SVM_P_Tune$results[SVM_P_Tune$results$degree==SVM_P_Tune$bestTune$degree &
SVM_P_Tune$results$scale==SVM_P_Tune$bestTune$scale &
SVM_P_Tune$results$C==SVM_P_Tune$bestTune$C,
c("ROC")])## [1] 0.9504889##################################
# Identifying and plotting the
# best model predictors
##################################
# model does not support variable importance measurement
##################################
# Independently evaluating the model
# on the test set
##################################
SVM_P_Test <- data.frame(SVM_P_Observed = PMA_PreModelling_Test_SVM_P$Log_Solubility_Class,
SVM_P_Predicted = predict(SVM_P_Tune,
PMA_PreModelling_Test_SVM_P[,!names(PMA_PreModelling_Test_SVM_P) %in% c("Log_Solubility_Class")],
type = "prob"))
SVM_P_Test## SVM_P_Observed SVM_P_Predicted.Low SVM_P_Predicted.High
## 1 High 4.437105e-05 9.999556e-01
## 2 High 9.863074e-05 9.999014e-01
## 3 High 5.297227e-02 9.470277e-01
## 4 High 1.364081e-03 9.986359e-01
## 5 High 4.056261e-03 9.959437e-01
## 6 High 1.935681e-04 9.998064e-01
## 7 High 1.894876e-04 9.998105e-01
## 8 High 8.461504e-05 9.999154e-01
## 9 High 7.590917e-05 9.999241e-01
## 10 High 1.515337e-01 8.484663e-01
## 11 High 1.253198e-01 8.746802e-01
## 12 High 1.580050e-02 9.841995e-01
## 13 High 3.381798e-04 9.996618e-01
## 14 High 2.823980e-03 9.971760e-01
## 15 High 1.681284e-02 9.831872e-01
## 16 High 1.512818e-02 9.848718e-01
## 17 High 4.038851e-03 9.959611e-01
## 18 High 8.274691e-04 9.991725e-01
## 19 High 1.113583e-02 9.888642e-01
## 20 High 4.911766e-02 9.508823e-01
## 21 High 9.898067e-04 9.990102e-01
## 22 High 2.339977e-03 9.976600e-01
## 23 High 1.306064e-02 9.869394e-01
## 24 High 7.235225e-03 9.927648e-01
## 25 High 3.412072e-02 9.658793e-01
## 26 High 2.954190e-03 9.970458e-01
## 27 High 1.521391e-03 9.984786e-01
## 28 High 8.935793e-04 9.991064e-01
## 29 High 8.212562e-01 1.787438e-01
## 30 High 1.457176e-02 9.854282e-01
## 31 High 4.213112e-01 5.786888e-01
## 32 High 1.438817e-03 9.985612e-01
## 33 High 1.382656e-03 9.986173e-01
## 34 High 3.875270e-04 9.996125e-01
## 35 High 2.084086e-03 9.979159e-01
## 36 High 1.807449e-02 9.819255e-01
## 37 High 9.113954e-04 9.990886e-01
## 38 High 7.335468e-03 9.926645e-01
## 39 High 8.801846e-03 9.911982e-01
## 40 High 2.758028e-02 9.724197e-01
## 41 High 1.059527e-03 9.989405e-01
## 42 High 1.135930e-01 8.864070e-01
## 43 High 4.056316e-02 9.594368e-01
## 44 High 1.072802e-04 9.998927e-01
## 45 High 9.056021e-03 9.909440e-01
## 46 High 3.450541e-02 9.654946e-01
## 47 High 7.514901e-03 9.924851e-01
## 48 High 1.463060e-02 9.853694e-01
## 49 High 5.965261e-03 9.940347e-01
## 50 High 6.998302e-03 9.930017e-01
## 51 High 4.214485e-03 9.957855e-01
## 52 High 4.890794e-03 9.951092e-01
## 53 High 1.177139e-01 8.822861e-01
## 54 High 5.587705e-02 9.441229e-01
## 55 High 3.211403e-01 6.788597e-01
## 56 High 7.301659e-02 9.269834e-01
## 57 High 4.725764e-02 9.527424e-01
## 58 High 6.376771e-02 9.362323e-01
## 59 High 8.894208e-02 9.110579e-01
## 60 High 5.459579e-01 4.540421e-01
## 61 High 8.435069e-03 9.915649e-01
## 62 High 1.808928e-02 9.819107e-01
## 63 High 1.530560e-02 9.846944e-01
## 64 High 1.121788e-01 8.878212e-01
## 65 High 1.630383e-01 8.369617e-01
## 66 High 1.682650e-01 8.317350e-01
## 67 High 8.472637e-01 1.527363e-01
## 68 High 4.978264e-01 5.021736e-01
## 69 High 4.121811e-02 9.587819e-01
## 70 High 3.813110e-01 6.186890e-01
## 71 High 2.058742e-02 9.794126e-01
## 72 High 3.424141e-01 6.575859e-01
## 73 High 1.535931e-02 9.846407e-01
## 74 High 8.362718e-01 1.637282e-01
## 75 High 2.310661e-01 7.689339e-01
## 76 High 4.337502e-01 5.662498e-01
## 77 High 3.517762e-01 6.482238e-01
## 78 High 4.227364e-02 9.577264e-01
## 79 High 2.895282e-01 7.104718e-01
## 80 High 1.418081e-01 8.581919e-01
## 81 High 8.232842e-02 9.176716e-01
## 82 High 4.374798e-02 9.562520e-01
## 83 High 6.295803e-01 3.704197e-01
## 84 High 1.545407e-02 9.845459e-01
## 85 High 2.048561e-01 7.951439e-01
## 86 High 6.162280e-02 9.383772e-01
## 87 High 1.680072e-01 8.319928e-01
## 88 High 1.319825e-01 8.680175e-01
## 89 High 2.940581e-01 7.059419e-01
## 90 High 1.429267e-02 9.857073e-01
## 91 High 1.808009e-01 8.191991e-01
## 92 High 1.891659e-01 8.108341e-01
## 93 High 3.791373e-01 6.208627e-01
## 94 High 2.616863e-02 9.738314e-01
## 95 High 1.012828e-01 8.987172e-01
## 96 High 1.666090e-01 8.333910e-01
## 97 High 4.756672e-01 5.243328e-01
## 98 High 3.370586e-01 6.629414e-01
## 99 High 1.926107e-02 9.807389e-01
## 100 High 1.287430e-01 8.712570e-01
## 101 High 1.808205e-01 8.191795e-01
## 102 High 2.973948e-01 7.026052e-01
## 103 High 1.273138e-01 8.726862e-01
## 104 High 2.893142e-01 7.106858e-01
## 105 High 8.968593e-01 1.031407e-01
## 106 High 6.767236e-02 9.323276e-01
## 107 High 3.893571e-01 6.106429e-01
## 108 High 2.771089e-01 7.228911e-01
## 109 High 6.014674e-01 3.985326e-01
## 110 High 3.001782e-01 6.998218e-01
## 111 High 2.330348e-01 7.669652e-01
## 112 High 8.496574e-01 1.503426e-01
## 113 High 4.360659e-01 5.639341e-01
## 114 High 7.705737e-02 9.229426e-01
## 115 High 4.011531e-01 5.988469e-01
## 116 High 8.868558e-01 1.131442e-01
## 117 High 9.847158e-01 1.528423e-02
## 118 High 9.220983e-01 7.790173e-02
## 119 Low 3.397053e-02 9.660295e-01
## 120 Low 5.257021e-01 4.742979e-01
## 121 Low 4.558101e-01 5.441899e-01
## 122 Low 7.818783e-03 9.921812e-01
## 123 Low 9.482311e-01 5.176886e-02
## 124 Low 4.311209e-01 5.688791e-01
## 125 Low 6.013589e-01 3.986411e-01
## 126 Low 5.302886e-02 9.469711e-01
## 127 Low 9.614139e-01 3.858608e-02
## 128 Low 5.533691e-01 4.466309e-01
## 129 Low 8.612155e-01 1.387845e-01
## 130 Low 5.203065e-01 4.796935e-01
## 131 Low 8.486217e-01 1.513783e-01
## 132 Low 5.803644e-01 4.196356e-01
## 133 Low 9.287323e-01 7.126769e-02
## 134 Low 6.441916e-01 3.558084e-01
## 135 Low 4.884047e-01 5.115953e-01
## 136 Low 8.239077e-01 1.760923e-01
## 137 Low 4.338176e-01 5.661824e-01
## 138 Low 6.599024e-01 3.400976e-01
## 139 Low 4.219484e-01 5.780516e-01
## 140 Low 1.860729e-01 8.139271e-01
## 141 Low 3.530747e-01 6.469253e-01
## 142 Low 1.166715e-01 8.833285e-01
## 143 Low 9.228837e-01 7.711631e-02
## 144 Low 6.100013e-01 3.899987e-01
## 145 Low 2.518927e-01 7.481073e-01
## 146 Low 8.477800e-01 1.522200e-01
## 147 Low 8.775036e-01 1.224964e-01
## 148 Low 6.460553e-01 3.539447e-01
## 149 Low 9.386742e-01 6.132583e-02
## 150 Low 9.465394e-01 5.346057e-02
## 151 Low 4.351581e-01 5.648419e-01
## 152 Low 9.529013e-01 4.709866e-02
## 153 Low 7.167478e-01 2.832522e-01
## 154 Low 8.558321e-01 1.441679e-01
## 155 Low 4.308504e-01 5.691496e-01
## 156 Low 8.454887e-01 1.545113e-01
## 157 Low 8.965019e-01 1.034981e-01
## 158 Low 5.433461e-01 4.566539e-01
## 159 Low 9.058133e-01 9.418672e-02
## 160 Low 9.602120e-01 3.978802e-02
## 161 Low 9.027195e-01 9.728052e-02
## 162 Low 9.108580e-01 8.914196e-02
## 163 Low 9.477831e-01 5.221692e-02
## 164 Low 9.871036e-01 1.289644e-02
## 165 Low 9.987761e-01 1.223916e-03
## 166 Low 9.232130e-01 7.678700e-02
## 167 Low 9.969155e-01 3.084534e-03
## 168 Low 6.455968e-01 3.544032e-01
## 169 Low 9.381964e-01 6.180362e-02
## 170 Low 9.908208e-01 9.179190e-03
## 171 Low 9.752634e-01 2.473664e-02
## 172 Low 9.215194e-01 7.848060e-02
## 173 Low 8.512954e-01 1.487046e-01
## 174 Low 9.998767e-01 1.232664e-04
## 175 Low 9.823109e-01 1.768907e-02
## 176 Low 8.428239e-01 1.571761e-01
## 177 Low 9.591561e-01 4.084385e-02
## 178 Low 9.696089e-01 3.039105e-02
## 179 Low 9.290788e-01 7.092120e-02
## 180 Low 8.050375e-01 1.949625e-01
## 181 Low 9.337396e-01 6.626036e-02
## 182 Low 7.898904e-01 2.101096e-01
## 183 Low 9.985306e-01 1.469425e-03
## 184 Low 9.992304e-01 7.695772e-04
## 185 Low 9.028139e-01 9.718614e-02
## 186 Low 9.710167e-01 2.898334e-02
## 187 Low 9.923206e-01 7.679375e-03
## 188 Low 9.357071e-01 6.429295e-02
## 189 Low 9.860034e-01 1.399662e-02
## 190 Low 9.856923e-01 1.430772e-02
## 191 Low 9.528866e-01 4.711340e-02
## 192 Low 9.184979e-01 8.150207e-02
## 193 Low 9.629996e-01 3.700045e-02
## 194 Low 9.669751e-01 3.302489e-02
## 195 Low 9.967992e-01 3.200789e-03
## 196 Low 9.636754e-01 3.632463e-02
## 197 Low 9.681232e-01 3.187685e-02
## 198 Low 9.219406e-01 7.805945e-02
## 199 Low 9.927099e-01 7.290081e-03
## 200 Low 9.883603e-01 1.163965e-02
## 201 Low 9.872716e-01 1.272841e-02
## 202 Low 9.897256e-01 1.027438e-02
## 203 Low 9.898915e-01 1.010853e-02
## 204 Low 9.860584e-01 1.394162e-02
## 205 Low 9.874249e-01 1.257505e-02
## 206 Low 9.952109e-01 4.789145e-03
## 207 Low 9.957363e-01 4.263718e-03
## 208 Low 9.909268e-01 9.073177e-03
## 209 Low 9.993597e-01 6.403427e-04
## 210 Low 9.948199e-01 5.180123e-03
## 211 Low 9.981661e-01 1.833947e-03
## 212 Low 9.977850e-01 2.214988e-03
## 213 Low 9.990890e-01 9.109874e-04
## 214 Low 9.995084e-01 4.916347e-04
## 215 Low 9.985671e-01 1.432851e-03
## 216 Low 9.991574e-01 8.425698e-04
## 217 High 2.861841e-04 9.997138e-01
## 218 High 2.525521e-04 9.997474e-01
## 219 High 1.932631e-04 9.998067e-01
## 220 High 3.589613e-04 9.996410e-01
## 221 High 1.309125e-02 9.869087e-01
## 222 High 1.953967e-02 9.804603e-01
## 223 High 5.416678e-03 9.945833e-01
## 224 High 3.593345e-03 9.964067e-01
## 225 High 3.952984e-01 6.047016e-01
## 226 High 7.173722e-02 9.282628e-01
## 227 High 6.556078e-03 9.934439e-01
## 228 High 4.631593e-02 9.536841e-01
## 229 High 3.191958e-04 9.996808e-01
## 230 High 9.328630e-02 9.067137e-01
## 231 High 5.569023e-02 9.443098e-01
## 232 High 2.576389e-03 9.974236e-01
## 233 High 3.111545e-02 9.688846e-01
## 234 High 2.238030e-02 9.776197e-01
## 235 High 2.836261e-02 9.716374e-01
## 236 High 2.375457e-01 7.624543e-01
## 237 High 4.087041e-01 5.912959e-01
## 238 High 4.593380e-02 9.540662e-01
## 239 High 1.177139e-01 8.822861e-01
## 240 High 1.056348e-01 8.943652e-01
## 241 High 3.137645e-03 9.968624e-01
## 242 High 2.791157e-02 9.720884e-01
## 243 High 1.831218e-02 9.816878e-01
## 244 High 7.599363e-01 2.400637e-01
## 245 High 2.214500e-01 7.785500e-01
## 246 High 5.039272e-03 9.949607e-01
## 247 High 2.641108e-02 9.735889e-01
## 248 High 1.270971e-02 9.872903e-01
## 249 High 4.820820e-02 9.517918e-01
## 250 High 5.446703e-01 4.553297e-01
## 251 High 1.746056e-01 8.253944e-01
## 252 High 5.305232e-01 4.694768e-01
## 253 High 1.224164e-01 8.775836e-01
## 254 High 7.132781e-01 2.867219e-01
## 255 High 1.485345e-01 8.514655e-01
## 256 High 1.834751e-02 9.816525e-01
## 257 High 7.286247e-03 9.927138e-01
## 258 High 1.619494e-01 8.380506e-01
## 259 High 6.408455e-01 3.591545e-01
## 260 High 1.943460e-01 8.056540e-01
## 261 High 5.822545e-02 9.417745e-01
## 262 High 3.767487e-02 9.623251e-01
## 263 High 1.900704e-01 8.099296e-01
## 264 High 3.476714e-01 6.523286e-01
## 265 High 6.845639e-01 3.154361e-01
## 266 High 4.977542e-02 9.502246e-01
## 267 High 5.772676e-01 4.227324e-01
## 268 High 2.854987e-02 9.714501e-01
## 269 Low 4.189723e-01 5.810277e-01
## 270 Low 3.866665e-01 6.133335e-01
## 271 Low 4.692530e-01 5.307470e-01
## 272 Low 7.015630e-01 2.984370e-01
## 273 Low 7.652021e-01 2.347979e-01
## 274 Low 8.254232e-01 1.745768e-01
## 275 Low 8.075412e-01 1.924588e-01
## 276 Low 9.443706e-01 5.562945e-02
## 277 Low 8.685546e-01 1.314454e-01
## 278 Low 3.642754e-01 6.357246e-01
## 279 Low 8.104561e-01 1.895439e-01
## 280 Low 8.730788e-01 1.269212e-01
## 281 Low 6.436814e-01 3.563186e-01
## 282 Low 9.556037e-01 4.439631e-02
## 283 Low 8.905941e-01 1.094059e-01
## 284 Low 9.857640e-01 1.423602e-02
## 285 Low 9.583932e-01 4.160682e-02
## 286 Low 6.444371e-01 3.555629e-01
## 287 Low 8.892668e-01 1.107332e-01
## 288 Low 8.103407e-01 1.896593e-01
## 289 Low 9.393219e-01 6.067812e-02
## 290 Low 8.607423e-01 1.392577e-01
## 291 Low 9.169157e-01 8.308427e-02
## 292 Low 7.877789e-01 2.122211e-01
## 293 Low 8.606541e-01 1.393459e-01
## 294 Low 9.590663e-01 4.093374e-02
## 295 Low 9.537861e-01 4.621387e-02
## 296 Low 8.156491e-01 1.843509e-01
## 297 Low 9.502762e-01 4.972382e-02
## 298 Low 8.670162e-01 1.329838e-01
## 299 Low 9.427929e-01 5.720708e-02
## 300 Low 9.884079e-01 1.159213e-02
## 301 Low 9.934260e-01 6.573965e-03
## 302 Low 9.417467e-01 5.825329e-02
## 303 Low 9.939330e-01 6.066998e-03
## 304 Low 9.825602e-01 1.743978e-02
## 305 Low 9.999661e-01 3.392876e-05
## 306 Low 9.943347e-01 5.665260e-03
## 307 Low 9.990516e-01 9.484101e-04
## 308 Low 9.997245e-01 2.754741e-04
## 309 Low 9.998293e-01 1.707135e-04
## 310 Low 9.999183e-01 8.165397e-05
## 311 Low 9.996739e-01 3.261319e-04
## 312 Low 9.971262e-01 2.873808e-03
## 313 High 7.277619e-02 9.272238e-01
## 314 High 3.912316e-01 6.087684e-01
## 315 Low 9.874103e-01 1.258970e-02
## 316 High 9.759034e-01 2.409659e-02##################################
# Reporting the independent evaluation results
# for the test set
##################################
SVM_P_Test_ROC <- roc(response = SVM_P_Test$SVM_P_Observed,
predictor = SVM_P_Test$SVM_P_Predicted.High,
levels = rev(levels(SVM_P_Test$SVM_P_Observed)))
(SVM_P_Test_ROCCurveAUC <- auc(SVM_P_Test_ROC)[1])## [1] 0.95011921.5.10 K-Nearest Neighbors (KNN)
[A] The k-nearest neighbors model was implemented through the caret package.
