Programming of Data Science
Group 3
| Name | Matrix Number |
|---|---|
| Hoo Xin Yu | S2117839 |
| Pei Lin Soh | S2193368 |
| Low Kian Haw | S2190839 |
| Clarice Lau Yeo Hang | S2192784 |
| Yeoh Joer | 22077700 |
Introduction
- Clarice input
Research Objective
- Clarice input
Data Description/ Source
The dataset is collected from Kaggle and it contains test and train dataset
Data Source: https://www.kaggle.com/datasets/prevek18/ames-housing-dataset
Import necessary libraries
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(readr)
library(ggplot2)
library(psych)##
## Attaching package: 'psych'## The following objects are masked from 'package:ggplot2':
##
## %+%, alphalibrary(gridExtra)##
## Attaching package: 'gridExtra'## The following object is masked from 'package:dplyr':
##
## combinelibrary(DescTools)##
## Attaching package: 'DescTools'## The following objects are masked from 'package:psych':
##
## AUC, ICC, SDlibrary(corrplot)## corrplot 0.92 loadedlibrary(caret)## Loading required package: lattice##
## Attaching package: 'caret'## The following objects are masked from 'package:DescTools':
##
## MAE, RMSElibrary(mlr)## Loading required package: ParamHelpers## Warning message: 'mlr' is in 'maintenance-only' mode since July 2019.
## Future development will only happen in 'mlr3'
## (<https://mlr3.mlr-org.com>). Due to the focus on 'mlr3' there might be
## uncaught bugs meanwhile in {mlr} - please consider switching.##
## Attaching package: 'mlr'## The following object is masked from 'package:caret':
##
## trainsuppressPackageStartupMessages({
library(dplyr)
library(readr)
library(ggplot2)
library(psych)
library(gridExtra)
library(DescTools)
library(corrplot)
library(caret)
library(mlr)
})Import Dataset
- Dataset contains information on housing features such as location, size, number of rooms, and other amenities
dataset <- read.csv("train.csv")
head(dataset)## Id MSSubClass MSZoning LotFrontage LotArea Street Alley LotShape LandContour
## 1 1 60 RL 65 8450 Pave <NA> Reg Lvl
## 2 2 20 RL 80 9600 Pave <NA> Reg Lvl
## 3 3 60 RL 68 11250 Pave <NA> IR1 Lvl
## 4 4 70 RL 60 9550 Pave <NA> IR1 Lvl
## 5 5 60 RL 84 14260 Pave <NA> IR1 Lvl
## 6 6 50 RL 85 14115 Pave <NA> IR1 Lvl
## Utilities LotConfig LandSlope Neighborhood Condition1 Condition2 BldgType
## 1 AllPub Inside Gtl CollgCr Norm Norm 1Fam
## 2 AllPub FR2 Gtl Veenker Feedr Norm 1Fam
## 3 AllPub Inside Gtl CollgCr Norm Norm 1Fam
## 4 AllPub Corner Gtl Crawfor Norm Norm 1Fam
## 5 AllPub FR2 Gtl NoRidge Norm Norm 1Fam
## 6 AllPub Inside Gtl Mitchel Norm Norm 1Fam
## HouseStyle OverallQual OverallCond YearBuilt YearRemodAdd RoofStyle RoofMatl
## 1 2Story 7 5 2003 2003 Gable CompShg