[B] The model contains 1 hyperparameter:
[B.1] k = number of neighbors made to vary across a range of values equal to 1 to 15
[C] The cross-validated model performance of the final model is summarized as follows:
[C.1] Final model configuration involves k=8
[C.2] ROC Curve AUC = 0.89489
[D] The model does not allow for ranking of predictors in terms of variable importance.
[E] The independent test model performance of the final model is summarized as follows:
[E.1] ROC Curve AUC = 0.88170
##################################
# Transforming factor predictors
# as required by the nature of the model
##################################
# Creating a local object
# for the train and test sets
##################################
PMA_PreModelling_Train_KNN <- as.data.frame(lapply(PMA_PreModelling_Train[,!names(PMA_PreModelling_Train) %in%
c("Log_Solubility_Class")],
function(x) as.numeric(as.character(x))))
PMA_PreModelling_Train_KNN$Log_Solubility_Class <- PMA_PreModelling_Train$Log_Solubility_Class
dim(PMA_PreModelling_Train_KNN)## [1] 951 221PMA_PreModelling_Test_KNN <- as.data.frame(lapply(PMA_PreModelling_Test[,!names(PMA_PreModelling_Test) %in%
c("Log_Solubility_Class")],
function(x) as.numeric(as.character(x))))
PMA_PreModelling_Test_KNN$Log_Solubility_Class <- PMA_PreModelling_Test$Log_Solubility_Class
dim(PMA_PreModelling_Test_KNN)## [1] 316 221##################################
# Creating consistent fold assignments
# for the 10-Fold Cross Validation process
##################################
set.seed(12345678)
KFold_Indices <- createFolds(PMA_PreModelling_Train_KNN$Log_Solubility_Class,
k = 10,
returnTrain=TRUE)
KFold_Control <- trainControl(method="cv",
index=KFold_Indices,
summaryFunction = twoClassSummary,
classProbs = TRUE)
##################################
# Setting the conditions
# for hyperparameter tuning
##################################
KNN_Grid = data.frame(k = 1:15)
##################################
# Running the k-nearest neighbors model
# by setting the caret method to 'knn'
##################################
set.seed(12345678)
KNN_Tune <- train(x = PMA_PreModelling_Train_KNN[,!names(PMA_PreModelling_Train_KNN) %in% c("Log_Solubility_Class")],
y = PMA_PreModelling_Train_KNN$Log_Solubility_Class,
method = "knn",
tuneGrid = KNN_Grid,
metric = "ROC",
preProc = c("center", "scale"),
trControl = KFold_Control)
##################################
# Reporting the cross-validation results
# for the train set
##################################
KNN_Tune## k-Nearest Neighbors
##
## 951 samples
## 220 predictors
## 2 classes: 'Low', 'High'
##
## Pre-processing: centered (220), scaled (220)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 857, 855, 857, 855, 856, 856, ...
## Resampling results across tuning parameters:
##
## k ROC Sens Spec
## 1 0.8165667 0.7705426 0.8625907
## 2 0.8498964 0.7329457 0.8380261
## 3 0.8695139 0.7074197 0.8722061
## 4 0.8805812 0.7237542 0.8646952
## 5 0.8881761 0.6981174 0.8779390
## 6 0.8890159 0.6723699 0.8911829
## 7 0.8929299 0.6536545 0.8951379
## 8 0.8948909 0.6700997 0.8951379
## 9 0.8932980 0.6488372 0.8913643
## 10 0.8924719 0.6442414 0.9064949
## 11 0.8917834 0.6559801 0.8988752
## 12 0.8903257 0.6605759 0.8950653
## 13 0.8886237 0.6442968 0.9027576
## 14 0.8892745 0.6534330 0.9064586
## 15 0.8877785 0.6418605 0.8988752
##
## ROC was used to select the optimal model using the largest value.
## The final value used for the model was k = 8.KNN_Tune$finalModel## 8-nearest neighbor model
## Training set outcome distribution:
##
## Low High
## 427 524KNN_Tune$results## k ROC Sens Spec ROCSD SensSD SpecSD
## 1 1 0.8165667 0.7705426 0.8625907 0.04805712 0.08491149 0.04031952
## 2 2 0.8498964 0.7329457 0.8380261 0.04287313 0.06804003 0.04016326
## 3 3 0.8695139 0.7074197 0.8722061 0.03543212 0.08107148 0.02826351
## 4 4 0.8805812 0.7237542 0.8646952 0.03061342 0.09403887 0.03072821
## 5 5 0.8881761 0.6981174 0.8779390 0.03118507 0.10247267 0.02362562
## 6 6 0.8890159 0.6723699 0.8911829 0.03099682 0.07660789 0.03402859
## 7 7 0.8929299 0.6536545 0.8951379 0.03099339 0.08447388 0.03589127
## 8 8 0.8948909 0.6700997 0.8951379 0.03312645 0.07348286 0.03366057
## 9 9 0.8932980 0.6488372 0.8913643 0.03893850 0.08004371 0.03545545
## 10 10 0.8924719 0.6442414 0.9064949 0.04301828 0.07785232 0.02905682
## 11 11 0.8917834 0.6559801 0.8988752 0.04130939 0.08744255 0.03579130
## 12 12 0.8903257 0.6605759 0.8950653 0.04351160 0.08004337 0.02562836
## 13 13 0.8886237 0.6442968 0.9027576 0.04293479 0.10062032 0.03128096
## 14 14 0.8892745 0.6534330 0.9064586 0.04380270 0.08873092 0.03044044
## 15 15 0.8877785 0.6418605 0.8988752 0.04471101 0.09231959 0.02527676(KNN_Train_ROCCurveAUC <- KNN_Tune$results[KNN_Tune$results$k==KNN_Tune$bestTune$k,
c("ROC")])## [1] 0.8948909##################################
# Identifying and plotting the
# best model predictors
##################################
# model does not support variable importance measurement
##################################
# Independently evaluating the model
# on the test set
##################################
KNN_Test <- data.frame(KNN_Observed = PMA_PreModelling_Test_KNN$Log_Solubility_Class,
KNN_Predicted = predict(KNN_Tune,
PMA_PreModelling_Test_KNN[,!names(PMA_PreModelling_Test_KNN) %in% c("Log_Solubility_Class")],
type = "prob"))
##################################
# Reporting the independent evaluation results
# for the test set
##################################
KNN_Test_ROC <- roc(response = KNN_Test$KNN_Observed,
predictor = KNN_Test$KNN_Predicted.High,
levels = rev(levels(KNN_Test$KNN_Observed)))
(KNN_Test_ROCCurveAUC <- auc(KNN_Test_ROC)[1])## [1] 0.8817051.5.11 Classification and Regression Trees (CART)
[A] The classification and regression trees model from the rpart package was implemented through the caret package.
[B] The model contains 1 hyperparameter:
[B.1] cp = complexity parameter threshold made to vary across a range of values equal to 0.001 to 0.020
[C] The cross-validated model performance of the final model is summarized as follows:
[C.1] Final model configuration involves cp=0.001
[C.2] ROC Curve AUC = 0.90236
[D] The model allows for ranking of predictors in terms of variable importance. The top-performing predictors in the model are as follows:
[D.1] MolWeight variable (numeric)
[D.2] NumCarbon variable (numeric)
[D.3] NumBonds variable (numeric)
[D.4] HydrophilicFactor variable (numeric)
[D.5] NumMultBonds variable (numeric)
[E] The independent test model performance of the final model is summarized as follows:
[E.1] ROC Curve AUC = 0.94522
##################################
# Creating a local object
# for the train and test sets
##################################
PMA_PreModelling_Train_CART <- PMA_PreModelling_Train
PMA_PreModelling_Test_CART <- PMA_PreModelling_Test
##################################
# Creating consistent fold assignments
# for the 10-Fold Cross Validation process
##################################
set.seed(12345678)
KFold_Indices <- createFolds(PMA_PreModelling_Train_CART$Log_Solubility_Class,
k = 10,
returnTrain=TRUE)
KFold_Control <- trainControl(method="cv",
index=KFold_Indices,
summaryFunction = twoClassSummary,
classProbs = TRUE)
##################################
# Setting the conditions
# for hyperparameter tuning
##################################
CART_Grid = data.frame(cp = c(0.001, 0.005, 0.010, 0.015, 0.020))
##################################
# Running the classification and regression trees model
# by setting the caret method to 'rpart'
##################################
set.seed(12345678)
CART_Tune <- train(x = PMA_PreModelling_Train_CART[,!names(PMA_PreModelling_Train_CART) %in% c("Log_Solubility_Class")],
y = PMA_PreModelling_Train_CART$Log_Solubility_Class,
method = "rpart",
tuneGrid = CART_Grid,
metric = "ROC",
trControl = KFold_Control)
##################################
# Reporting the cross-validation results
# for the train set
##################################
CART_Tune## CART
##
## 951 samples
## 220 predictors
## 2 classes: 'Low', 'High'
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 857, 855, 857, 855, 856, 856, ...
## Resampling results across tuning parameters:
##
## cp ROC Sens Spec
## 0.001 0.9023673 0.8125692 0.8551524
## 0.005 0.8923973 0.8195460 0.8512700
## 0.010 0.8717310 0.8476190 0.8416183
## 0.015 0.8547744 0.8451827 0.8282293
## 0.020 0.8374508 0.8641750 0.8034107
##
## ROC was used to select the optimal model using the largest value.
## The final value used for the model was cp = 0.001.CART_Tune$finalModel## n= 951
##
## node), split, n, loss, yval, (yprob)
## * denotes terminal node
##
## 1) root 951 427 High (0.44900105 0.55099895)
## 2) NumCarbon>=0.08489128 424 102 Low (0.75943396 0.24056604)
## 4) SurfaceArea1< -0.5808955 119 3 Low (0.97478992 0.02521008) *
## 5) SurfaceArea1>=-0.5808955 305 99 Low (0.67540984 0.32459016)
## 10) MolWeight>=0.6824776 188 35 Low (0.81382979 0.18617021)
## 20) FP075=0 74 3 Low (0.95945946 0.04054054) *
## 21) FP075=1 114 32 Low (0.71929825 0.28070175)
## 42) FP198=0 105 24 Low (0.77142857 0.22857143)
## 84) FP009=1 30 1 Low (0.96666667 0.03333333) *
## 85) FP009=0 75 23 Low (0.69333333 0.30666667)
## 170) FP088=0 58 14 Low (0.75862069 0.24137931)
## 340) SurfaceArea1< 1.438317 36 5 Low (0.86111111 0.13888889) *
## 341) SurfaceArea1>=1.438317 22 9 Low (0.59090909 0.40909091)
## 682) NumRotBonds< 0.5184444 11 2 Low (0.81818182 0.18181818) *
## 683) NumRotBonds>=0.5184444 11 4 High (0.36363636 0.63636364) *
## 171) FP088=1 17 8 High (0.47058824 0.52941176) *
## 43) FP198=1 9 1 High (0.11111111 0.88888889) *
## 11) MolWeight< 0.6824776 117 53 High (0.45299145 0.54700855)
## 22) FP178=1 19 1 Low (0.94736842 0.05263158) *
## 23) FP178=0 98 35 High (0.35714286 0.64285714)
## 46) NumCarbon>=0.4506182 49 23 Low (0.53061224 0.46938776)
## 92) HydrophilicFactor< 0.3739684 40 14 Low (0.65000000 0.35000000)
## 184) FP166=0 10 0 Low (1.00000000 0.00000000) *
## 185) FP166=1 30 14 Low (0.53333333 0.46666667)
## 370) FP065=1 21 7 Low (0.66666667 0.33333333)
## 740) HydrophilicFactor>=-0.2286019 8 0 Low (1.00000000 0.00000000) *
## 741) HydrophilicFactor< -0.2286019 13 6 High (0.46153846 0.53846154) *
## 371) FP065=0 9 2 High (0.22222222 0.77777778) *
## 93) HydrophilicFactor>=0.3739684 9 0 High (0.00000000 1.00000000) *
## 47) NumCarbon< 0.4506182 49 9 High (0.18367347 0.81632653)
## 94) FP094=1 7 3 Low (0.57142857 0.42857143) *
## 95) FP094=0 42 5 High (0.11904762 0.88095238) *
## 3) NumCarbon< 0.08489128 527 105 High (0.19924099 0.80075901)
## 6) MolWeight>=0.3719905 59 17 Low (0.71186441 0.28813559)
## 12) FP115=0 46 7 Low (0.84782609 0.15217391)
## 24) FP171=0 37 2 Low (0.94594595 0.05405405) *
## 25) FP171=1 9 4 High (0.44444444 0.55555556) *
## 13) FP115=1 13 3 High (0.23076923 0.76923077) *
## 7) MolWeight< 0.3719905 468 63 High (0.13461538 0.86538462)
## 14) HydrophilicFactor< -0.789432 33 5 Low (0.84848485 0.15151515)
## 28) NumBonds>=-0.5566408 26 0 Low (1.00000000 0.00000000) *
## 29) NumBonds< -0.5566408 7 2 High (0.28571429 0.71428571) *
## 15) HydrophilicFactor>=-0.789432 435 35 High (0.08045977 0.91954023)
## 30) FP013=1 42 17 High (0.40476190 0.59523810)
## 60) FP060=0 26 10 Low (0.61538462 0.38461538)
## 120) MolWeight>=-0.1146511 9 0 Low (1.00000000 0.00000000) *
## 121) MolWeight< -0.1146511 17 7 High (0.41176471 0.58823529) *
## 61) FP060=1 16 1 High (0.06250000 0.93750000) *
## 31) FP013=0 393 18 High (0.04580153 0.95419847)
## 62) FP206=1 31 11 High (0.35483871 0.64516129)
## 124) NumOxygen< -0.6211843 7 1 Low (0.85714286 0.14285714) *
## 125) NumOxygen>=-0.6211843 24 5 High (0.20833333 0.79166667)
## 250) NumRotBonds>=1.764021 7 2 Low (0.71428571 0.28571429) *
## 251) NumRotBonds< 1.764021 17 0 High (0.00000000 1.00000000) *
## 63) FP206=0 362 7 High (0.01933702 0.98066298) *CART_Tune$results## cp ROC Sens Spec ROCSD SensSD SpecSD
## 1 0.001 0.9023673 0.8125692 0.8551524 0.02471610 0.04684097 0.05412641
## 2 0.005 0.8923973 0.8195460 0.8512700 0.02507914 0.06010888 0.04694613
## 3 0.010 0.8717310 0.8476190 0.8416183 0.04129882 0.05592549 0.05733463
## 4 0.015 0.8547744 0.8451827 0.8282293 0.04327629 0.05152127 0.07139618
## 5 0.020 0.8374508 0.8641750 0.8034107 0.04423715 0.05003381 0.06839680(CART_Train_ROCCurveAUC <- CART_Tune$results[CART_Tune$results$cp==CART_Tune$bestTune$cp,
c("ROC")])## [1] 0.9023673##################################
# Identifying and plotting the
# best model predictors
##################################
CART_VarImp <- varImp(CART_Tune, scale = TRUE)
plot(CART_VarImp,
top=25,
scales=list(y=list(cex = .95)),
main="Ranked Variable Importance : Classification and Regression Trees",
xlab="Scaled Variable Importance Metrics",
ylab="Predictors",
cex=2,
origin=0,
alpha=0.45)
##################################
# Independently evaluating the model
# on the test set
##################################
CART_Test <- data.frame(CART_Observed = PMA_PreModelling_Test_CART$Log_Solubility_Class,
CART_Predicted = predict(CART_Tune,
PMA_PreModelling_Test_CART[,!names(PMA_PreModelling_Test_CART) %in% c("Log_Solubility_Class")],
type = "prob"))
CART_Test## CART_Observed CART_Predicted.Low CART_Predicted.High
## 20 High 0.01933702 0.98066298
## 21 High 0.01933702 0.98066298
## 23 High 0.01933702 0.98066298
## 25 High 0.01933702 0.98066298
## 28 High 0.01933702 0.98066298
## 31 High 0.01933702 0.98066298
## 32 High 0.01933702 0.98066298
## 33 High 0.01933702 0.98066298
## 34 High 0.01933702 0.98066298
## 37 High 0.01933702 0.98066298
## 38 High 0.01933702 0.98066298
## 42 High 0.11904762 0.88095238
## 49 High 0.01933702 0.98066298
## 54 High 0.01933702 0.98066298
## 55 High 0.01933702 0.98066298
## 58 High 0.01933702 0.98066298
## 60 High 0.01933702 0.98066298
## 61 High 0.01933702 0.98066298
## 65 High 0.01933702 0.98066298
## 69 High 0.01933702 0.98066298
## 73 High 0.01933702 0.98066298
## 86 High 0.01933702 0.98066298
## 90 High 0.01933702 0.98066298
## 91 High 0.01933702 0.98066298
## 93 High 0.01933702 0.98066298
## 96 High 0.01933702 0.98066298
## 98 High 0.01933702 0.98066298
## 100 High 0.01933702 0.98066298
## 104 High 0.11111111 0.88888889
## 112 High 0.01933702 0.98066298
## 115 High 0.46153846 0.53846154
## 119 High 0.01933702 0.98066298
## 128 High 0.01933702 0.98066298
## 130 High 0.01933702 0.98066298
## 139 High 0.01933702 0.98066298
## 143 High 0.01933702 0.98066298
## 145 High 0.01933702 0.98066298
## 146 High 0.01933702 0.98066298
## 149 High 0.01933702 0.98066298
## 150 High 0.01933702 0.98066298
## 152 High 0.01933702 0.98066298
## 157 High 1.00000000 0.00000000
## 161 High 0.01933702 0.98066298
## 162 High 0.01933702 0.98066298
## 166 High 0.01933702 0.98066298
## 167 High 0.01933702 0.98066298
## 173 High 0.01933702 0.98066298
## 176 High 0.01933702 0.98066298
## 182 High 0.01933702 0.98066298
## 187 High 0.01933702 0.98066298
## 190 High 0.01933702 0.98066298
## 194 High 0.01933702 0.98066298
## 195 High 0.01933702 0.98066298
## 201 High 0.01933702 0.98066298
## 207 High 0.01933702 0.98066298
## 208 High 0.01933702 0.98066298
## 215 High 0.01933702 0.98066298
## 222 High 0.01933702 0.98066298
## 224 High 0.01933702 0.98066298
## 231 High 0.11904762 0.88095238
## 236 High 0.01933702 0.98066298
## 237 High 0.01933702 0.98066298
## 240 High 0.01933702 0.98066298
## 243 High 0.01933702 0.98066298
## 248 High 0.01933702 0.98066298
## 251 High 0.86111111 0.13888889
## 256 High 0.11904762 0.88095238
## 258 High 0.06250000 0.93750000
## 262 High 0.01933702 0.98066298
## 266 High 0.01933702 0.98066298
## 272 High 0.44444444 0.55555556
## 280 High 0.94736842 0.05263158
## 283 High 0.01933702 0.98066298
## 286 High 0.94594595 0.05405405
## 287 High 0.01933702 0.98066298
## 289 High 0.01933702 0.98066298
## 290 High 0.11904762 0.88095238
## 298 High 0.01933702 0.98066298
## 305 High 0.01933702 0.98066298
## 306 High 0.57142857 0.42857143
## 312 High 0.01933702 0.98066298
## 320 High 0.01933702 0.98066298
## 325 High 0.01933702 0.98066298
## 332 High 0.00000000 1.00000000
## 333 High 0.01933702 0.98066298
## 335 High 0.01933702 0.98066298
## 339 High 0.97478992 0.02521008
## 346 High 0.11904762 0.88095238
## 347 High 0.01933702 0.98066298
## 350 High 0.00000000 1.00000000
## 353 High 0.01933702 0.98066298
## 358 High 0.11904762 0.88095238
## 365 High 0.06250000 0.93750000
## 367 High 0.01933702 0.98066298
## 370 High 0.01933702 0.98066298
## 379 High 0.01933702 0.98066298
## 386 High 0.28571429 0.71428571
## 394 High 0.94736842 0.05263158
## 396 High 0.01933702 0.98066298
## 400 High 0.01933702 0.98066298
## 404 High 0.01933702 0.98066298
## 405 High 0.01933702 0.98066298
## 413 High 0.57142857 0.42857143
## 415 High 0.01933702 0.98066298
## 417 High 0.28571429 0.71428571
## 418 High 0.11904762 0.88095238
## 423 High 0.41176471 0.58823529
## 434 High 0.01933702 0.98066298
## 437 High 0.23076923 0.76923077
## 440 High 0.81818182 0.18181818
## 449 High 0.57142857 0.42857143
## 450 High 0.06250000 0.93750000
## 457 High 0.57142857 0.42857143
## 467 High 0.81818182 0.18181818
## 469 High 0.23076923 0.76923077
## 474 High 0.86111111 0.13888889
## 475 High 0.86111111 0.13888889
## 485 High 0.94736842 0.05263158
## 504 Low 0.95945946 0.04054054
## 511 Low 0.96666667 0.03333333
## 512 Low 1.00000000 0.00000000
## 517 Low 0.01933702 0.98066298
## 519 Low 0.95945946 0.04054054
## 520 Low 0.01933702 0.98066298
## 522 Low 0.22222222 0.77777778
## 527 Low 1.00000000 0.00000000
## 528 Low 1.00000000 0.00000000
## 529 Low 0.94736842 0.05263158
## 537 Low 0.85714286 0.14285714
## 540 Low 0.95945946 0.04054054
## 541 Low 1.00000000 0.00000000
## 547 Low 0.86111111 0.13888889
## 550 Low 0.81818182 0.18181818
## 555 Low 0.00000000 1.00000000
## 564 Low 0.94594595 0.05405405
## 570 Low 0.94736842 0.05263158
## 573 Low 0.94594595 0.05405405
## 575 Low 1.00000000 0.00000000
## 578 Low 1.00000000 0.00000000
## 581 Low 0.06250000 0.93750000
## 585 Low 0.94594595 0.05405405
## 590 Low 1.00000000 0.00000000
## 601 Low 0.95945946 0.04054054
## 602 Low 0.11904762 0.88095238
## 607 Low 0.46153846 0.53846154
## 610 Low 0.97478992 0.02521008
## 618 Low 0.81818182 0.18181818
## 624 Low 0.94594595 0.05405405
## 626 Low 0.94736842 0.05263158
## 627 Low 1.00000000 0.00000000
## 634 Low 0.11111111 0.88888889
## 640 Low 0.47058824 0.52941176
## 642 Low 1.00000000 0.00000000
## 643 Low 0.97478992 0.02521008
## 644 Low 0.46153846 0.53846154
## 645 Low 0.11904762 0.88095238
## 646 Low 0.97478992 0.02521008
## 647 Low 0.96666667 0.03333333
## 652 Low 0.85714286 0.14285714
## 658 Low 0.95945946 0.04054054
## 659 Low 0.97478992 0.02521008
## 660 Low 0.95945946 0.04054054
## 664 Low 0.86111111 0.13888889
## 666 Low 0.94594595 0.05405405
## 667 Low 0.95945946 0.04054054
## 675 Low 0.97478992 0.02521008
## 680 Low 0.11111111 0.88888889
## 681 Low 0.86111111 0.13888889
## 687 Low 0.97478992 0.02521008
## 694 Low 0.95945946 0.04054054
## 697 Low 0.94594595 0.05405405
## 701 Low 1.00000000 0.00000000
## 705 Low 0.95945946 0.04054054
## 707 Low 0.95945946 0.04054054
## 710 Low 0.97478992 0.02521008
## 716 Low 0.95945946 0.04054054
## 719 Low 0.47058824 0.52941176
## 720 Low 0.95945946 0.04054054
## 725 Low 0.95945946 0.04054054
## 727 Low 1.00000000 0.00000000
## 730 Low 0.94594595 0.05405405
## 738 Low 0.97478992 0.02521008
## 745 Low 0.97478992 0.02521008
## 748 Low 0.94736842 0.05263158
## 751 Low 0.95945946 0.04054054
## 756 Low 0.96666667 0.03333333
## 766 Low 0.95945946 0.04054054
## 769 Low 0.94594595 0.05405405
## 783 Low 0.97478992 0.02521008
## 785 Low 0.97478992 0.02521008
## 790 Low 0.95945946 0.04054054
## 793 Low 0.46153846 0.53846154
## 795 Low 0.95945946 0.04054054
## 796 Low 0.95945946 0.04054054
## 797 Low 0.95945946 0.04054054
## 801 Low 0.94594595 0.05405405
## 811 Low 0.94594595 0.05405405
## 812 Low 0.95945946 0.04054054
## 815 Low 0.95945946 0.04054054
## 816 Low 0.94594595 0.05405405
## 817 Low 0.97478992 0.02521008
## 824 Low 0.97478992 0.02521008
## 825 Low 0.97478992 0.02521008
## 826 Low 0.97478992 0.02521008
## 830 Low 0.97478992 0.02521008
## 837 Low 0.97478992 0.02521008
## 838 Low 0.94594595 0.05405405
## 844 Low 0.97478992 0.02521008
## 845 Low 0.97478992 0.02521008
## 847 Low 0.97478992 0.02521008
## 850 Low 0.97478992 0.02521008
## 852 Low 0.97478992 0.02521008
## 853 Low 0.97478992 0.02521008
## 861 Low 0.97478992 0.02521008
## 868 Low 0.97478992 0.02521008
## 874 Low 0.97478992 0.02521008
## 879 High 0.01933702 0.98066298
## 895 High 0.01933702 0.98066298
## 899 High 0.01933702 0.98066298
## 903 High 0.01933702 0.98066298
## 917 High 0.01933702 0.98066298
## 927 High 0.01933702 0.98066298
## 929 High 0.01933702 0.98066298
## 931 High 0.00000000 1.00000000
## 933 High 0.11904762 0.88095238
## 944 High 0.01933702 0.98066298
## 947 High 0.01933702 0.98066298
## 949 High 0.01933702 0.98066298
## 953 High 0.01933702 0.98066298
## 958 High 0.01933702 0.98066298
## 961 High 0.85714286 0.14285714
## 963 High 0.01933702 0.98066298
## 964 High 0.01933702 0.98066298
## 973 High 0.01933702 0.98066298
## 976 High 0.01933702 0.98066298
## 977 High 0.01933702 0.98066298
## 980 High 0.36363636 0.63636364
## 983 High 0.01933702 0.98066298
## 984 High 0.01933702 0.98066298
## 986 High 0.01933702 0.98066298
## 989 High 0.01933702 0.98066298
## 991 High 0.01933702 0.98066298
## 996 High 0.01933702 0.98066298
## 997 High 0.01933702 0.98066298
## 999 High 0.41176471 0.58823529
## 1000 High 0.01933702 0.98066298
## 1003 High 0.01933702 0.98066298
## 1008 High 0.01933702 0.98066298
## 1009 High 0.01933702 0.98066298
## 1014 High 0.01933702 0.98066298
## 1015 High 0.00000000 1.00000000
## 1040 High 0.01933702 0.98066298
## 1042 High 0.11904762 0.88095238
## 1043 High 0.01933702 0.98066298
## 1050 High 0.01933702 0.98066298
## 1052 High 0.01933702 0.98066298
## 1056 High 0.23076923 0.76923077
## 1070 High 0.11904762 0.88095238
## 1073 High 0.41176471 0.58823529
## 1074 High 0.01933702 0.98066298
## 1079 High 0.00000000 1.00000000
## 1080 High 0.11904762 0.88095238
## 1085 High 0.01933702 0.98066298
## 1087 High 0.22222222 0.77777778
## 1096 High 0.86111111 0.13888889
## 1099 High 0.00000000 1.00000000
## 1100 High 0.57142857 0.42857143
## 1102 High 0.23076923 0.76923077
## 1107 Low 1.00000000 0.00000000
## 1109 Low 0.95945946 0.04054054
## 1114 Low 0.28571429 0.71428571
## 1118 Low 0.00000000 1.00000000
## 1123 Low 0.96666667 0.03333333
## 1132 Low 0.22222222 0.77777778
## 1134 Low 1.00000000 0.00000000
## 1137 Low 1.00000000 0.00000000
## 1154 Low 0.94594595 0.05405405
## 1155 Low 1.00000000 0.00000000
## 1157 Low 0.95945946 0.04054054
## 1162 Low 0.97478992 0.02521008
## 1164 Low 1.00000000 0.00000000
## 1171 Low 0.95945946 0.04054054
## 1172 Low 0.94594595 0.05405405
## 1175 Low 0.95945946 0.04054054
## 1177 Low 0.94736842 0.05263158
## 1179 Low 0.96666667 0.03333333
## 1183 Low 1.00000000 0.00000000
## 1185 Low 0.95945946 0.04054054
## 1189 Low 0.95945946 0.04054054
## 1211 Low 0.97478992 0.02521008
## 1218 Low 0.47058824 0.52941176
## 1224 Low 1.00000000 0.00000000
## 1225 Low 1.00000000 0.00000000
## 1227 Low 0.95945946 0.04054054
## 1232 Low 0.95945946 0.04054054
## 1235 Low 0.46153846 0.53846154
## 1238 Low 0.95945946 0.04054054
## 1240 Low 0.96666667 0.03333333
## 1241 Low 0.97478992 0.02521008
## 1248 Low 0.97478992 0.02521008
## 1258 Low 0.94594595 0.05405405
## 1261 Low 0.97478992 0.02521008
## 1263 Low 0.97478992 0.02521008
## 1269 Low 0.96666667 0.03333333
## 1270 Low 0.86111111 0.13888889
## 1271 Low 0.97478992 0.02521008
## 1272 Low 0.97478992 0.02521008
## 1280 Low 0.97478992 0.02521008
## 1286 Low 0.97478992 0.02521008
## 1287 Low 0.97478992 0.02521008
## 1289 Low 0.97478992 0.02521008
## 1290 Low 0.97478992 0.02521008
## 1291 High 0.01933702 0.98066298
## 1294 High 0.11904762 0.88095238
## 1305 Low 0.95945946 0.04054054
## 1308 High 0.95945946 0.04054054##################################
# Reporting the independent evaluation results
# for the test set
##################################
CART_Test_ROC <- roc(response = CART_Test$CART_Observed,
predictor = CART_Test$CART_Predicted.High,
levels = rev(levels(CART_Test$CART_Observed)))
(CART_Test_ROCCurveAUC <- auc(CART_Test_ROC)[1])## [1] 0.94522821.5.12 Conditional Inference Trees (CTREE)
[A] The conditional inference trees model from the party package was implemented through the caret package.
[B] The model contains 1 hyperparameter:
[B.1] mincriterion = 1-p-value threshold made to vary across a range of values equal to 0.75 to 0.99
[C] The cross-validated model performance of the final model is summarized as follows:
[C.1] Final model configuration involves mincriterion=0.95
[C.2] ROC Curve AUC = 0.90967
[D] The model allows for ranking of predictors in terms of variable importance. The top-performing predictors in the model are as follows:
[D.1] MolWeight variable (numeric)
[D.2] NumCarbon variable (numeric)
[D.3] NumBonds variable (numeric)
[D.4] NumRings variable (numeric)
[D.5] NumMultBonds variable (numeric)
[E] The independent test model performance of the final model is summarized as follows:
[E.1] ROC Curve AUC = 0.89647
##################################
# Creating a local object
# for the train and test sets
##################################
PMA_PreModelling_Train_CTREE <- PMA_PreModelling_Train
PMA_PreModelling_Test_CTREE <- PMA_PreModelling_Test
##################################
# Creating consistent fold assignments
# for the 10-Fold Cross Validation process
##################################
set.seed(12345678)
KFold_Indices <- createFolds(PMA_PreModelling_Train_CTREE$Log_Solubility_Class,
k = 10,
returnTrain=TRUE)
KFold_Control <- trainControl(method="cv",
index=KFold_Indices,
summaryFunction = twoClassSummary,
classProbs = TRUE)
##################################
# Setting the conditions
# for hyperparameter tuning
##################################
CTREE_Grid = data.frame(mincriterion = sort(c(0.95, seq(0.75, 0.99, length = 2))))
##################################
# Running the conditional inference trees model
# by setting the caret method to 'ctree'
##################################
set.seed(12345678)
CTREE_Tune <- train(x = PMA_PreModelling_Train_CTREE[,!names(PMA_PreModelling_Train_CTREE) %in% c("Log_Solubility_Class")],
y = PMA_PreModelling_Train_CTREE$Log_Solubility_Class,
method = "ctree",
tuneGrid = CTREE_Grid,
metric = "ROC",
trControl = KFold_Control)
##################################
# Reporting the cross-validation results
# for the train set
##################################
CTREE_Tune## Conditional Inference Tree
##
## 951 samples
## 220 predictors
## 2 classes: 'Low', 'High'
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 857, 855, 857, 855, 856, 856, ...