## 2 1Story 6 8 1976 1976 Gable CompShg
## 3 2Story 7 5 2001 2002 Gable CompShg
## 4 2Story 7 5 1915 1970 Gable CompShg
## 5 2Story 8 5 2000 2000 Gable CompShg
## 6 1.5Fin 5 5 1993 1995 Gable CompShg
## Exterior1st Exterior2nd MasVnrType MasVnrArea ExterQual ExterCond Foundation
## 1 VinylSd VinylSd BrkFace 196 Gd TA PConc
## 2 MetalSd MetalSd None 0 TA TA CBlock
## 3 VinylSd VinylSd BrkFace 162 Gd TA PConc
## 4 Wd Sdng Wd Shng None 0 TA TA BrkTil
## 5 VinylSd VinylSd BrkFace 350 Gd TA PConc
## 6 VinylSd VinylSd None 0 TA TA Wood
## BsmtQual BsmtCond BsmtExposure BsmtFinType1 BsmtFinSF1 BsmtFinType2
## 1 Gd TA No GLQ 706 Unf
## 2 Gd TA Gd ALQ 978 Unf
## 3 Gd TA Mn GLQ 486 Unf
## 4 TA Gd No ALQ 216 Unf
## 5 Gd TA Av GLQ 655 Unf
## 6 Gd TA No GLQ 732 Unf
## BsmtFinSF2 BsmtUnfSF TotalBsmtSF Heating HeatingQC CentralAir Electrical
## 1 0 150 856 GasA Ex Y SBrkr
## 2 0 284 1262 GasA Ex Y SBrkr
## 3 0 434 920 GasA Ex Y SBrkr
## 4 0 540 756 GasA Gd Y SBrkr
## 5 0 490 1145 GasA Ex Y SBrkr
## 6 0 64 796 GasA Ex Y SBrkr
## X1stFlrSF X2ndFlrSF LowQualFinSF GrLivArea BsmtFullBath BsmtHalfBath FullBath
## 1 856 854 0 1710 1 0 2
## 2 1262 0 0 1262 0 1 2
## 3 920 866 0 1786 1 0 2
## 4 961 756 0 1717 1 0 1
## 5 1145 1053 0 2198 1 0 2
## 6 796 566 0 1362 1 0 1
## HalfBath BedroomAbvGr KitchenAbvGr KitchenQual TotRmsAbvGrd Functional
## 1 1 3 1 Gd 8 Typ
## 2 0 3 1 TA 6 Typ
## 3 1 3 1 Gd 6 Typ
## 4 0 3 1 Gd 7 Typ
## 5 1 4 1 Gd 9 Typ
## 6 1 1 1 TA 5 Typ
## Fireplaces FireplaceQu GarageType GarageYrBlt GarageFinish GarageCars
## 1 0 <NA> Attchd 2003 RFn 2
## 2 1 TA Attchd 1976 RFn 2
## 3 1 TA Attchd 2001 RFn 2
## 4 1 Gd Detchd 1998 Unf 3
## 5 1 TA Attchd 2000 RFn 3
## 6 0 <NA> Attchd 1993 Unf 2
## GarageArea GarageQual GarageCond PavedDrive WoodDeckSF OpenPorchSF
## 1 548 TA TA Y 0 61
## 2 460 TA TA Y 298 0
## 3 608 TA TA Y 0 42
## 4 642 TA TA Y 0 35
## 5 836 TA TA Y 192 84
## 6 480 TA TA Y 40 30
## EnclosedPorch X3SsnPorch ScreenPorch PoolArea PoolQC Fence MiscFeature
## 1 0 0 0 0 <NA> <NA> <NA>
## 2 0 0 0 0 <NA> <NA> <NA>
## 3 0 0 0 0 <NA> <NA> <NA>
## 4 272 0 0 0 <NA> <NA> <NA>
## 5 0 0 0 0 <NA> <NA> <NA>
## 6 0 320 0 0 <NA> MnPrv Shed
## MiscVal MoSold YrSold SaleType SaleCondition SalePrice
## 1 0 2 2008 WD Normal 208500
## 2 0 5 2007 WD Normal 181500
## 3 0 9 2008 WD Normal 223500
## 4 0 2 2006 WD Abnorml 140000
## 5 0 12 2008 WD Normal 250000
## 6 700 10 2009 WD Normal 143000Dataset Overview
There are 1460 records (rows) and 81 attributes (columns).
Dataset are mostly made up of numerical value (int64 & float64).
cat("Total rows & columns:", dim(dataset), '\n\n')## Total rows & columns: 1460 81str(dataset)## 'data.frame': 1460 obs. of 81 variables:
## $ Id : int 1 2 3 4 5 6 7 8 9 10 ...
## $ MSSubClass : int 60 20 60 70 60 50 20 60 50 190 ...
## $ MSZoning : chr "RL" "RL" "RL" "RL" ...
## $ LotFrontage : int 65 80 68 60 84 85 75 NA 51 50 ...
## $ LotArea : int 8450 9600 11250 9550 14260 14115 10084 10382 6120 7420 ...
## $ Street : chr "Pave" "Pave" "Pave" "Pave" ...
## $ Alley : chr NA NA NA NA ...
## $ LotShape : chr "Reg" "Reg" "IR1" "IR1" ...
## $ LandContour : chr "Lvl" "Lvl" "Lvl" "Lvl" ...
## $ Utilities : chr "AllPub" "AllPub" "AllPub" "AllPub" ...
## $ LotConfig : chr "Inside" "FR2" "Inside" "Corner" ...
## $ LandSlope : chr "Gtl" "Gtl" "Gtl" "Gtl" ...
## $ Neighborhood : chr "CollgCr" "Veenker" "CollgCr" "Crawfor" ...
## $ Condition1 : chr "Norm" "Feedr" "Norm" "Norm" ...
## $ Condition2 : chr "Norm" "Norm" "Norm" "Norm" ...
## $ BldgType : chr "1Fam" "1Fam" "1Fam" "1Fam" ...
## $ HouseStyle : chr "2Story" "1Story" "2Story" "2Story" ...
## $ OverallQual : int 7 6 7 7 8 5 8 7 7 5 ...
## $ OverallCond : int 5 8 5 5 5 5 5 6 5 6 ...
## $ YearBuilt : int 2003 1976 2001 1915 2000 1993 2004 1973 1931 1939 ...
## $ YearRemodAdd : int 2003 1976 2002 1970 2000 1995 2005 1973 1950 1950 ...
## $ RoofStyle : chr "Gable" "Gable" "Gable" "Gable" ...
## $ RoofMatl : chr "CompShg" "CompShg" "CompShg" "CompShg" ...
## $ Exterior1st : chr "VinylSd" "MetalSd" "VinylSd" "Wd Sdng" ...
## $ Exterior2nd : chr "VinylSd" "MetalSd" "VinylSd" "Wd Shng" ...
## $ MasVnrType : chr "BrkFace" "None" "BrkFace" "None" ...
## $ MasVnrArea : int 196 0 162 0 350 0 186 240 0 0 ...
## $ ExterQual : chr "Gd" "TA" "Gd" "TA" ...
## $ ExterCond : chr "TA" "TA" "TA" "TA" ...
## $ Foundation : chr "PConc" "CBlock" "PConc" "BrkTil" ...
## $ BsmtQual : chr "Gd" "Gd" "Gd" "TA" ...
## $ BsmtCond : chr "TA" "TA" "TA" "Gd" ...
## $ BsmtExposure : chr "No" "Gd" "Mn" "No" ...
## $ BsmtFinType1 : chr "GLQ" "ALQ" "GLQ" "ALQ" ...
## $ BsmtFinSF1 : int 706 978 486 216 655 732 1369 859 0 851 ...
## $ BsmtFinType2 : chr "Unf" "Unf" "Unf" "Unf" ...
## $ BsmtFinSF2 : int 0 0 0 0 0 0 0 32 0 0 ...
## $ BsmtUnfSF : int 150 284 434 540 490 64 317 216 952 140 ...
## $ TotalBsmtSF : int 856 1262 920 756 1145 796 1686 1107 952 991 ...
## $ Heating : chr "GasA" "GasA" "GasA" "GasA" ...
## $ HeatingQC : chr "Ex" "Ex" "Ex" "Gd" ...
## $ CentralAir : chr "Y" "Y" "Y" "Y" ...
## $ Electrical : chr "SBrkr" "SBrkr" "SBrkr" "SBrkr" ...
## $ X1stFlrSF : int 856 1262 920 961 1145 796 1694 1107 1022 1077 ...
## $ X2ndFlrSF : int 854 0 866 756 1053 566 0 983 752 0 ...
## $ LowQualFinSF : int 0 0 0 0 0 0 0 0 0 0 ...
## $ GrLivArea : int 1710 1262 1786 1717 2198 1362 1694 2090 1774 1077 ...