## Resampling results across tuning parameters:
##
## mincriterion ROC Sens Spec
## 0.75 0.9074458 0.8639535 0.8357402
## 0.95 0.9096727 0.8780731 0.8168723
## 0.99 0.9040982 0.8993909 0.7977866
##
## ROC was used to select the optimal model using the largest value.
## The final value used for the model was mincriterion = 0.95.CTREE_Tune$finalModel##
## Conditional inference tree with 18 terminal nodes
##
## Response: .outcome
## Inputs: FP001, FP002, FP003, FP004, FP005, FP006, FP007, FP008, FP009, FP010, FP011, FP012, FP013, FP014, FP015, FP016, FP017, FP018, FP019, FP020, FP021, FP022, FP023, FP024, FP025, FP026, FP027, FP028, FP029, FP030, FP031, FP032, FP033, FP034, FP035, FP036, FP037, FP038, FP039, FP040, FP041, FP042, FP043, FP044, FP045, FP046, FP047, FP048, FP049, FP050, FP051, FP052, FP053, FP054, FP055, FP056, FP057, FP058, FP059, FP060, FP061, FP062, FP063, FP064, FP065, FP066, FP067, FP068, FP069, FP070, FP071, FP072, FP073, FP074, FP075, FP076, FP077, FP078, FP079, FP080, FP081, FP082, FP083, FP084, FP085, FP086, FP087, FP088, FP089, FP090, FP091, FP092, FP093, FP094, FP095, FP096, FP097, FP098, FP099, FP100, FP101, FP102, FP103, FP104, FP105, FP106, FP107, FP108, FP109, FP110, FP111, FP112, FP113, FP114, FP115, FP116, FP117, FP118, FP119, FP120, FP121, FP122, FP123, FP124, FP125, FP126, FP127, FP128, FP129, FP130, FP131, FP132, FP133, FP134, FP135, FP136, FP137, FP138, FP139, FP140, FP141, FP142, FP143, FP144, FP145, FP146, FP147, FP148, FP149, FP150, FP151, FP152, FP153, FP155, FP156, FP157, FP158, FP159, FP160, FP161, FP162, FP163, FP164, FP165, FP166, FP167, FP168, FP169, FP170, FP171, FP172, FP173, FP174, FP175, FP176, FP177, FP178, FP179, FP180, FP181, FP182, FP183, FP184, FP185, FP186, FP187, FP188, FP189, FP190, FP191, FP192, FP193, FP194, FP195, FP196, FP197, FP198, FP201, FP202, FP203, FP204, FP205, FP206, FP207, FP208, MolWeight, NumBonds, NumMultBonds, NumRotBonds, NumDblBonds, NumCarbon, NumNitrogen, NumOxygen, NumSulfer, NumChlorine, NumHalogen, NumRings, HydrophilicFactor, SurfaceArea1, SurfaceArea2
## Number of observations: 951
##
## 1) MolWeight <= 0.2222905; criterion = 1, statistic = 322.106
## 2) FP072 == {0}; criterion = 1, statistic = 98.274
## 3) NumCarbon <= -0.4425175; criterion = 1, statistic = 60.278
## 4) FP172 == {0}; criterion = 1, statistic = 25.438
## 5) FP050 == {1}; criterion = 1, statistic = 30.749
## 6)* weights = 19
## 5) FP050 == {0}
## 7)* weights = 103
## 4) FP172 == {1}
## 8)* weights = 12
## 3) NumCarbon > -0.4425175
## 9) NumNitrogen <= -0.685246; criterion = 1, statistic = 34.514
## 10)* weights = 45
## 9) NumNitrogen > -0.685246
## 11)* weights = 29
## 2) FP072 == {1}
## 12) FP059 == {0}; criterion = 1, statistic = 78.968
## 13) NumCarbon <= 0.1817764; criterion = 1, statistic = 25.002
## 14)* weights = 302
## 13) NumCarbon > 0.1817764
## 15)* weights = 10
## 12) FP059 == {1}
## 16)* weights = 22
## 1) MolWeight > 0.2222905
## 17) FP075 == {0}; criterion = 1, statistic = 40.657
## 18) FP171 == {1}; criterion = 0.998, statistic = 19.88
## 19) NumCarbon <= 0.3642386; criterion = 0.995, statistic = 17.87
## 20)* weights = 11
## 19) NumCarbon > 0.3642386
## 21)* weights = 24
## 18) FP171 == {0}
## 22) FP025 == {1}; criterion = 1, statistic = 31.349
## 23)* weights = 26
## 22) FP025 == {0}
## 24) FP126 == {1}; criterion = 0.994, statistic = 23.836
## 25)* weights = 10
## 24) FP126 == {0}
## 26) FP055 == {1}; criterion = 0.99, statistic = 16.625
## 27)* weights = 8
## 26) FP055 == {0}
## 28)* weights = 133
## 17) FP075 == {1}
## 29) FP061 == {0}; criterion = 0.996, statistic = 18.375
## 30)* weights = 47
## 29) FP061 == {1}
## 31) MolWeight <= 0.6620108; criterion = 0.996, statistic = 18.221
## 32)* weights = 38
## 31) MolWeight > 0.6620108
## 33) FP198 == {0}; criterion = 0.997, statistic = 18.785
## 34)* weights = 104
## 33) FP198 == {1}
## 35)* weights = 8CTREE_Tune$results## mincriterion ROC Sens Spec ROCSD SensSD SpecSD
## 1 0.75 0.9074458 0.8639535 0.8357402 0.01513588 0.07335027 0.05733407
## 2 0.95 0.9096727 0.8780731 0.8168723 0.01486612 0.07203564 0.06543021
## 3 0.99 0.9040982 0.8993909 0.7977866 0.01746151 0.03982612 0.05232463(CTREE_Train_ROCCurveAUC <- CTREE_Tune$results[CTREE_Tune$results$mincriterion==CTREE_Tune$bestTune$mincriterion,
c("ROC")])## [1] 0.9096727##################################
# Identifying and plotting the
# best model predictors
##################################
CTREE_VarImp <- varImp(CTREE_Tune, scale = TRUE)
plot(CTREE_VarImp,
top=25,
scales=list(y=list(cex = .95)),
main="Ranked Variable Importance : Conditional Inference Trees",
xlab="Scaled Variable Importance Metrics",
ylab="Predictors",
cex=2,
origin=0,
alpha=0.45)
##################################
# Independently evaluating the model
# on the test set
##################################
CTREE_Test <- data.frame(CTREE_Observed = PMA_PreModelling_Test_CTREE$Log_Solubility_Class,
CTREE_Predicted = predict(CTREE_Tune,
PMA_PreModelling_Test_CTREE[,!names(PMA_PreModelling_Test_CTREE) %in% c("Log_Solubility_Class")],
type = "prob"))
CTREE_Test## CTREE_Observed CTREE_Predicted.Low CTREE_Predicted.High
## 1 High 0.01986755 0.98013245
## 2 High 0.01986755 0.98013245
## 3 High 0.01986755 0.98013245
## 4 High 0.09708738 0.90291262
## 5 High 0.01986755 0.98013245
## 6 High 0.01986755 0.98013245
## 7 High 0.01986755 0.98013245
## 8 High 0.01986755 0.98013245
## 9 High 0.01986755 0.98013245
## 10 High 0.09708738 0.90291262
## 11 High 0.09708738 0.90291262
## 12 High 0.60000000 0.40000000
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## 14 High 0.01986755 0.98013245
## 15 High 0.09708738 0.90291262
## 16 High 0.09708738 0.90291262
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## 19 High 0.01986755 0.98013245
## 20 High 0.09708738 0.90291262
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## 23 High 0.01986755 0.98013245
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## 25 High 0.01986755 0.98013245
## 26 High 0.09708738 0.90291262
## 27 High 0.54545455 0.45454545
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## 35 High 0.01986755 0.98013245
## 36 High 0.01986755 0.98013245
## 37 High 0.01986755 0.98013245
## 38 High 0.01986755 0.98013245
## 39 High 0.01986755 0.98013245
## 40 High 0.01986755 0.98013245
## 41 High 0.01986755 0.98013245
## 42 High 0.83333333 0.16666667
## 43 High 0.01986755 0.98013245
## 44 High 0.01986755 0.98013245
## 45 High 0.01986755 0.98013245
## 46 High 0.09708738 0.90291262
## 47 High 0.01986755 0.98013245
## 48 High 0.01986755 0.98013245
## 49 High 0.09708738 0.90291262
## 50 High 0.01986755 0.98013245
## 51 High 0.01986755 0.98013245
## 52 High 0.09708738 0.90291262
## 53 High 0.01986755 0.98013245
## 54 High 0.01986755 0.98013245
## 55 High 0.01986755 0.98013245
## 56 High 0.01986755 0.98013245
## 57 High 0.09708738 0.90291262
## 58 High 0.01986755 0.98013245
## 59 High 0.01986755 0.98013245
## 60 High 0.41379310 0.58620690
## 61 High 0.01986755 0.98013245
## 62 High 0.09708738 0.90291262
## 63 High 0.01986755 0.98013245
## 64 High 0.01986755 0.98013245
## 65 High 0.01986755 0.98013245
## 66 High 0.89361702 0.10638298
## 67 High 0.60000000 0.40000000
## 68 High 0.01986755 0.98013245
## 69 High 0.01986755 0.98013245
## 70 High 0.01986755 0.98013245
## 71 High 0.89361702 0.10638298
## 72 High 0.13157895 0.86842105
## 73 High 0.54545455 0.45454545
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## 75 High 0.41379310 0.58620690
## 76 High 0.09090909 0.90909091
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## 79 High 0.01986755 0.98013245
## 80 High 1.00000000 0.00000000
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## 83 High 0.54545455 0.45454545
## 84 High 0.01986755 0.98013245
## 85 High 0.41379310 0.58620690
## 86 High 0.01986755 0.98013245
## 87 High 0.41379310 0.58620690
## 88 High 0.60000000 0.40000000
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## 90 High 0.54545455 0.45454545
## 91 High 0.01986755 0.98013245
## 92 High 0.60000000 0.40000000
## 93 High 0.01986755 0.98013245
## 94 High 0.01986755 0.98013245
## 95 High 0.09708738 0.90291262
## 96 High 0.01986755 0.98013245
## 97 High 0.09708738 0.90291262
## 98 High 0.89361702 0.10638298
## 99 High 0.01986755 0.98013245
## 100 High 0.09708738 0.90291262
## 101 High 0.09708738 0.90291262
## 102 High 0.01986755 0.98013245
## 103 High 0.41379310 0.58620690
## 104 High 0.01986755 0.98013245
## 105 High 0.63157895 0.36842105
## 106 High 0.89361702 0.10638298
## 107 High 0.83333333 0.16666667
## 108 High 0.41379310 0.58620690
## 109 High 0.74038462 0.25961538
## 110 High 0.74038462 0.25961538
## 111 High 0.13157895 0.86842105
## 112 High 0.01986755 0.98013245
## 113 High 0.13157895 0.86842105
## 114 High 0.74038462 0.25961538
## 115 High 0.74038462 0.25961538
## 116 High 0.89361702 0.10638298
## 117 High 0.89361702 0.10638298
## 118 High 0.69230769 0.30769231
## 119 Low 1.00000000 0.00000000
## 120 Low 0.74038462 0.25961538
## 121 Low 0.89361702 0.10638298
## 122 Low 0.01986755 0.98013245
## 123 Low 0.87500000 0.12500000
## 124 Low 0.09708738 0.90291262
## 125 Low 0.89361702 0.10638298
## 126 Low 0.89361702 0.10638298
## 127 Low 0.63157895 0.36842105
## 128 Low 0.89361702 0.10638298
## 129 Low 0.63157895 0.36842105
## 130 Low 1.00000000 0.00000000
## 131 Low 0.41379310 0.58620690
## 132 Low 0.74038462 0.25961538
## 133 Low 0.74038462 0.25961538
## 134 Low 0.89361702 0.10638298
## 135 Low 1.00000000 0.00000000
## 136 Low 1.00000000 0.00000000
## 137 Low 0.69230769 0.30769231
## 138 Low 0.41379310 0.58620690
## 139 Low 0.63157895 0.36842105
## 140 Low 0.01986755 0.98013245
## 141 Low 1.00000000 0.00000000
## 142 Low 0.69230769 0.30769231
## 143 Low 1.00000000 0.00000000
## 144 Low 0.89361702 0.10638298
## 145 Low 0.60000000 0.40000000
## 146 Low 0.41379310 0.58620690
## 147 Low 0.74038462 0.25961538
## 148 Low 1.00000000 0.00000000
## 149 Low 0.54545455 0.45454545
## 150 Low 0.83333333 0.16666667
## 151 Low 0.00000000 1.00000000
## 152 Low 0.74038462 0.25961538
## 153 Low 0.09708738 0.90291262
## 154 Low 0.41379310 0.58620690
## 155 Low 1.00000000 0.00000000
## 156 Low 0.09090909 0.90909091
## 157 Low 0.41379310 0.58620690
## 158 Low 0.74038462 0.25961538
## 159 Low 0.63157895 0.36842105
## 160 Low 0.87500000 0.12500000
## 161 Low 0.41379310 0.58620690
## 162 Low 0.87500000 0.12500000
## 163 Low 0.89361702 0.10638298
## 164 Low 1.00000000 0.00000000
## 165 Low 0.80000000 0.20000000
## 166 Low 0.41379310 0.58620690
## 167 Low 0.89361702 0.10638298
## 168 Low 0.74038462 0.25961538
## 169 Low 0.41379310 0.58620690
## 170 Low 1.00000000 0.00000000
## 171 Low 0.74038462 0.25961538
## 172 Low 0.41379310 0.58620690
## 173 Low 1.00000000 0.00000000
## 174 Low 0.69230769 0.30769231
## 175 Low 1.00000000 0.00000000
## 176 Low 1.00000000 0.00000000
## 177 Low 0.74038462 0.25961538
## 178 Low 1.00000000 0.00000000
## 179 Low 1.00000000 0.00000000
## 180 Low 0.41379310 0.58620690
## 181 Low 1.00000000 0.00000000
## 182 Low 0.60000000 0.40000000
## 183 Low 0.41379310 0.58620690
## 184 Low 1.00000000 0.00000000
## 185 Low 1.00000000 0.00000000
## 186 Low 0.89361702 0.10638298
## 187 Low 0.87500000 0.12500000
## 188 Low 1.00000000 0.00000000
## 189 Low 1.00000000 0.00000000
## 190 Low 0.41379310 0.58620690
## 191 Low 0.87500000 0.12500000
## 192 Low 0.60000000 0.40000000
## 193 Low 1.00000000 0.00000000
## 194 Low 1.00000000 0.00000000
## 195 Low 1.00000000 0.00000000
## 196 Low 1.00000000 0.00000000
## 197 Low 1.00000000 0.00000000
## 198 Low 1.00000000 0.00000000
## 199 Low 1.00000000 0.00000000
## 200 Low 0.74038462 0.25961538
## 201 Low 1.00000000 0.00000000
## 202 Low 1.00000000 0.00000000
## 203 Low 1.00000000 0.00000000
## 204 Low 1.00000000 0.00000000
## 205 Low 0.41379310 0.58620690
## 206 Low 1.00000000 0.00000000
## 207 Low 0.74038462 0.25961538
## 208 Low 0.41379310 0.58620690
## 209 Low 1.00000000 0.00000000
## 210 Low 0.95833333 0.04166667
## 211 Low 1.00000000 0.00000000
## 212 Low 1.00000000 0.00000000
## 213 Low 1.00000000 0.00000000
## 214 Low 1.00000000 0.00000000
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## 216 Low 1.00000000 0.00000000
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## 218 High 0.01986755 0.98013245
## 219 High 0.09708738 0.90291262
## 220 High 0.01986755 0.98013245
## 221 High 0.01986755 0.98013245
## 222 High 0.01986755 0.98013245
## 223 High 0.01986755 0.98013245
## 224 High 0.01986755 0.98013245
## 225 High 0.80000000 0.20000000
## 226 High 0.09708738 0.90291262
## 227 High 0.01986755 0.98013245
## 228 High 0.01986755 0.98013245
## 229 High 0.01986755 0.98013245
## 230 High 0.01986755 0.98013245
## 231 High 0.63157895 0.36842105
## 232 High 0.01986755 0.98013245
## 233 High 0.01986755 0.98013245
## 234 High 0.09708738 0.90291262
## 235 High 0.09708738 0.90291262
## 236 High 0.01986755 0.98013245
## 237 High 0.89361702 0.10638298
## 238 High 0.01986755 0.98013245
## 239 High 0.01986755 0.98013245
## 240 High 0.01986755 0.98013245
## 241 High 0.01986755 0.98013245
## 242 High 0.09708738 0.90291262
## 243 High 0.09708738 0.90291262
## 244 High 0.09708738 0.90291262
## 245 High 0.83333333 0.16666667
## 246 High 0.01986755 0.98013245
## 247 High 0.09708738 0.90291262
## 248 High 0.01986755 0.98013245
## 249 High 0.01986755 0.98013245
## 250 High 0.41379310 0.58620690
## 251 High 0.13157895 0.86842105
## 252 High 0.01986755 0.98013245
## 253 High 0.13157895 0.86842105
## 254 High 0.41379310 0.58620690
## 255 High 0.01986755 0.98013245
## 256 High 0.09708738 0.90291262
## 257 High 0.74038462 0.25961538
## 258 High 0.13157895 0.86842105
## 259 High 0.09708738 0.90291262
## 260 High 0.09708738 0.90291262
## 261 High 0.01986755 0.98013245
## 262 High 0.60000000 0.40000000
## 263 High 0.09708738 0.90291262
## 264 High 0.60000000 0.40000000
## 265 High 0.89361702 0.10638298
## 266 High 0.13157895 0.86842105
## 267 High 0.60000000 0.40000000
## 268 High 0.13157895 0.86842105
## 269 Low 0.41379310 0.58620690
## 270 Low 0.87500000 0.12500000
## 271 Low 0.41379310 0.58620690
## 272 Low 0.41379310 0.58620690
## 273 Low 0.74038462 0.25961538
## 274 Low 0.60000000 0.40000000
## 275 Low 0.95833333 0.04166667
## 276 Low 0.83333333 0.16666667
## 277 Low 1.00000000 0.00000000
## 278 Low 0.89361702 0.10638298
## 279 Low 1.00000000 0.00000000
## 280 Low 0.41379310 0.58620690
## 281 Low 0.09708738 0.90291262
## 282 Low 1.00000000 0.00000000
## 283 Low 1.00000000 0.00000000
## 284 Low 0.69230769 0.30769231
## 285 Low 0.54545455 0.45454545
## 286 Low 0.74038462 0.25961538
## 287 Low 0.63157895 0.36842105
## 288 Low 0.95833333 0.04166667
## 289 Low 0.95833333 0.04166667
## 290 Low 0.41379310 0.58620690
## 291 Low 0.74038462 0.25961538
## 292 Low 0.83333333 0.16666667
## 293 Low 0.41379310 0.58620690
## 294 Low 0.95833333 0.04166667
## 295 Low 1.00000000 0.00000000
## 296 Low 1.00000000 0.00000000
## 297 Low 0.87500000 0.12500000
## 298 Low 0.74038462 0.25961538
## 299 Low 0.41379310 0.58620690
## 300 Low 0.41379310 0.58620690
## 301 Low 0.74038462 0.25961538
## 302 Low 1.00000000 0.00000000
## 303 Low 1.00000000 0.00000000
## 304 Low 0.74038462 0.25961538
## 305 Low 0.74038462 0.25961538
## 306 Low 1.00000000 0.00000000
## 307 Low 1.00000000 0.00000000
## 308 Low 1.00000000 0.00000000
## 309 Low 1.00000000 0.00000000
## 310 Low 1.00000000 0.00000000
## 311 Low 1.00000000 0.00000000
## 312 Low 1.00000000 0.00000000
## 313 High 0.01986755 0.98013245
## 314 High 0.60000000 0.40000000
## 315 Low 0.87500000 0.12500000
## 316 High 0.95833333 0.04166667##################################
# Reporting the independent evaluation results
# for the test set
##################################
CTREE_Test_ROC <- roc(response = CTREE_Test$CTREE_Observed,
predictor = CTREE_Test$CTREE_Predicted.High,
levels = rev(levels(CTREE_Test$CTREE_Observed)))
(CTREE_Test_ROCCurveAUC <- auc(CTREE_Test_ROC)[1])## [1] 0.89647921.5.13 C5.0 Decision Trees (C50)
[A] The C5.0 decision trees model from the C50 and plyr packages was implemented through the caret package.
[B] The model contains 3 hyperparameters:
[B.1] trials = number of boosting iterations made to vary across a range of values equal to 1 to 100
[B.2] model = model type made to vary across a range of levels equal to TREE and RULES
[B.3] winnow = winnow made to vary across a range of levels equal to TRUE and FALSE
[C] The cross-validated model performance of the final model is summarized as follows:
[C.1] Final model configuration involves trials=40, method=RULES and winnow=FALSE
[C.2] ROC Curve AUC = 0.96540
[D] The model allows for ranking of predictors in terms of variable importance. The top-performing predictors in the model are as follows:
[D.1] NumBonds variable (numeric)
[D.2] HydrophilicFactor variable (numeric)
[D.3] NumCarbon variable (numeric)
[D.4] Molweight variable (numeric)
[D.5] FP197 variable (factor)
[E] The independent test model performance of the final model is summarized as follows:
[E.1] ROC Curve AUC = 0.97635
##################################
# Creating a local object
# for the train and test sets
##################################
PMA_PreModelling_Train_C50 <- PMA_PreModelling_Train
PMA_PreModelling_Test_C50 <- PMA_PreModelling_Test
##################################
# Creating consistent fold assignments
# for the 10-Fold Cross Validation process
##################################
set.seed(12345678)
KFold_Indices <- createFolds(PMA_PreModelling_Train_C50$Log_Solubility_Class,
k = 10,
returnTrain=TRUE)
KFold_Control <- trainControl(method="cv",
index=KFold_Indices,
summaryFunction = twoClassSummary,
classProbs = TRUE)
##################################
# Setting the conditions
# for hyperparameter tuning
##################################
C50_Grid = expand.grid(trials = c(1:9, (1:10)*10),
model = c("tree", "rules"),
winnow = c(TRUE, FALSE))
##################################
# Running the C5.0 decision trees model
# by setting the caret method to 'C5.0'
##################################
set.seed(12345678)
C50_Tune <- train(x = PMA_PreModelling_Train_C50[,!names(PMA_PreModelling_Train_C50) %in% c("Log_Solubility_Class")],
y = PMA_PreModelling_Train_C50$Log_Solubility_Class,
method = "C5.0",
tuneGrid = C50_Grid,
metric = "ROC",
trControl = KFold_Control)
##################################
# Reporting the cross-validation results
# for the train set
##################################
C50_Tune## C5.0
##
## 951 samples
## 220 predictors
## 2 classes: 'Low', 'High'
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 857, 855, 857, 855, 856, 856, ...
## Resampling results across tuning parameters:
##
## model winnow trials ROC Sens Spec
## rules FALSE 1 0.8754712 0.8523256 0.8663280
## rules FALSE 2 0.9139992 0.8802326 0.8586357
## rules FALSE 3 0.9312186 0.8497785 0.8817852
## rules FALSE 4 0.9418542 0.8803987 0.8645138
## rules FALSE 5 0.9495156 0.8756368 0.8760160
## rules FALSE 6 0.9545297 0.9013843 0.8721335
## rules FALSE 7 0.9540497 0.8942414 0.8702830
## rules FALSE 8 0.9556435 0.9176633 0.8702467
## rules FALSE 9 0.9545048 0.9128461 0.8721698
## rules FALSE 10 0.9553917 0.9011074 0.8740566
## rules FALSE 20 0.9627843 0.9059801 0.8837083
## rules FALSE 30 0.9642571 0.9082503 0.8799347
## rules FALSE 40 0.9654007 0.9155039 0.8837808
## rules FALSE 50 0.9645413 0.9153931 0.8799710
## rules FALSE 60 0.9638177 0.9083610 0.8837808
## rules FALSE 70 0.9640453 0.9083056 0.8799347
## rules FALSE 80 0.9635541 0.9153378 0.8799347
## rules FALSE 90 0.9642681 0.9200997 0.8799347
## rules FALSE 100 0.9634606 0.9200997 0.8799347
## rules TRUE 1 0.8925361 0.8569214 0.8912554
## rules TRUE 2 0.9101197 0.8546512 0.8645864
## rules TRUE 3 0.9273596 0.8497231 0.8875181
## rules TRUE 4 0.9358808 0.8781285 0.8799710
## rules TRUE 5 0.9428694 0.8827796 0.8912917
## rules TRUE 6 0.9440485 0.8803433 0.8779753
## rules TRUE 7 0.9466928 0.8803433 0.8799347
## rules TRUE 8 0.9498695 0.8921373 0.8894412
## rules TRUE 9 0.9506061 0.8850498 0.8837083
## rules TRUE 10 0.9528304 0.8827243 0.8799347
## rules TRUE 20 0.9609361 0.8898117 0.8818578
## rules TRUE 30 0.9613386 0.8898671 0.8894775
## rules TRUE 40 0.9617762 0.8945183 0.8875544
## rules TRUE 50 0.9610015 0.8921927 0.8913643
## rules TRUE 60 0.9604662 0.8945736 0.8875181
## rules TRUE 70 0.9610535 0.8899225 0.8856313
## rules TRUE 80 0.9615022 0.8852159 0.8875544
## rules TRUE 90 0.9608758 0.8898671 0.8837446
## rules TRUE 100 0.9606082 0.8921927 0.8818215
## tree FALSE 1 0.9251507 0.8590255 0.8644775
## tree FALSE 2 0.9242512 0.8382614 0.8816401
## tree FALSE 3 0.9375375 0.8686600 0.8817126
## tree FALSE 4 0.9466693 0.8684939 0.8873367
## tree FALSE 5 0.9505678 0.8826689 0.8816038
## tree FALSE 6 0.9514910 0.8991141 0.8759071
## tree FALSE 7 0.9533817 0.8944075 0.8855225
## tree FALSE 8 0.9527229 0.8896456 0.8760160
## tree FALSE 9 0.9539725 0.8733112 0.8855588
## tree FALSE 10 0.9546979 0.8920266 0.8817489
## tree FALSE 20 0.9591829 0.8897564 0.8970972
## tree FALSE 30 0.9611743 0.8967331 0.8989840
## tree FALSE 40 0.9609107 0.8967885 0.8914006
## tree FALSE 50 0.9629556 0.8944629 0.8952104
## tree FALSE 60 0.9620595 0.8944075 0.8932874
## tree FALSE 70 0.9628225 0.8991141 0.8971335
## tree FALSE 80 0.9627740 0.8873754 0.8971335
## tree FALSE 90 0.9635952 0.8897010 0.8933237
## tree FALSE 100 0.9631377 0.8873200 0.8933237
## tree TRUE 1 0.9282666 0.8379845 0.8665094
## tree TRUE 2 0.9102836 0.8359911 0.8951016
## tree TRUE 3 0.9277501 0.8544297 0.8856313
## tree TRUE 4 0.9364175 0.8522702 0.8894412
## tree TRUE 5 0.9426873 0.8595238 0.8894049
## tree TRUE 6 0.9476441 0.8568660 0.9027576
## tree TRUE 7 0.9503419 0.8593023 0.8836357
## tree TRUE 8 0.9532930 0.8686047 0.8914006
## tree TRUE 9 0.9534653 0.8756921 0.8875907
## tree TRUE 10 0.9533833 0.8593023 0.8952467
## tree TRUE 20 0.9564897 0.8734773 0.8895138
## tree TRUE 30 0.9586314 0.8759136 0.8876270
## tree TRUE 40 0.9597348 0.8759136 0.8856676
## tree TRUE 50 0.9607841 0.8781838 0.8837808
## tree TRUE 60 0.9599619 0.8782946 0.8876270
## tree TRUE 70 0.9598905 0.8875969 0.8876270
## tree TRUE 80 0.9594845 0.8829457 0.8876270
## tree TRUE 90 0.9597357 0.8829457 0.8914369
## tree TRUE 100 0.9595649 0.8806202 0.8914369
##
## ROC was used to select the optimal model using the largest value.
## The final values used for the model were trials = 40, model = rules and
## winnow = FALSE.C50_Tune$finalModel##
## Call:
## (function (x, y, trials = 1, rules = FALSE, weights = NULL, control
## 1.23060333905164, -0.309270049682714, -1.07920674404989,
## 2.00054003341881, 2.00054
##
## Rule-Based Model
## Number of samples: 951
## Number of predictors: 220
##
## Number of boosting iterations: 40
## Average number of rules: 24.1
##
## Non-standard options: attempt to group attributesC50_Tune$results## model winnow trials ROC Sens Spec ROCSD SensSD
## 39 rules FALSE 1 0.8754712 0.8523256 0.8663280 0.020123929 0.06921646
## 58 rules TRUE 1 0.8925361 0.8569214 0.8912554 0.028081192 0.05063962
## 1 tree FALSE 1 0.9251507 0.8590255 0.8644775 0.027267901 0.08010132
## 20 tree TRUE 1 0.9282666 0.8379845 0.8665094 0.019019183 0.06949847
## 40 rules FALSE 2 0.9139992 0.8802326 0.8586357 0.024519619 0.06104610
## 59 rules TRUE 2 0.9101197 0.8546512 0.8645864 0.019574620 0.04723783
## 2 tree FALSE 2 0.9242512 0.8382614 0.8816401 0.019890210 0.08680223
## 21 tree TRUE 2 0.9102836 0.8359911 0.8951016 0.016535669 0.06036470
## 41 rules FALSE 3 0.9312186 0.8497785 0.8817852 0.022697450 0.06209568
## 60 rules TRUE 3 0.9273596 0.8497231 0.8875181 0.022338765 0.07100797
## 3 tree FALSE 3 0.9375375 0.8686600 0.8817126 0.012717207 0.06484938
## 22 tree TRUE 3 0.9277501 0.8544297 0.8856313 0.017687438 0.05720028
## 42 rules FALSE 4 0.9418542 0.8803987 0.8645138 0.020462972 0.06749559
## 61 rules TRUE 4 0.9358808 0.8781285 0.8799710 0.021582812 0.05505165
## 4 tree FALSE 4 0.9466693 0.8684939 0.8873367 0.013042441 0.07670975
## 23 tree TRUE 4 0.9364175 0.8522702 0.8894412 0.018550163 0.04208341
## 43 rules FALSE 5 0.9495156 0.8756368 0.8760160 0.016756734 0.05804377
## 62 rules TRUE 5 0.9428694 0.8827796 0.8912917 0.024728078 0.05877042
## 5 tree FALSE 5 0.9505678 0.8826689 0.8816038 0.012228006 0.05352303
## 24 tree TRUE 5 0.9426873 0.8595238 0.8894049 0.017064601 0.04101446
## 44 rules FALSE 6 0.9545297 0.9013843 0.8721335 0.016486902 0.05439803
## 63 rules TRUE 6 0.9440485 0.8803433 0.8779753 0.020479258 0.04784632
## 6 tree FALSE 6 0.9514910 0.8991141 0.8759071 0.014782063 0.04844165
## 25 tree TRUE 6 0.9476441 0.8568660 0.9027576 0.015478762 0.04969921
## 45 rules FALSE 7 0.9540497 0.8942414 0.8702830 0.015353099 0.06616054
## 64 rules TRUE 7 0.9466928 0.8803433 0.8799347 0.018837204 0.04796721
## 7 tree FALSE 7 0.9533817 0.8944075 0.8855225 0.013925129 0.03774449
## 26 tree TRUE 7 0.9503419 0.8593023 0.8836357 0.013041675 0.03730181
## 46 rules FALSE 8 0.9556435 0.9176633 0.8702467 0.012386967 0.05410264
## 65 rules TRUE 8 0.9498695 0.8921373 0.8894412 0.017867684 0.03907638
## 8 tree FALSE 8 0.9527229 0.8896456 0.8760160 0.013035417 0.04781327
## 27 tree TRUE 8 0.9532930 0.8686047 0.8914006 0.013194317 0.04112726
## 47 rules FALSE 9 0.9545048 0.9128461 0.8721698 0.012901729 0.06448717
## 66 rules TRUE 9 0.9506061 0.8850498 0.8837083 0.017884983 0.04383931
## 9 tree FALSE 9 0.9539725 0.8733112 0.8855588 0.013237853 0.04919251
## 28 tree TRUE 9 0.9534653 0.8756921 0.8875907 0.012363399 0.03013779
## 48 rules FALSE 10 0.9553917 0.9011074 0.8740566 0.012931834 0.07000687
## 67 rules TRUE 10 0.9528304 0.8827243 0.8799347 0.018159244 0.03378669
## 10 tree FALSE 10 0.9546979 0.8920266 0.8817489 0.012619546 0.03776971
## 29 tree TRUE 10 0.9533833 0.8593023 0.8952467 0.012330017 0.03887943
## 49 rules FALSE 20 0.9627843 0.9059801 0.8837083 0.013959967 0.04911489
## 68 rules TRUE 20 0.9609361 0.8898117 0.8818578 0.013828196 0.02541040
## 11 tree FALSE 20 0.9591829 0.8897564 0.8970972 0.011906887 0.04475922
## 30 tree TRUE 20 0.9564897 0.8734773 0.8895138 0.013299528 0.04018987
## 50 rules FALSE 30 0.9642571 0.9082503 0.8799347 0.010351842 0.04997863
## 69 rules TRUE 30 0.9613386 0.8898671 0.8894775 0.011839750 0.03986066
## 12 tree FALSE 30 0.9611743 0.8967331 0.8989840 0.009945763 0.04383624
## 31 tree TRUE 30 0.9586314 0.8759136 0.8876270 0.014027718 0.04425405
## 51 rules FALSE 40 0.9654007 0.9155039 0.8837808 0.010938803 0.04200514
## 70 rules TRUE 40 0.9617762 0.8945183 0.8875544 0.012147590 0.03716347
## 13 tree FALSE 40 0.9609107 0.8967885 0.8914006 0.009378583 0.05232563
## 32 tree TRUE 40 0.9597348 0.8759136 0.8856676 0.012918611 0.03813811
## 52 rules FALSE 50 0.9645413 0.9153931 0.8799710 0.010353401 0.03796026
## 71 rules TRUE 50 0.9610015 0.8921927 0.8913643 0.010740704 0.03536434
## 14 tree FALSE 50 0.9629556 0.8944629 0.8952104 0.010039726 0.05233930
## 33 tree TRUE 50 0.9607841 0.8781838 0.8837808 0.013422075 0.03446569
## 53 rules FALSE 60 0.9638177 0.9083610 0.8837808 0.010354489 0.04701664
## 72 rules TRUE 60 0.9604662 0.8945736 0.8875181 0.011801838 0.03532497
## 15 tree FALSE 60 0.9620595 0.8944075 0.8932874 0.010122127 0.04384929
## 34 tree TRUE 60 0.9599619 0.8782946 0.8876270 0.012890401 0.03585962
## 54 rules FALSE 70 0.9640453 0.9083056 0.8799347 0.010167855 0.04723491
## 73 rules TRUE 70 0.9610535 0.8899225 0.8856313 0.011120628 0.03123194
## 16 tree FALSE 70 0.9628225 0.8991141 0.8971335 0.010213449 0.04198859
## 35 tree TRUE 70 0.9598905 0.8875969 0.8876270 0.013225333 0.03608236
## 55 rules FALSE 80 0.9635541 0.9153378 0.8799347 0.009734285 0.04269630
## 74 rules TRUE 80 0.9615022 0.8852159 0.8875544 0.011480370 0.03560627
## 17 tree FALSE 80 0.9627740 0.8873754 0.8971335 0.009982550 0.04171706
## 36 tree TRUE 80 0.9594845 0.8829457 0.8876270 0.012558967 0.03792290
## 56 rules FALSE 90 0.9642681 0.9200997 0.8799347 0.009792287 0.03437964
## 75 rules TRUE 90 0.9608758 0.8898671 0.8837446 0.012210998 0.03143162
## 18 tree FALSE 90 0.9635952 0.8897010 0.8933237 0.009251954 0.04068568
## 37 tree TRUE 90 0.9597357 0.8829457 0.8914369 0.011591678 0.03792290
## 57 rules FALSE 100 0.9634606 0.9200997 0.8799347 0.009639079 0.03437964
## 76 rules TRUE 100 0.9606082 0.8921927 0.8818215 0.012138268 0.02774701
## 19 tree FALSE 100 0.9631377 0.8873200 0.8933237 0.009237875 0.03888627
## 38 tree TRUE 100 0.9595649 0.8806202 0.8914369 0.011957611 0.03532497
## SpecSD
## 39 0.05948617
## 58 0.05492303
## 1 0.05234230
## 20 0.05226348
## 40 0.05332739
## 59 0.05280739
## 2 0.06232832
## 21 0.03268801
## 41 0.04279647
## 60 0.04957934
## 3 0.03665989
## 22 0.04100084
## 42 0.05422507
## 61 0.06085627
## 4 0.04833127
## 23 0.04086656
## 43 0.04431397
## 62 0.05179528
## 5 0.03600158
## 24 0.04560432
## 44 0.05433072
## 63 0.05257286
## 6 0.04881636
## 25 0.03162282
## 45 0.06109125
## 64 0.05683215
## 7 0.04204556
## 26 0.04357429
## 46 0.05096306
## 65 0.05064455
## 8 0.04223745
## 27 0.05045239
## 47 0.05850621
## 66 0.05354258
## 9 0.03902346
## 28 0.05075527
## 48 0.06344503
## 67 0.05225564
## 10 0.04803562
## 29 0.05052917
## 49 0.04949495
## 68 0.05268159
## 11 0.04565318
## 30 0.05030378
## 50 0.05219682
## 69 0.04962275
## 12 0.03990896
## 31 0.05305481
## 51 0.04921807
## 70 0.05181258
## 13 0.04885921
## 32 0.05139217
## 52 0.05359516
## 71 0.05148907
## 14 0.04741597
## 33 0.05169177
## 53 0.05541358
## 72 0.05344845
## 15 0.04654212
## 34 0.05317049
## 54 0.05520050
## 73 0.05066210
## 16 0.04903411
## 35 0.04745336
## 55 0.05520050
## 74 0.05178292
## 17 0.04903411
## 36 0.05317049
## 56 0.05213793
## 75 0.05255231
## 18 0.04977339
## 37 0.05130082
## 57 0.05213793
## 76 0.05128977
## 19 0.05056186
## 38 0.05130082(C50_Train_ROCCurveAUC <- C50_Tune$results[C50_Tune$results$trials==C50_Tune$bestTune$trials &
C50_Tune$results$model==C50_Tune$bestTune$model &
C50_Tune$results$winnow==C50_Tune$bestTune$winnow,
c("ROC")])## [1] 0.9654007##################################
# Identifying and plotting the
# best model predictors
##################################
C50_VarImp <- varImp(C50_Tune, scale = TRUE)
plot(C50_VarImp,