## $ BsmtFullBath : int 1 0 1 1 1 1 1 1 0 1 ...
## $ BsmtHalfBath : int 0 1 0 0 0 0 0 0 0 0 ...
## $ FullBath : int 2 2 2 1 2 1 2 2 2 1 ...
## $ HalfBath : int 1 0 1 0 1 1 0 1 0 0 ...
## $ BedroomAbvGr : int 3 3 3 3 4 1 3 3 2 2 ...
## $ KitchenAbvGr : int 1 1 1 1 1 1 1 1 2 2 ...
## $ KitchenQual : chr "Gd" "TA" "Gd" "Gd" ...
## $ TotRmsAbvGrd : int 8 6 6 7 9 5 7 7 8 5 ...
## $ Functional : chr "Typ" "Typ" "Typ" "Typ" ...
## $ Fireplaces : int 0 1 1 1 1 0 1 2 2 2 ...
## $ FireplaceQu : chr NA "TA" "TA" "Gd" ...
## $ GarageType : chr "Attchd" "Attchd" "Attchd" "Detchd" ...
## $ GarageYrBlt : int 2003 1976 2001 1998 2000 1993 2004 1973 1931 1939 ...
## $ GarageFinish : chr "RFn" "RFn" "RFn" "Unf" ...
## $ GarageCars : int 2 2 2 3 3 2 2 2 2 1 ...
## $ GarageArea : int 548 460 608 642 836 480 636 484 468 205 ...
## $ GarageQual : chr "TA" "TA" "TA" "TA" ...
## $ GarageCond : chr "TA" "TA" "TA" "TA" ...
## $ PavedDrive : chr "Y" "Y" "Y" "Y" ...
## $ WoodDeckSF : int 0 298 0 0 192 40 255 235 90 0 ...
## $ OpenPorchSF : int 61 0 42 35 84 30 57 204 0 4 ...
## $ EnclosedPorch: int 0 0 0 272 0 0 0 228 205 0 ...
## $ X3SsnPorch : int 0 0 0 0 0 320 0 0 0 0 ...
## $ ScreenPorch : int 0 0 0 0 0 0 0 0 0 0 ...
## $ PoolArea : int 0 0 0 0 0 0 0 0 0 0 ...
## $ PoolQC : chr NA NA NA NA ...
## $ Fence : chr NA NA NA NA ...
## $ MiscFeature : chr NA NA NA NA ...
## $ MiscVal : int 0 0 0 0 0 700 0 350 0 0 ...
## $ MoSold : int 2 5 9 2 12 10 8 11 4 1 ...
## $ YrSold : int 2008 2007 2008 2006 2008 2009 2007 2009 2008 2008 ...
## $ SaleType : chr "WD" "WD" "WD" "WD" ...
## $ SaleCondition: chr "Normal" "Normal" "Normal" "Abnorml" ...
## $ SalePrice : int 208500 181500 223500 140000 250000 143000 307000 200000 129900 118000 ...Data Pre-processing
Check for sum of duplicates between columns
- No duplication inside the dataset.
duplicates <- sum(duplicated(dataset))
cat(paste("Number of duplicates:", duplicates))## Number of duplicates: 0Remove Meaningless Columns
At this stage, we have removed irrelevant columns from the dataset.
‘Id’ column is removed, as it is a unique identifier for each customer.
‘GarageCars’ column is removed, as it provides redundant information already captured by the ‘GarageArea’ column.
We also removed the ‘Exterior2nd’ column, as it represents a limited set of additional choices for exterior covering.
Furthermore, we removed the ‘GarageYrBlt’ column, as the year of construction is typically the same as the ‘YearBuilt’ column.
Finally, we removed the ‘TotRmsAbvGrd’ column, as it provides a similar meaning as the ‘First Floor’ square footage.