top=25,
scales=list(y=list(cex = .95)),
main="Ranked Variable Importance : C5.0 Decision Trees",
xlab="Scaled Variable Importance Metrics",
ylab="Predictors",
cex=2,
origin=0,
alpha=0.45)
##################################
# Independently evaluating the model
# on the test set
##################################
C50_Test <- data.frame(C50_Observed = PMA_PreModelling_Test_C50$Log_Solubility_Class,
C50_Predicted = predict(C50_Tune,
PMA_PreModelling_Test_C50[,!names(PMA_PreModelling_Test_C50) %in% c("Log_Solubility_Class")],
type = "prob"))
C50_Test## C50_Observed C50_Predicted.Low C50_Predicted.High
## 20 High 0.02655426 0.97344574
## 21 High 0.00000000 1.00000000
## 23 High 0.10015616 0.89984384
## 25 High 0.02061370 0.97938630
## 28 High 0.00000000 1.00000000
## 31 High 0.00000000 1.00000000
## 32 High 0.00000000 1.00000000
## 33 High 0.00000000 1.00000000
## 34 High 0.00000000 1.00000000
## 37 High 0.09558943 0.90441057
## 38 High 0.06953967 0.93046033
## 42 High 0.32696840 0.67303160
## 49 High 0.00000000 1.00000000
## 54 High 0.02063550 0.97936450
## 55 High 0.05495791 0.94504209
## 58 High 0.04087557 0.95912443
## 60 High 0.00000000 1.00000000
## 61 High 0.00000000 1.00000000
## 65 High 0.08831699 0.91168301
## 69 High 0.11449175 0.88550825
## 73 High 0.00000000 1.00000000
## 86 High 0.00000000 1.00000000
## 90 High 0.02063675 0.97936325
## 91 High 0.00000000 1.00000000
## 93 High 0.07186342 0.92813658
## 96 High 0.00000000 1.00000000
## 98 High 0.00000000 1.00000000
## 100 High 0.00000000 1.00000000
## 104 High 0.34768129 0.65231871
## 112 High 0.07305187 0.92694813
## 115 High 0.58938542 0.41061458
## 119 High 0.00000000 1.00000000
## 128 High 0.00000000 1.00000000
## 130 High 0.00000000 1.00000000
## 139 High 0.00000000 1.00000000
## 143 High 0.00000000 1.00000000
## 145 High 0.02472847 0.97527153
## 146 High 0.01574654 0.98425346
## 149 High 0.00000000 1.00000000
## 150 High 0.05367221 0.94632779
## 152 High 0.00000000 1.00000000
## 157 High 0.54137724 0.45862276
## 161 High 0.00000000 1.00000000
## 162 High 0.00000000 1.00000000
## 166 High 0.09277745 0.90722255
## 167 High 0.02411020 0.97588980
## 173 High 0.07151496 0.92848504
## 176 High 0.07198621 0.92801379
## 182 High 0.00000000 1.00000000
## 187 High 0.07308630 0.92691370
## 190 High 0.02769794 0.97230206
## 194 High 0.00000000 1.00000000
## 195 High 0.06254860 0.93745140
## 201 High 0.02767477 0.97232523
## 207 High 0.05437344 0.94562656
## 208 High 0.13798288 0.86201712
## 215 High 0.00000000 1.00000000
## 222 High 0.07513590 0.92486410
## 224 High 0.08287661 0.91712339
## 231 High 0.37372475 0.62627525
## 236 High 0.04103627 0.95896373
## 237 High 0.00000000 1.00000000
## 240 High 0.12079654 0.87920346
## 243 High 0.04061238 0.95938762
## 248 High 0.07974000 0.92026000
## 251 High 0.65865433 0.34134567
## 256 High 0.33441285 0.66558715
## 258 High 0.25863382 0.74136618
## 262 High 0.13665190 0.86334810
## 266 High 0.24532222 0.75467778
## 272 High 0.52133143 0.47866857
## 280 High 0.33335344 0.66664656
## 283 High 0.04288112 0.95711888
## 286 High 0.57234189 0.42765811
## 287 High 0.02870784 0.97129216
## 289 High 0.27147950 0.72852050
## 290 High 0.19882578 0.80117422
## 298 High 0.04486507 0.95513493
## 305 High 0.08582089 0.91417911
## 306 High 0.18447679 0.81552321
## 312 High 0.12865759 0.87134241
## 320 High 0.07140400 0.92859600
## 325 High 0.57801652 0.42198348
## 332 High 0.19367484 0.80632516
## 333 High 0.21915643 0.78084357
## 335 High 0.06819486 0.93180514
## 339 High 0.64044252 0.35955748
## 346 High 0.30029703 0.69970297
## 347 High 0.05700086 0.94299914
## 350 High 0.23904131 0.76095869
## 353 High 0.25506033 0.74493967
## 358 High 0.25410383 0.74589617
## 365 High 0.56033685 0.43966315
## 367 High 0.09239235 0.90760765
## 370 High 0.11573113 0.88426887
## 379 High 0.12238739 0.87761261
## 386 High 0.56797547 0.43202453
## 394 High 0.57974243 0.42025757
## 396 High 0.00000000 1.00000000
## 400 High 0.10428785 0.89571215
## 404 High 0.16768464 0.83231536
## 405 High 0.18722497 0.81277503
## 413 High 0.28472931 0.71527069
## 415 High 0.27545287 0.72454713
## 417 High 0.72339913 0.27660087
## 418 High 0.50995046 0.49004954
## 423 High 0.49519040 0.50480960
## 434 High 0.18027816 0.81972184
## 437 High 0.45983519 0.54016481
## 440 High 0.69802420 0.30197580
## 449 High 0.66121376 0.33878624
## 450 High 0.30891869 0.69108131
## 457 High 0.52254076 0.47745924
## 467 High 0.64614193 0.35385807
## 469 High 0.68060946 0.31939054
## 474 High 0.78376219 0.21623781
## 475 High 0.71175191 0.28824809
## 485 High 0.70769250 0.29230750
## 504 Low 0.55757690 0.44242310
## 511 Low 0.38540018 0.61459982
## 512 Low 0.63775425 0.36224575
## 517 Low 0.05347474 0.94652526
## 519 Low 0.85433291 0.14566709
## 520 Low 0.45699331 0.54300669
## 522 Low 0.86255060 0.13744940
## 527 Low 0.51996002 0.48003998
## 528 Low 0.88762875 0.11237125
## 529 Low 0.53908072 0.46091928
## 537 Low 0.76314617 0.23685383
## 540 Low 0.65609390 0.34390610
## 541 Low 0.87702545 0.12297455
## 547 Low 0.56799924 0.43200076
## 550 Low 0.80341287 0.19658713
## 555 Low 0.65177670 0.34822330
## 564 Low 0.59098769 0.40901231
## 570 Low 0.84818688 0.15181312
## 573 Low 0.86078262 0.13921738
## 575 Low 0.84157433 0.15842567
## 578 Low 0.84272529 0.15727471
## 581 Low 0.38198622 0.61801378
## 585 Low 0.81829764 0.18170236
## 590 Low 0.61083106 0.38916894
## 601 Low 0.98558164 0.01441836
## 602 Low 0.60401408 0.39598592
## 607 Low 0.44669929 0.55330071
## 610 Low 0.73117479 0.26882521
## 618 Low 0.66603962 0.33396038
## 624 Low 0.89189433 0.10810567
## 626 Low 0.92868358 0.07131642
## 627 Low 0.91974261 0.08025739
## 634 Low 0.31936753 0.68063247
## 640 Low 0.88274317 0.11725683
## 642 Low 0.84819935 0.15180065
## 643 Low 0.86172115 0.13827885
## 644 Low 0.82066203 0.17933797
## 645 Low 0.71012342 0.28987658
## 646 Low 0.91867892 0.08132108
## 647 Low 0.91319466 0.08680534
## 652 Low 0.91736402 0.08263598
## 658 Low 0.89316226 0.10683774
## 659 Low 0.97215330 0.02784670
## 660 Low 0.91665130 0.08334870
## 664 Low 0.91918463 0.08081537
## 666 Low 0.81269491 0.18730509
## 667 Low 0.97275169 0.02724831
## 675 Low 0.92769201 0.07230799
## 680 Low 0.86128796 0.13871204
## 681 Low 0.81408831 0.18591169
## 687 Low 0.98493734 0.01506266
## 694 Low 0.95871131 0.04128869
## 697 Low 0.88150319 0.11849681
## 701 Low 0.82150966 0.17849034
## 705 Low 0.95821185 0.04178815
## 707 Low 0.98223904 0.01776096
## 710 Low 0.95579735 0.04420265
## 716 Low 0.94284932 0.05715068
## 719 Low 0.75669678 0.24330322
## 720 Low 0.98569627 0.01430373
## 725 Low 0.95859368 0.04140632
## 727 Low 0.87018540 0.12981460
## 730 Low 0.95202026 0.04797974
## 738 Low 0.91308664 0.08691336
## 745 Low 0.91463298 0.08536702
## 748 Low 0.98289523 0.01710477
## 751 Low 0.95857778 0.04142222
## 756 Low 0.91959620 0.08040380
## 766 Low 0.93279140 0.06720860
## 769 Low 0.93926193 0.06073807
## 783 Low 1.00000000 0.00000000
## 785 Low 0.91453805 0.08546195
## 790 Low 0.91623500 0.08376500
## 793 Low 0.78007711 0.21992289
## 795 Low 0.95861275 0.04138725
## 796 Low 0.94263940 0.05736060
## 797 Low 0.94214449 0.05785551
## 801 Low 0.91331484 0.08668516
## 811 Low 1.00000000 0.00000000
## 812 Low 0.96953762 0.03046238
## 815 Low 0.98605448 0.01394552
## 816 Low 0.84296671 0.15703329
## 817 Low 0.98229247 0.01770753
## 824 Low 1.00000000 0.00000000
## 825 Low 1.00000000 0.00000000
## 826 Low 0.98342377 0.01657623
## 830 Low 1.00000000 0.00000000
## 837 Low 1.00000000 0.00000000
## 838 Low 0.87679966 0.12320034
## 844 Low 1.00000000 0.00000000
## 845 Low 1.00000000 0.00000000
## 847 Low 0.97245007 0.02754993
## 850 Low 1.00000000 0.00000000
## 852 Low 1.00000000 0.00000000
## 853 Low 1.00000000 0.00000000
## 861 Low 1.00000000 0.00000000
## 868 Low 1.00000000 0.00000000
## 874 Low 1.00000000 0.00000000
## 879 High 0.05420092 0.94579908
## 895 High 0.02096607 0.97903393
## 899 High 0.02738544 0.97261456
## 903 High 0.02614719 0.97385281
## 917 High 0.00000000 1.00000000
## 927 High 0.07090086 0.92909914
## 929 High 0.02577611 0.97422389
## 931 High 0.16136237 0.83863763
## 933 High 0.51046449 0.48953551
## 944 High 0.06847903 0.93152097
## 947 High 0.02646615 0.97353385
## 949 High 0.15656496 0.84343504
## 953 High 0.00000000 1.00000000
## 958 High 0.09757865 0.90242135
## 961 High 0.25809291 0.74190709
## 963 High 0.10729888 0.89270112
## 964 High 0.00000000 1.00000000
## 973 High 0.01639165 0.98360835
## 976 High 0.05709965 0.94290035
## 977 High 0.10332249 0.89667751
## 980 High 0.62681849 0.37318151
## 983 High 0.16718613 0.83281387
## 984 High 0.06254860 0.93745140
## 986 High 0.05263976 0.94736024
## 989 High 0.04912551 0.95087449
## 991 High 0.07013778 0.92986222
## 996 High 0.00000000 1.00000000
## 997 High 0.12023414 0.87976586
## 999 High 0.19575319 0.80424681
## 1000 High 0.11072472 0.88927528
## 1003 High 0.00000000 1.00000000
## 1008 High 0.00000000 1.00000000
## 1009 High 0.03509462 0.96490538
## 1014 High 0.27286503 0.72713497
## 1015 High 0.46790912 0.53209088
## 1040 High 0.15580504 0.84419496
## 1042 High 0.15020655 0.84979345
## 1043 High 0.53447819 0.46552181
## 1050 High 0.28582765 0.71417235
## 1052 High 0.06603163 0.93396837
## 1056 High 0.36279591 0.63720409
## 1070 High 0.31066953 0.68933047
## 1073 High 0.22259853 0.77740147
## 1074 High 0.13849911 0.86150089
## 1079 High 0.32835673 0.67164327
## 1080 High 0.40953975 0.59046025
## 1085 High 0.38582480 0.61417520
## 1087 High 0.50433378 0.49566622
## 1096 High 0.81719471 0.18280529
## 1099 High 0.32006657 0.67993343
## 1100 High 0.58225511 0.41774489
## 1102 High 0.27908234 0.72091766
## 1107 Low 0.80718189 0.19281811
## 1109 Low 0.81594540 0.18405460
## 1114 Low 0.76441806 0.23558194
## 1118 Low 0.70406518 0.29593482
## 1123 Low 0.65004534 0.34995466
## 1132 Low 0.98503092 0.01496908
## 1134 Low 0.69708338 0.30291662
## 1137 Low 0.86226992 0.13773008
## 1154 Low 0.94608462 0.05391538
## 1155 Low 0.42648387 0.57351613
## 1157 Low 0.90119806 0.09880194
## 1162 Low 0.84317290 0.15682710
## 1164 Low 0.86431708 0.13568292
## 1171 Low 0.98465297 0.01534703
## 1172 Low 0.93757842 0.06242158
## 1175 Low 0.90263208 0.09736792
## 1177 Low 1.00000000 0.00000000
## 1179 Low 0.92638055 0.07361945
## 1183 Low 0.84320955 0.15679045
## 1185 Low 0.75743165 0.24256835
## 1189 Low 0.93052040 0.06947960
## 1211 Low 0.93210858 0.06789142
## 1218 Low 0.83060734 0.16939266
## 1224 Low 0.75158852 0.24841148
## 1225 Low 0.76163588 0.23836412
## 1227 Low 0.96159929 0.03840071
## 1232 Low 0.95834118 0.04165882
## 1235 Low 0.85307109 0.14692891
## 1238 Low 0.92428798 0.07571202
## 1240 Low 0.90245364 0.09754636
## 1241 Low 0.97196344 0.02803656
## 1248 Low 1.00000000 0.00000000
## 1258 Low 0.87679966 0.12320034
## 1261 Low 1.00000000 0.00000000
## 1263 Low 0.98531864 0.01468136
## 1269 Low 0.85106195 0.14893805
## 1270 Low 0.97575850 0.02424150
## 1271 Low 1.00000000 0.00000000
## 1272 Low 1.00000000 0.00000000
## 1280 Low 1.00000000 0.00000000
## 1286 Low 0.97514152 0.02485848
## 1287 Low 0.97461916 0.02538084
## 1289 Low 1.00000000 0.00000000
## 1290 Low 1.00000000 0.00000000
## 1291 High 0.22947704 0.77052296
## 1294 High 0.35263931 0.64736069
## 1305 Low 0.88365575 0.11634425
## 1308 High 0.93307123 0.06692877##################################
# Reporting the independent evaluation results
# for the test set
##################################
C50_Test_ROC <- roc(response = C50_Test$C50_Observed,
predictor = C50_Test$C50_Predicted.High,
levels = rev(levels(C50_Test$C50_Observed)))
(C50_Test_ROCCurveAUC <- auc(C50_Test_ROC)[1])## [1] 0.97635311.5.14 Random Forest (RF)
[A] The random forest model from the randomForest package was implemented through the caret package.
[B] The model contains 1 hyperparameter:
[B.1] mtry = number of randomly selected predictors made to vary across a range of values equal to 25 to 125
[C] The cross-validated model performance of the final model is summarized as follows:
[C.1] Final model configuration involves mtry=125
[C.2] ROC Curve AUC = 0.96507
[D] The model allows for ranking of predictors in terms of variable importance. The top-performing predictors in the model are as follows:
[D.1] MolWeight variable (numeric)
[D.2] NumCarbon variable (numeric)
[D.3] HydroPhilicFactor variable (numeric)
[D.4] SurfaceArea1 variable (numeric)
[D.5] NumRotBonds variable (numeric)
[E] The independent test model performance of the final model is summarized as follows:
[E.1] ROC Curve AUC = 0.98207
##################################
# Creating a local object
# for the train and test sets
##################################
PMA_PreModelling_Train_RF <- PMA_PreModelling_Train
PMA_PreModelling_Test_RF <- PMA_PreModelling_Test
##################################
# Creating consistent fold assignments
# for the 10-Fold Cross Validation process
##################################
set.seed(12345678)
KFold_Indices <- createFolds(PMA_PreModelling_Train_RF$Log_Solubility_Class,
k = 10,
returnTrain=TRUE)
KFold_Control <- trainControl(method="cv",
index=KFold_Indices,
summaryFunction = twoClassSummary,
classProbs = TRUE)
##################################
# Setting the conditions
# for hyperparameter tuning
##################################
RF_Grid = data.frame(mtry = c(25,75,125))
##################################
# Running the random forest model
# by setting the caret method to 'rf'
##################################
set.seed(12345678)
RF_Tune <- train(x = PMA_PreModelling_Train_RF[,!names(PMA_PreModelling_Train_RF) %in% c("Log_Solubility_Class")],
y = PMA_PreModelling_Train_RF$Log_Solubility_Class,
method = "rf",
tuneGrid = RF_Grid,
metric = "ROC",
trControl = KFold_Control)
##################################
# Reporting the cross-validation results
# for the train set
##################################
RF_Tune## Random Forest
##
## 951 samples
## 220 predictors
## 2 classes: 'Low', 'High'
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 857, 855, 857, 855, 856, 856, ...
## Resampling results across tuning parameters:
##
## mtry ROC Sens Spec
## 25 0.9639193 0.9061462 0.8817852
## 75 0.9650175 0.9202104 0.8779390
## 125 0.9650737 0.9203212 0.8798621
##
## ROC was used to select the optimal model using the largest value.
## The final value used for the model was mtry = 125.RF_Tune$finalModel##
## Call:
## randomForest(x = x, y = y, mtry = param$mtry)
## Type of random forest: classification
## Number of trees: 500
## No. of variables tried at each split: 125
##
## OOB estimate of error rate: 9.99%
## Confusion matrix:
## Low High class.error
## Low 393 34 0.07962529
## High 61 463 0.11641221RF_Tune$results## mtry ROC Sens Spec ROCSD SensSD SpecSD
## 1 25 0.9639193 0.9061462 0.8817852 0.01129087 0.04705140 0.04453780
## 2 75 0.9650175 0.9202104 0.8779390 0.01109720 0.03005539 0.04320822
## 3 125 0.9650737 0.9203212 0.8798621 0.01095588 0.03843884 0.04395980(RF_Train_ROCCurveAUC <- RF_Tune$results[RF_Tune$results$mtry==RF_Tune$bestTune$mtry,
c("ROC")])## [1] 0.9650737##################################
# Identifying and plotting the
# best model predictors
##################################
RF_VarImp <- varImp(RF_Tune, scale = TRUE)
plot(RF_VarImp,
top=25,
scales=list(y=list(cex = .95)),
main="Ranked Variable Importance : Random Forest",
xlab="Scaled Variable Importance Metrics",
ylab="Predictors",
cex=2,
origin=0,
alpha=0.45)
##################################
# Independently evaluating the model
# on the test set
##################################
RF_Test <- data.frame(RF_Observed = PMA_PreModelling_Test_RF$Log_Solubility_Class,
RF_Predicted = predict(RF_Tune,
PMA_PreModelling_Test_RF[,!names(PMA_PreModelling_Test_RF) %in% c("Log_Solubility_Class")],
type = "prob"))
RF_Test## RF_Observed RF_Predicted.Low RF_Predicted.High
## 20 High 0.000 1.000
## 21 High 0.000 1.000
## 23 High 0.040 0.960
## 25 High 0.004 0.996
## 28 High 0.000 1.000
## 31 High 0.000 1.000
## 32 High 0.000 1.000
## 33 High 0.002 0.998
## 34 High 0.002 0.998
## 37 High 0.008 0.992
## 38 High 0.002 0.998
## 42 High 0.394 0.606
## 49 High 0.000 1.000
## 54 High 0.000 1.000
## 55 High 0.000 1.000
## 58 High 0.026 0.974
## 60 High 0.000 1.000
## 61 High 0.002 0.998
## 65 High 0.000 1.000
## 69 High 0.014 0.986
## 73 High 0.006 0.994
## 86 High 0.008 0.992
## 90 High 0.000 1.000
## 91 High 0.004 0.996
## 93 High 0.000 1.000
## 96 High 0.030 0.970
## 98 High 0.004 0.996
## 100 High 0.000 1.000
## 104 High 0.418 0.582
## 112 High 0.012 0.988
## 115 High 0.550 0.450
## 119 High 0.000 1.000
## 128 High 0.000 1.000
## 130 High 0.026 0.974
## 139 High 0.002 0.998
## 143 High 0.000 1.000
## 145 High 0.000 1.000
## 146 High 0.000 1.000
## 149 High 0.002 0.998
## 150 High 0.004 0.996
## 152 High 0.002 0.998
## 157 High 0.526 0.474
## 161 High 0.000 1.000
## 162 High 0.000 1.000
## 166 High 0.152 0.848
## 167 High 0.000 1.000
## 173 High 0.012 0.988
## 176 High 0.000 1.000
## 182 High 0.000 1.000
## 187 High 0.000 1.000
## 190 High 0.002 0.998
## 194 High 0.048 0.952
## 195 High 0.002 0.998
## 201 High 0.000 1.000
## 207 High 0.020 0.980
## 208 High 0.162 0.838
## 215 High 0.000 1.000
## 222 High 0.038 0.962
## 224 High 0.006 0.994
## 231 High 0.174 0.826
## 236 High 0.000 1.000
## 237 High 0.002 0.998
## 240 High 0.110 0.890
## 243 High 0.000 1.000
## 248 High 0.002 0.998
## 251 High 0.526 0.474
## 256 High 0.170 0.830
## 258 High 0.182 0.818
## 262 High 0.174 0.826
## 266 High 0.090 0.910
## 272 High 0.480 0.520
## 280 High 0.434 0.566
## 283 High 0.024 0.976
## 286 High 0.532 0.468
## 287 High 0.018 0.982
## 289 High 0.260 0.740
## 290 High 0.144 0.856
## 298 High 0.008 0.992
## 305 High 0.006 0.994
## 306 High 0.186 0.814
## 312 High 0.004 0.996
## 320 High 0.000 1.000
## 325 High 0.530 0.470
## 332 High 0.064 0.936
## 333 High 0.360 0.640
## 335 High 0.008 0.992
## 339 High 0.542 0.458
## 346 High 0.070 0.930
## 347 High 0.038 0.962
## 350 High 0.122 0.878
## 353 High 0.020 0.980
## 358 High 0.032 0.968
## 365 High 0.328 0.672
## 367 High 0.018 0.982
## 370 High 0.120 0.880
## 379 High 0.024 0.976
## 386 High 0.436 0.564
## 394 High 0.554 0.446
## 396 High 0.212 0.788
## 400 High 0.046 0.954
## 404 High 0.148 0.852
## 405 High 0.058 0.942
## 413 High 0.160 0.840
## 415 High 0.032 0.968
## 417 High 0.374 0.626
## 418 High 0.660 0.340
## 423 High 0.588 0.412
## 434 High 0.016 0.984
## 437 High 0.456 0.544
## 440 High 0.484 0.516
## 449 High 0.542 0.458
## 450 High 0.182 0.818
## 457 High 0.448 0.552
## 467 High 0.494 0.506
## 469 High 0.534 0.466
## 474 High 0.728 0.272
## 475 High 0.820 0.180
## 485 High 0.540 0.460
## 504 Low 0.616 0.384
## 511 Low 0.440 0.560
## 512 Low 0.642 0.358
## 517 Low 0.024 0.976
## 519 Low 0.748 0.252
## 520 Low 0.228 0.772
## 522 Low 0.746 0.254
## 527 Low 0.734 0.266
## 528 Low 0.994 0.006
## 529 Low 0.570 0.430
## 537 Low 0.810 0.190
## 540 Low 0.842 0.158
## 541 Low 1.000 0.000
## 547 Low 0.572 0.428
## 550 Low 0.710 0.290
## 555 Low 0.610 0.390
## 564 Low 0.512 0.488
## 570 Low 0.658 0.342
## 573 Low 0.906 0.094
## 575 Low 0.984 0.016
## 578 Low 0.912 0.088
## 581 Low 0.104 0.896
## 585 Low 0.958 0.042
## 590 Low 0.516 0.484
## 601 Low 0.894 0.106
## 602 Low 0.822 0.178
## 607 Low 0.310 0.690
## 610 Low 0.638 0.362
## 618 Low 0.726 0.274
## 624 Low 0.964 0.036
## 626 Low 0.882 0.118
## 627 Low 0.948 0.052
## 634 Low 0.346 0.654
## 640 Low 0.764 0.236
## 642 Low 0.958 0.042
## 643 Low 1.000 0.000
## 644 Low 0.868 0.132
## 645 Low 0.838 0.162
## 646 Low 0.972 0.028
## 647 Low 0.842 0.158
## 652 Low 0.906 0.094
## 658 Low 0.912 0.088
## 659 Low 0.994 0.006
## 660 Low 0.916 0.084
## 664 Low 0.878 0.122
## 666 Low 0.888 0.112
## 667 Low 0.924 0.076
## 675 Low 0.994 0.006
## 680 Low 0.908 0.092
## 681 Low 0.798 0.202
## 687 Low 0.994 0.006
## 694 Low 0.936 0.064
## 697 Low 0.918 0.082
## 701 Low 0.990 0.010
## 705 Low 0.950 0.050
## 707 Low 0.936 0.064
## 710 Low 0.990 0.010
## 716 Low 0.986 0.014
## 719 Low 0.868 0.132
## 720 Low 1.000 0.000
## 725 Low 0.986 0.014
## 727 Low 0.994 0.006
## 730 Low 0.960 0.040
## 738 Low 0.926 0.074
## 745 Low 0.984 0.016
## 748 Low 0.956 0.044
## 751 Low 0.980 0.020
## 756 Low 0.938 0.062
## 766 Low 0.922 0.078
## 769 Low 0.944 0.056
## 783 Low 1.000 0.000
## 785 Low 0.988 0.012
## 790 Low 0.898 0.102
## 793 Low 0.796 0.204
## 795 Low 0.986 0.014
## 796 Low 0.988 0.012
## 797 Low 0.900 0.100
## 801 Low 0.938 0.062
## 811 Low 0.992 0.008
## 812 Low 0.998 0.002
## 815 Low 0.982 0.018
## 816 Low 0.956 0.044
## 817 Low 0.998 0.002
## 824 Low 1.000 0.000
## 825 Low 1.000 0.000
## 826 Low 0.998 0.002
## 830 Low 1.000 0.000
## 837 Low 0.994 0.006
## 838 Low 0.954 0.046
## 844 Low 1.000 0.000
## 845 Low 0.994 0.006
## 847 Low 1.000 0.000
## 850 Low 1.000 0.000
## 852 Low 1.000 0.000
## 853 Low 1.000 0.000
## 861 Low 1.000 0.000
## 868 Low 1.000 0.000
## 874 Low 1.000 0.000
## 879 High 0.000 1.000
## 895 High 0.000 1.000
## 899 High 0.014 0.986
## 903 High 0.000 1.000
## 917 High 0.014 0.986
## 927 High 0.000 1.000
## 929 High 0.002 0.998
## 931 High 0.020 0.980
## 933 High 0.286 0.714
## 944 High 0.030 0.970
## 947 High 0.000 1.000
## 949 High 0.034 0.966
## 953 High 0.000 1.000
## 958 High 0.096 0.904
## 961 High 0.090 0.910
## 963 High 0.018 0.982
## 964 High 0.000 1.000
## 973 High 0.006 0.994
## 976 High 0.000 1.000
## 977 High 0.004 0.996
## 980 High 0.510 0.490
## 983 High 0.044 0.956
## 984 High 0.002 0.998
## 986 High 0.000 1.000
## 989 High 0.014 0.986
## 991 High 0.008 0.992
## 996 High 0.000 1.000
## 997 High 0.016 0.984
## 999 High 0.158 0.842
## 1000 High 0.004 0.996
## 1003 High 0.000 1.000
## 1008 High 0.000 1.000
## 1009 High 0.000 1.000
## 1014 High 0.144 0.856
## 1015 High 0.428 0.572
## 1040 High 0.016 0.984
## 1042 High 0.116 0.884
## 1043 High 0.394 0.606
## 1050 High 0.084 0.916
## 1052 High 0.004 0.996
## 1056 High 0.354 0.646
## 1070 High 0.172 0.828
## 1073 High 0.186 0.814
## 1074 High 0.018 0.982
## 1079 High 0.014 0.986
## 1080 High 0.262 0.738
## 1085 High 0.084 0.916
## 1087 High 0.488 0.512
## 1096 High 0.906 0.094
## 1099 High 0.196 0.804
## 1100 High 0.430 0.570
## 1102 High 0.466 0.534
## 1107 Low 0.976 0.024
## 1109 Low 0.592 0.408
## 1114 Low 0.594 0.406
## 1118 Low 0.516 0.484
## 1123 Low 0.816 0.184
## 1132 Low 0.906 0.094
## 1134 Low 0.520 0.480
## 1137 Low 0.940 0.060
## 1154 Low 0.964 0.036
## 1155 Low 0.704 0.296
## 1157 Low 0.958 0.042
## 1162 Low 0.982 0.018
## 1164 Low 0.954 0.046
## 1171 Low 0.980 0.020
## 1172 Low 0.922 0.078
## 1175 Low 0.796 0.204
## 1177 Low 0.978 0.022
## 1179 Low 0.850 0.150
## 1183 Low 0.966 0.034
## 1185 Low 0.882 0.118
## 1189 Low 0.948 0.052
## 1211 Low 0.992 0.008
## 1218 Low 0.848 0.152
## 1224 Low 0.906 0.094
## 1225 Low 0.954 0.046
## 1227 Low 0.984 0.016
## 1232 Low 0.988 0.012
## 1235 Low 0.804 0.196
## 1238 Low 0.864 0.136
## 1240 Low 0.910 0.090
## 1241 Low 0.996 0.004
## 1248 Low 1.000 0.000
## 1258 Low 0.954 0.046
## 1261 Low 0.976 0.024
## 1263 Low 0.998 0.002
## 1269 Low 0.952 0.048
## 1270 Low 0.908 0.092
## 1271 Low 1.000 0.000
## 1272 Low 1.000 0.000
## 1280 Low 1.000 0.000
## 1286 Low 0.996 0.004
## 1287 Low 0.984 0.016
## 1289 Low 1.000 0.000
## 1290 Low 1.000 0.000
## 1291 High 0.024 0.976
## 1294 High 0.462 0.538
## 1305 Low 0.874 0.126
## 1308 High 0.792 0.208##################################
# Reporting the independent evaluation results
# for the test set
##################################
RF_Test_ROC <- roc(response = RF_Test$RF_Observed,
predictor = RF_Test$RF_Predicted.High,
levels = rev(levels(RF_Test$RF_Observed)))
(RF_Test_ROCCurveAUC <- auc(RF_Test_ROC)[1])## [1] 0.98207281.5.15 Bagged Trees (BTREE)
[A] The bagged trees model from the ipred, plyr and e1071 packages was implemented through the caret package.
[B] The model does not contain any hyperparameter.
[C] The cross-validated model performance of the final model is summarized as follows:
[C.1] Final model configuration is fixed due to the absence of a hyperparameter
[C.2] ROC Curve AUC = 0.95881
[D] The model allows for ranking of predictors in terms of variable importance. The top-performing predictors in the model are as follows:
[D.1] MolWeight variable (numeric)
[D.2] NumCarbon variable (numeric)
[D.3] NumBonds variable (numeric)
[D.4] HydrophilicFactor variable (numeric)
[D.5] FP076 variable (factor)
[E] The independent test model performance of the final model is summarized as follows:
[E.1] ROC Curve AUC = 0.97528
##################################
# Creating a local object
# for the train and test sets
##################################
PMA_PreModelling_Train_BTREE <- PMA_PreModelling_Train
PMA_PreModelling_Test_BTREE <- PMA_PreModelling_Test
##################################
# Creating consistent fold assignments
# for the 10-Fold Cross Validation process
##################################
set.seed(12345678)
KFold_Indices <- createFolds(PMA_PreModelling_Train_BTREE$Log_Solubility,
k = 10,
returnTrain=TRUE)
KFold_Control <- trainControl(method="cv",
index=KFold_Indices,
summaryFunction = twoClassSummary,
classProbs = TRUE)
##################################
# Setting the conditions
# for hyperparameter tuning
##################################
# No hyperparameter tuning process conducted
##################################
# Running the bagged trees model
# by setting the caret method to 'treebag'
##################################
set.seed(12345678)
BTREE_Tune <- train(x = PMA_PreModelling_Train_BTREE[,!names(PMA_PreModelling_Train_BTREE) %in% c("Log_Solubility_Class")],
y = PMA_PreModelling_Train_BTREE$Log_Solubility_Class,
method = "treebag",
nbagg = 50,
metric = "ROC",
trControl = KFold_Control)
##################################
# Reporting the cross-validation results
# for the train set
##################################
BTREE_Tune## Bagged CART
##
## 951 samples
## 220 predictors
## 2 classes: 'Low', 'High'
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 857, 855, 857, 855, 856, 856, ...