# Subset the dataset by removing specific columns
dataset <- subset(dataset, select = -c(Id, GarageCars, Exterior2nd, GarageYrBlt, TotRmsAbvGrd))Check for Missing Values
There are a total of 19 columns with missing values
5 of them have missing values higher than 20%
Columns with missing values higher than 20%: PoolQC, MiscFeature, Alley, Fence, FireplaceQu
Column with missing values higher than 20% will be removed in this stage
# Calculate missing percentage
missing_percentages <- colSums(is.na(dataset)) / nrow(dataset) * 100
# Create dataframe with column names and missing percentages
missing_dataset <- data.frame(
column_name = names(missing_percentages),
missing_percentage = missing_percentages
) %>%
# Sort the dataframe by missing percentages in descending order
arrange(desc(missing_percentage)) %>%
# Filter out columns with 0 missing percentages
filter(missing_percentage > 0)
# Print the missing dataset
print(missing_dataset)## column_name missing_percentage
## PoolQC PoolQC 99.52054795
## MiscFeature MiscFeature 96.30136986
## Alley Alley 93.76712329
## Fence Fence 80.75342466
## FireplaceQu FireplaceQu 47.26027397
## LotFrontage LotFrontage 17.73972603
## GarageType GarageType 5.54794521
## GarageFinish GarageFinish 5.54794521
## GarageQual GarageQual 5.54794521
## GarageCond GarageCond 5.54794521
## BsmtExposure BsmtExposure 2.60273973
## BsmtFinType2 BsmtFinType2 2.60273973
## BsmtQual BsmtQual 2.53424658
## BsmtCond BsmtCond 2.53424658
## BsmtFinType1 BsmtFinType1 2.53424658
## MasVnrType MasVnrType 0.54794521
## MasVnrArea MasVnrArea 0.54794521
## Electrical Electrical 0.06849315Columns with missing values more than 20% is removed
#Remove columns with missing values more than 20%
dataset <- subset(dataset, select = -c(PoolQC, MiscFeature, Alley, Fence, FireplaceQu))Impute numerical missing data using mean & Impute categorical missing data using mode
Median is chosen to fill in missing values, rather than the mean.
The mean is sensitive to extreme values and can be heavily influenced by outliers in the data, which can lead to biased estimates.
In contrast, the median is a robust measure of central tendency that is less sensitive to extreme values and is more appropriate for skewed data.
# Identify numerical columns & replace missing numerical values with mean
num_cols <- sapply(dataset, is.numeric)
for (col in names(dataset[, num_cols])) {
col_mean <- mean(dataset[, col], na.rm = TRUE)
dataset[, col][is.na(dataset[, col])] <- rep(col_mean, sum(is.na(dataset[, col])))
}# Identify categorical columns & replace missing categorical values with mode
cat_cols <- sapply(dataset, is.factor) | sapply(dataset, is.character)
for (col in names(dataset[, cat_cols])) {
dataset[, col][is.na(dataset[, col])] <- as.character(Mode(dataset[, col], na.rm = TRUE))
}Explore Data - Exploratory Data Analysis (EDA)
Plot Distribution of Numeric Data
- Majority of numerical columns’ distribution are right-skewed (32 attributes), however, 2 of them are left-skewed
# Select numerical columns using the "is.numeric" function
numerical_cols <- names(dataset)[sapply(dataset, is.numeric)]
categorical_cols <- names(dataset)[sapply(dataset, is.factor) | sapply(dataset, is.character)]
# Create new data frames with only numerical and categorical columns
numerical_data <- dataset[numerical_cols]
categorical_data <- dataset[categorical_cols]# Display the first six rows of the numerical data frame
head(numerical_data)## MSSubClass LotFrontage LotArea OverallQual OverallCond YearBuilt YearRemodAdd