## Resampling results:
##
## ROC Sens Spec
## 0.9588129 0.9249169 0.883672BTREE_Tune$finalModel##
## Bagging classification trees with 50 bootstrap replicationsBTREE_Tune$results## parameter ROC Sens Spec ROCSD SensSD SpecSD
## 1 none 0.9588129 0.9249169 0.883672 0.01461297 0.02693862 0.04348798(BTREE_Train_ROCCurveAUC <- BTREE_Tune$results$ROC)## [1] 0.9588129##################################
# Identifying and plotting the
# best model predictors
##################################
BTREE_VarImp <- varImp(BTREE_Tune, scale = TRUE)
plot(BTREE_VarImp,
top=25,
scales=list(y=list(cex = .95)),
main="Ranked Variable Importance : Bagged Trees",
xlab="Scaled Variable Importance Metrics",
ylab="Predictors",
cex=2,
origin=0,
alpha=0.45)
##################################
# Independently evaluating the model
# on the test set
##################################
BTREE_Test <- data.frame(BTREE_Observed = PMA_PreModelling_Test_BTREE$Log_Solubility_Class,
BTREE_Predicted = predict(BTREE_Tune,
PMA_PreModelling_Test_BTREE[,!names(PMA_PreModelling_Test_BTREE) %in% c("Log_Solubility_Class")],
type = "prob"))
BTREE_Test## BTREE_Observed BTREE_Predicted.Low BTREE_Predicted.High
## 1 High 0.00 1.00
## 2 High 0.00 1.00
## 3 High 0.04 0.96
## 4 High 0.00 1.00
## 5 High 0.00 1.00
## 6 High 0.00 1.00
## 7 High 0.00 1.00
## 8 High 0.00 1.00
## 9 High 0.00 1.00
## 10 High 0.00 1.00
## 11 High 0.00 1.00
## 12 High 0.38 0.62
## 13 High 0.00 1.00
## 14 High 0.00 1.00
## 15 High 0.00 1.00
## 16 High 0.00 1.00
## 17 High 0.00 1.00
## 18 High 0.00 1.00
## 19 High 0.00 1.00
## 20 High 0.00 1.00
## 21 High 0.00 1.00
## 22 High 0.00 1.00
## 23 High 0.00 1.00
## 24 High 0.00 1.00
## 25 High 0.00 1.00
## 26 High 0.10 0.90
## 27 High 0.00 1.00
## 28 High 0.00 1.00
## 29 High 0.48 0.52
## 30 High 0.00 1.00
## 31 High 0.60 0.40
## 32 High 0.00 1.00
## 33 High 0.00 1.00
## 34 High 0.10 0.90
## 35 High 0.00 1.00
## 36 High 0.00 1.00
## 37 High 0.00 1.00
## 38 High 0.00 1.00
## 39 High 0.00 1.00
## 40 High 0.00 1.00
## 41 High 0.00 1.00
## 42 High 0.58 0.42
## 43 High 0.02 0.98
## 44 High 0.00 1.00
## 45 High 0.10 0.90
## 46 High 0.00 1.00
## 47 High 0.00 1.00
## 48 High 0.00 1.00
## 49 High 0.00 1.00
## 50 High 0.00 1.00
## 51 High 0.00 1.00
## 52 High 0.00 1.00
## 53 High 0.00 1.00
## 54 High 0.00 1.00
## 55 High 0.02 0.98
## 56 High 0.30 0.70
## 57 High 0.00 1.00
## 58 High 0.02 0.98
## 59 High 0.02 0.98
## 60 High 0.10 0.90
## 61 High 0.00 1.00
## 62 High 0.00 1.00
## 63 High 0.18 0.82
## 64 High 0.00 1.00
## 65 High 0.00 1.00
## 66 High 0.46 0.54
## 67 High 0.08 0.92
## 68 High 0.18 0.82
## 69 High 0.28 0.72
## 70 High 0.08 0.92
## 71 High 0.40 0.60
## 72 High 0.42 0.58
## 73 High 0.00 1.00
## 74 High 0.60 0.40
## 75 High 0.00 1.00
## 76 High 0.16 0.84
## 77 High 0.12 0.88
## 78 High 0.00 1.00
## 79 High 0.00 1.00
## 80 High 0.34 0.66
## 81 High 0.00 1.00
## 82 High 0.02 0.98
## 83 High 0.68 0.32
## 84 High 0.06 0.94
## 85 High 0.48 0.52
## 86 High 0.00 1.00
## 87 High 0.64 0.36
## 88 High 0.06 0.94
## 89 High 0.02 0.98
## 90 High 0.20 0.80
## 91 High 0.00 1.00
## 92 High 0.02 0.98
## 93 High 0.54 0.46
## 94 High 0.00 1.00
## 95 High 0.06 0.94
## 96 High 0.04 0.96
## 97 High 0.44 0.56
## 98 High 0.64 0.36
## 99 High 0.30 0.70
## 100 High 0.06 0.94
## 101 High 0.06 0.94
## 102 High 0.00 1.00
## 103 High 0.12 0.88
## 104 High 0.06 0.94
## 105 High 0.34 0.66
## 106 High 0.72 0.28
## 107 High 0.66 0.34
## 108 High 0.00 1.00
## 109 High 0.60 0.40
## 110 High 0.56 0.44
## 111 High 0.58 0.42
## 112 High 0.14 0.86
## 113 High 0.42 0.58
## 114 High 0.52 0.48
## 115 High 0.54 0.46
## 116 High 0.80 0.20
## 117 High 0.86 0.14
## 118 High 0.58 0.42
## 119 Low 0.64 0.36
## 120 Low 0.48 0.52
## 121 Low 0.72 0.28
## 122 Low 0.00 1.00
## 123 Low 0.78 0.22
## 124 Low 0.26 0.74
## 125 Low 0.74 0.26
## 126 Low 0.74 0.26
## 127 Low 1.00 0.00
## 128 Low 0.78 0.22
## 129 Low 0.74 0.26
## 130 Low 0.86 0.14
## 131 Low 1.00 0.00
## 132 Low 0.54 0.46
## 133 Low 0.74 0.26
## 134 Low 0.60 0.40
## 135 Low 0.56 0.44
## 136 Low 0.74 0.26
## 137 Low 0.90 0.10
## 138 Low 1.00 0.00
## 139 Low 0.92 0.08
## 140 Low 0.04 0.96
## 141 Low 0.92 0.08
## 142 Low 0.60 0.40
## 143 Low 0.98 0.02
## 144 Low 0.82 0.18
## 145 Low 0.20 0.80
## 146 Low 0.46 0.54
## 147 Low 0.76 0.24
## 148 Low 0.90 0.10
## 149 Low 0.94 0.06
## 150 Low 0.98 0.02
## 151 Low 0.44 0.56
## 152 Low 0.84 0.16
## 153 Low 0.92 0.08
## 154 Low 1.00 0.00
## 155 Low 0.82 0.18
## 156 Low 0.92 0.08
## 157 Low 1.00 0.00
## 158 Low 0.80 0.20
## 159 Low 0.80 0.20
## 160 Low 0.78 0.22
## 161 Low 1.00 0.00
## 162 Low 0.90 0.10
## 163 Low 0.94 0.06
## 164 Low 0.84 0.16
## 165 Low 0.92 0.08
## 166 Low 0.98 0.02
## 167 Low 0.90 0.10
## 168 Low 0.80 0.20
## 169 Low 1.00 0.00
## 170 Low 0.98 0.02
## 171 Low 0.90 0.10
## 172 Low 1.00 0.00
## 173 Low 0.98 0.02
## 174 Low 1.00 0.00
## 175 Low 0.98 0.02
## 176 Low 0.98 0.02
## 177 Low 0.82 0.18
## 178 Low 1.00 0.00
## 179 Low 0.98 0.02
## 180 Low 1.00 0.00
## 181 Low 0.98 0.02
## 182 Low 1.00 0.00
## 183 Low 0.96 0.04
## 184 Low 0.96 0.04
## 185 Low 0.96 0.04
## 186 Low 0.86 0.14
## 187 Low 0.90 0.10
## 188 Low 0.96 0.04
## 189 Low 1.00 0.00
## 190 Low 1.00 0.00
## 191 Low 0.90 0.10
## 192 Low 0.84 0.16
## 193 Low 1.00 0.00
## 194 Low 0.98 0.02
## 195 Low 0.94 0.06
## 196 Low 0.94 0.06
## 197 Low 0.98 0.02
## 198 Low 0.98 0.02
## 199 Low 1.00 0.00
## 200 Low 0.96 0.04
## 201 Low 1.00 0.00
## 202 Low 1.00 0.00
## 203 Low 1.00 0.00
## 204 Low 1.00 0.00
## 205 Low 1.00 0.00
## 206 Low 1.00 0.00
## 207 Low 0.96 0.04
## 208 Low 1.00 0.00
## 209 Low 1.00 0.00
## 210 Low 0.98 0.02
## 211 Low 1.00 0.00
## 212 Low 1.00 0.00
## 213 Low 1.00 0.00
## 214 Low 1.00 0.00
## 215 Low 1.00 0.00
## 216 Low 1.00 0.00
## 217 High 0.00 1.00
## 218 High 0.00 1.00
## 219 High 0.00 1.00
## 220 High 0.00 1.00
## 221 High 0.02 0.98
## 222 High 0.00 1.00
## 223 High 0.00 1.00
## 224 High 0.00 1.00
## 225 High 0.28 0.72
## 226 High 0.10 0.90
## 227 High 0.00 1.00
## 228 High 0.02 0.98
## 229 High 0.00 1.00
## 230 High 0.08 0.92
## 231 High 0.04 0.96
## 232 High 0.00 1.00
## 233 High 0.00 1.00
## 234 High 0.00 1.00
## 235 High 0.00 1.00
## 236 High 0.02 0.98
## 237 High 0.54 0.46
## 238 High 0.04 0.96
## 239 High 0.00 1.00
## 240 High 0.00 1.00
## 241 High 0.04 0.96
## 242 High 0.00 1.00
## 243 High 0.00 1.00
## 244 High 0.00 1.00
## 245 High 0.14 0.86
## 246 High 0.00 1.00
## 247 High 0.00 1.00
## 248 High 0.00 1.00
## 249 High 0.00 1.00
## 250 High 0.08 0.92
## 251 High 0.40 0.60
## 252 High 0.04 0.96
## 253 High 0.10 0.90
## 254 High 0.48 0.52
## 255 High 0.20 0.80
## 256 High 0.00 1.00
## 257 High 0.36 0.64
## 258 High 0.10 0.90
## 259 High 0.14 0.86
## 260 High 0.02 0.98
## 261 High 0.02 0.98
## 262 High 0.42 0.58
## 263 High 0.04 0.96
## 264 High 0.40 0.60
## 265 High 0.94 0.06
## 266 High 0.16 0.84
## 267 High 0.36 0.64
## 268 High 0.52 0.48
## 269 Low 0.98 0.02
## 270 Low 0.58 0.42
## 271 Low 0.78 0.22
## 272 Low 0.54 0.46
## 273 Low 0.74 0.26
## 274 Low 0.92 0.08
## 275 Low 0.42 0.58
## 276 Low 0.96 0.04
## 277 Low 0.98 0.02
## 278 Low 0.70 0.30
## 279 Low 0.94 0.06
## 280 Low 0.98 0.02
## 281 Low 0.92 0.08
## 282 Low 0.98 0.02
## 283 Low 0.86 0.14
## 284 Low 0.84 0.16
## 285 Low 1.00 0.00
## 286 Low 0.88 0.12
## 287 Low 1.00 0.00
## 288 Low 0.98 0.02
## 289 Low 0.98 0.02
## 290 Low 1.00 0.00
## 291 Low 0.84 0.16
## 292 Low 0.92 0.08
## 293 Low 0.98 0.02
## 294 Low 0.98 0.02
## 295 Low 1.00 0.00
## 296 Low 0.72 0.28
## 297 Low 0.82 0.18
## 298 Low 0.90 0.10
## 299 Low 1.00 0.00
## 300 Low 1.00 0.00
## 301 Low 0.96 0.04
## 302 Low 0.96 0.04
## 303 Low 1.00 0.00
## 304 Low 0.94 0.06
## 305 Low 0.90 0.10
## 306 Low 1.00 0.00
## 307 Low 1.00 0.00
## 308 Low 1.00 0.00
## 309 Low 0.98 0.02
## 310 Low 0.98 0.02
## 311 Low 1.00 0.00
## 312 Low 1.00 0.00
## 313 High 0.02 0.98
## 314 High 0.44 0.56
## 315 Low 0.86 0.14
## 316 High 0.88 0.12##################################
# Reporting the independent evaluation results
# for the test set
##################################
BTREE_Test_ROC <- roc(response = BTREE_Test$BTREE_Observed,
predictor = BTREE_Test$BTREE_Predicted.High,
levels = rev(levels(BTREE_Test$BTREE_Observed)))
(BTREE_Test_ROCCurveAUC <- auc(BTREE_Test_ROC)[1])## [1] 0.97528191.5.16 Model Evaluation Summary
Model performance comparison:
[A] The models which demonstrated the best and most consistent ROC Curve AUC metrics are as follows:
[A.1] C50: C5.0 Decision Trees (C50 and plyr packages)
[A.1.1] Cross-Validation ROC Curve AUC = 0.96540, Test ROC Curve AUC = 0.97635
[A.2] RF: Random Forest (randomForest package)
[A.2.1] Cross-Validation ROC Curve AUC = 0.96507, Test ROC Curve AUC = 0.98207
[A.3] BTREE: Bagged Trees (ipred, plyr and e1071 packages)
[A.2.1] Cross-Validation ROC Curve AUC = 0.95881, Test ROC Curve AUC = 0.97528
##################################
# Consolidating all evaluation results
# for the train and test sets
# using the ROC Curve AUC metric
##################################
Model <- c('LR','LDA','FDA','MDA','NB','NSC','AVNN','SVM_R','SVM_P','KNN','CART','CTREE','C50','RF','BTREE',
'LR','LDA','FDA','MDA','NB','NSC','AVNN','SVM_R','SVM_P','KNN','CART','CTREE','C50','RF','BTREE')
Set <- c(rep('Cross-Validation',15),rep('Test',15))
ROCCurveAUC <- c(LR_Train_ROCCurveAUC,LDA_Train_ROCCurveAUC,FDA_Train_ROCCurveAUC,MDA_Train_ROCCurveAUC,NB_Train_ROCCurveAUC,
NSC_Train_ROCCurveAUC,AVNN_Train_ROCCurveAUC,SVM_R_Train_ROCCurveAUC,SVM_P_Train_ROCCurveAUC,KNN_Train_ROCCurveAUC,
CART_Train_ROCCurveAUC,CTREE_Train_ROCCurveAUC,C50_Train_ROCCurveAUC,RF_Train_ROCCurveAUC,BTREE_Train_ROCCurveAUC,
LR_Test_ROCCurveAUC,LDA_Test_ROCCurveAUC,FDA_Test_ROCCurveAUC,MDA_Test_ROCCurveAUC,NB_Test_ROCCurveAUC,
NSC_Test_ROCCurveAUC,AVNN_Test_ROCCurveAUC,SVM_R_Test_ROCCurveAUC,SVM_P_Test_ROCCurveAUC,KNN_Test_ROCCurveAUC,
CART_Test_ROCCurveAUC,CTREE_Test_ROCCurveAUC,C50_Test_ROCCurveAUC,RF_Test_ROCCurveAUC,BTREE_Test_ROCCurveAUC)
ROCCurveAUC_Summary <- as.data.frame(cbind(Model,Set,ROCCurveAUC))
ROCCurveAUC_Summary$ROCCurveAUC <- as.numeric(as.character(ROCCurveAUC_Summary$ROCCurveAUC))
ROCCurveAUC_Summary$Set <- factor(ROCCurveAUC_Summary$Set,
levels = c("Cross-Validation",
"Test"))
ROCCurveAUC_Summary$Model <- factor(ROCCurveAUC_Summary$Model,
levels = c("LR",
"LDA",
"FDA",
"MDA",
"NB",
"NSC",
"AVNN",
"SVM_R",
"SVM_P",
"KNN",
"CART",
"CTREE",
"C50",
"RF",
"BTREE"))
print(ROCCurveAUC_Summary, row.names=FALSE)## Model Set ROCCurveAUC
## LR Cross-Validation 0.8616392
## LDA Cross-Validation 0.9096763
## FDA Cross-Validation 0.9494893
## MDA Cross-Validation 0.9065884
## NB Cross-Validation 0.8818276
## NSC Cross-Validation 0.8662268
## AVNN Cross-Validation 0.9157703
## SVM_R Cross-Validation 0.9551422
## SVM_P Cross-Validation 0.9504889
## KNN Cross-Validation 0.8948909
## CART Cross-Validation 0.9023673
## CTREE Cross-Validation 0.9096727
## C50 Cross-Validation 0.9654007
## RF Cross-Validation 0.9650737
## BTREE Cross-Validation 0.9588129
## LR Test 0.8730345
## LDA Test 0.9213792
## FDA Test 0.9593355
## MDA Test 0.9213792
## NB Test 0.8856057
## NSC Test 0.8877077
## AVNN Test 0.9189135
## SVM_R Test 0.9501597
## SVM_P Test 0.9501192
## KNN Test 0.8817050
## CART Test 0.9452282
## CTREE Test 0.8964792
## C50 Test 0.9763531
## RF Test 0.9820728
## BTREE Test 0.9752819(ROCCurveAUC_Plot <- dotplot(Model ~ ROCCurveAUC,
data = ROCCurveAUC_Summary,
groups = Set,
main = "Classification Model Performance Comparison",
ylab = "Model",
xlab = "ROC Curve AUC",
auto.key = list(adj = 1),
type=c("p", "h"),
origin = 0,
alpha = 0.45,
pch = 16,
cex = 2))
1.6 References
[Book] Applied Predictive Modeling by Max Kuhn and Kjell Johnson
[Book] An Introduction to Statistical Learning by Gareth James, Daniela Witten, Trevor Hastie and Rob Tibshirani
[Book] Multivariate Data Visualization with R by Deepayan Sarkar
[Book] Machine Learning by Samuel Jackson
[Book] Data Modeling Methods by Jacob Larget
[R Package] AppliedPredictiveModeling by Max Kuhn
[R Package] caret by Max Kuhn
[R Package] rpart by Terry Therneau and Beth Atkinson
[R Package] lattice by Deepayan Sarkar
[R Package] dplyr by Hadley Wickham
[R Package] moments by Lukasz Komsta and Frederick
[R Package] skimr by Elin Waring
[R Package] RANN by Sunil Arya, David Mount, Samuel Kemp and Gregory Jefferis
[R Package] corrplot by Taiyun Wei
[R Package] tidyverse by Hadley Wickham
[R Package] lares by Bernardo Lares
[R Package] DMwR by Luis Torgo
[R Package] gridExtra by Baptiste Auguie and Anton Antonov
[R Package] rattle by Graham Williams
[R Package] rpart.plot by Stephen Milborrow
[R Package] RColorBrewer by Erich Neuwirth
[R Package] stats by R Core Team
[R Package] pls by Kristian Hovde Liland
[R Package] nnet by Brian Ripley
[R Package] elasticnet by Hui Zou
[R Package] earth by Stephen Milborrow
[R Package] party by Torsten Hothorn
[R Package] kernlab by Alexandros Karatzoglou
[R Package] randomForest by Andy Liaw
[R Package] pROC by Xavier Robin
[R Package] mda by Trevor Hastie
[R Package] klaR by Christian Roever, Nils Raabe, Karsten Luebke, Uwe Ligges, Gero Szepannek, Marc Zentgraf and David Meyer
[R Package] pamr by Trevor Hastie, Rob Tibshirani, Balasubramanian Narasimhan and Gil Chu
[Article] The caret Package by Max Kuhn
[Article] A Short Introduction to the caret Package by Max Kuhn
[Article] Caret Package – A Practical Guide to Machine Learning in R by Selva Prabhakaran
[Article] Tuning Machine Learning Models Using the Caret R Package by Jason Brownlee
[Article] Lattice Graphs by Alboukadel Kassambara
[Article] A Tour of Machine Learning Algorithms by Jason Brownlee
[Article] Decision Tree Algorithm Examples In Data Mining by Software Testing Help Team
[Article] 4 Types of Classification Tasks in Machine Learning by Jason Brownlee
[Article] Spot-Check Classification Machine Learning Algorithms in Python with scikit-learn by Jason Brownlee
[Article] Feature Engineering and Selection: A Practical Approach for Predictive Models by Max Kuhn and Kjell Johnson
[Article] An Introduction to Naive Bayes Algorithm for Beginners by Turing Team
[Article] Machine Learning Tutorial: A Step-by-Step Guide for Beginners by Mayank Banoula
[Article] Nearest Shrunken Centroids With Python by Jason Brownlee
[Article] Discriminant Analysis Essentials in R by Alboukadel Kassambara
[Article] Linear Discriminant Analysis, Explained by Xiaozhou Yang
[Article] Flexible Discriminant Analysis by BCCVL Team
[Article] Classification Tree by BCCVL Team
[Article] Random Forest by BCCVL Team
[Article] Boosted Regression Tree by BCCVL Team
[Article] Artificial Neural Network by BCCVL Team
[Article] Generalized Linear Model by BCCVL Team
[Article] Generalized Boosting Model by BCCVL Team
[Article] C5.0: An Informal Tutorial by RuleQuest Team
[Article] What is Nearest Shrunken Centroid Classification? by Rob Tibshirani
[Course] Applied Data Mining and Statistical Learning by Penn State Eberly College of Science
[Course] Regression Methods by Penn State Eberly College of Science
[Course] Applied Regression Analysis by Penn State Eberly College of Science
[Course] Applied Data Mining and Statistical Learning by Penn State Eberly College of Science