## 1 60 65 8450 7 5 2003 2003
## 2 20 80 9600 6 8 1976 1976
## 3 60 68 11250 7 5 2001 2002
## 4 70 60 9550 7 5 1915 1970
## 5 60 84 14260 8 5 2000 2000
## 6 50 85 14115 5 5 1993 1995
## MasVnrArea BsmtFinSF1 BsmtFinSF2 BsmtUnfSF TotalBsmtSF X1stFlrSF X2ndFlrSF
## 1 196 706 0 150 856 856 854
## 2 0 978 0 284 1262 1262 0
## 3 162 486 0 434 920 920 866
## 4 0 216 0 540 756 961 756
## 5 350 655 0 490 1145 1145 1053
## 6 0 732 0 64 796 796 566
## LowQualFinSF GrLivArea BsmtFullBath BsmtHalfBath FullBath HalfBath
## 1 0 1710 1 0 2 1
## 2 0 1262 0 1 2 0
## 3 0 1786 1 0 2 1
## 4 0 1717 1 0 1 0
## 5 0 2198 1 0 2 1
## 6 0 1362 1 0 1 1
## BedroomAbvGr KitchenAbvGr Fireplaces GarageArea WoodDeckSF OpenPorchSF
## 1 3 1 0 548 0 61
## 2 3 1 1 460 298 0
## 3 3 1 1 608 0 42
## 4 3 1 1 642 0 35
## 5 4 1 1 836 192 84
## 6 1 1 0 480 40 30
## EnclosedPorch X3SsnPorch ScreenPorch PoolArea MiscVal MoSold YrSold SalePrice
## 1 0 0 0 0 0 2 2008 208500
## 2 0 0 0 0 0 5 2007 181500
## 3 0 0 0 0 0 9 2008 223500
## 4 272 0 0 0 0 2 2006 140000
## 5 0 0 0 0 0 12 2008 250000
## 6 0 320 0 0 700 10 2009 143000# Create a function to plot probability density plot and skewness
library(gridExtra)
# Create a function to plot probability density plot and skewness
plot_density <- function(column, col_name) {
# Compute the skewness of the data
skewness <- skew(column)
# Set the plot color based on the skewness
if (skewness < 0) {
plot_color <- "blue"
} else {
plot_color <- "red"
}
# Create the density plot
plot_title <- col_name # Rename the plot title with the column name
density_plot <- ggplot(data = data.frame(column), aes(x = column)) +
geom_density(fill = plot_color, alpha = 0.3) +
ggtitle(plot_title)
return(density_plot)
}# Apply the plot_density function to each column of numerical data in numerical_data
# Select the first 20 column names from numerical_data
first_20 <- names(numerical_data)[1:20]
# Apply the plot_density function to each selected column
plots <- lapply(first_20, function(col_name) {
plot_density(numerical_data[[col_name]], col_name)
})
# Arrange the resulting plots in a grid with 5 columns
grid.arrange(grobs = plots, ncol = 5)
# Select the first 20 column names from numerical_data
rest_14 <- names(numerical_data)[21:34]
# Apply the plot_density function to each selected column
plots <- lapply(rest_14, function(col_name) {
plot_density(numerical_data[[col_name]], col_name)
})
# Arrange the resulting plots in a grid with 5
grid.arrange(grobs = plots, ncol = 5)
Check Outliers using boxplot
Outliers are found in most of the columns - 29 attributes
“MSSubClass”, “LotFrontage”, “LotArea”, “OverallQual”, “OverallCond”, “YearBuilt”, “MasVnrArea”, “BsmtFinSF1”, “BsmtFinSF2”, “BsmtUnfSF”, “TotalBsmtSF”, “X1stFlrSF”, “X2ndFlrSF”, “LowQualFinSF”, “GrLivArea”, “BsmtFullBath”, “BsmtHalfBath”, “BedroomAbvGr”, “KitchenAbvGr”, “Fireplaces”, “GarageArea”, “WoodDeckSF”, “OpenPorchSF”, “EnclosedPorch”, “X3SsnPorch”, “ScreenPorch”, “PoolArea”, “MiscVal”, “SalePrice”
# Create a list to store the column names with outliers
columns_with_outliers <- c()
# Create a list of boxplots for the first 20 attributes
boxplot_numerical_first20attributes <- lapply(1:20, function(i) {
# Calculate the lower and upper fences for outlier detection
Q1 <- quantile(numerical_data[, i], 0.25)
Q3 <- quantile(numerical_data[, i], 0.75)
IQR <- Q3 - Q1
lower_fence <- Q1 - 1.5 * IQR
upper_fence <- Q3 + 1.5 * IQR
# Check for outliers
outliers <- numerical_data[, i] < lower_fence | numerical_data[, i] > upper_fence
# Add the column name to the list if outliers are present
if (any(outliers)) {
columns_with_outliers <<- c(columns_with_outliers, colnames(numerical_data)[i])
}
# Create the boxplot
ggplot(numerical_data, aes(x = 1, y = numerical_data[, i])) +
geom_boxplot() +
ggtitle(paste0("Boxplot of", colnames(numerical_data)[i])) +
xlab("") +
ylab(colnames(numerical_data)[i])
})
# Arrange the resulting boxplots in a grid with 5 columns
grid.arrange(grobs = boxplot_numerical_first20attributes, ncol = 5)
# Create a list of boxplots for the rest
boxplot_numerical_restattributes <- lapply(21:34, function(i) {
# Calculate the lower and upper fences for outlier detection
Q1 <- quantile(numerical_data[, i], 0.25)
Q3 <- quantile(numerical_data[, i], 0.75)
IQR <- Q3 - Q1
lower_fence <- Q1 - 1.5 * IQR
upper_fence <- Q3 + 1.5 * IQR
# Check for outliers
outliers <- numerical_data[, i] < lower_fence | numerical_data[, i] > upper_fence
# Add the column name to the list if outliers are present
if (any(outliers)) {
columns_with_outliers <<- c(columns_with_outliers, colnames(numerical_data)[i])
}
# Create the boxplot
ggplot(numerical_data, aes(x = 1, y = numerical_data[, i])) +
geom_boxplot() +
ggtitle(paste0("Boxplot of", colnames(numerical_data)[i])) +
xlab("") +
ylab(colnames(numerical_data)[i])
})
# Arrange the resulting boxplots in a grid with 5 columns
grid.arrange(grobs = boxplot_numerical_restattributes, ncol = 5)
# Print the column names with outliers
print(columns_with_outliers)## [1] "MSSubClass" "LotFrontage" "LotArea" "OverallQual"
## [5] "OverallCond" "YearBuilt" "MasVnrArea" "BsmtFinSF1"
## [9] "BsmtFinSF2" "BsmtUnfSF" "TotalBsmtSF" "X1stFlrSF"
## [13] "X2ndFlrSF" "LowQualFinSF" "GrLivArea" "BsmtFullBath"
## [17] "BsmtHalfBath" "BedroomAbvGr" "KitchenAbvGr" "Fireplaces"
## [21] "GarageArea" "WoodDeckSF" "OpenPorchSF" "EnclosedPorch"
## [25] "X3SsnPorch" "ScreenPorch" "PoolArea" "MiscVal"
## [29] "SalePrice"Perform Correlation Matrix
Correlation with >0.8 and above:
X1stFlrSF & TotalBsmtSF || 0.81953
# Create a heatmap of the correlation matrix
correlation_matrix <- cor(numerical_data, method = "pearson")
corrplot(correlation_matrix, method = "color", type = "upper", order = "hclust", tl.col = "black", tl.cex = 0.3, tl.srt = 90)
# Print correlation higher than 0.8
high_corr <- which(abs((correlation_matrix) > 0.8 | correlation_matrix < -0.8)& correlation_matrix!= 1, arr.ind=TRUE)
high_corr_values <- correlation_matrix[high_corr]
high_corr_df <- data.frame(row = high_corr[, 1], col = high_corr[, 2], corr = high_corr_values)
high_corr_df## row col corr
## X1stFlrSF 13 12 0.81953
## TotalBsmtSF 12 13 0.81953Categorical Data
- There are total of 37 categorical data column
# Display the first six rows of the categorical data frame
head(categorical_data)## MSZoning Street LotShape LandContour Utilities LotConfig LandSlope
## 1 RL Pave Reg Lvl AllPub Inside Gtl
## 2 RL Pave Reg Lvl AllPub FR2 Gtl
## 3 RL Pave IR1 Lvl AllPub Inside Gtl
## 4 RL Pave IR1 Lvl AllPub Corner Gtl
## 5 RL Pave IR1 Lvl AllPub FR2 Gtl
## 6 RL Pave IR1 Lvl AllPub Inside Gtl
## Neighborhood Condition1 Condition2 BldgType HouseStyle RoofStyle RoofMatl
## 1 CollgCr Norm Norm 1Fam 2Story Gable CompShg
## 2 Veenker Feedr Norm 1Fam 1Story Gable CompShg
## 3 CollgCr Norm Norm 1Fam 2Story Gable CompShg
## 4 Crawfor Norm Norm 1Fam 2Story Gable CompShg
## 5 NoRidge Norm Norm 1Fam 2Story Gable CompShg
## 6 Mitchel Norm Norm 1Fam 1.5Fin Gable CompShg
## Exterior1st MasVnrType ExterQual ExterCond Foundation BsmtQual BsmtCond
## 1 VinylSd BrkFace Gd TA PConc Gd TA
## 2 MetalSd None TA TA CBlock Gd TA
## 3 VinylSd BrkFace Gd TA PConc Gd TA
## 4 Wd Sdng None TA TA BrkTil TA Gd
## 5 VinylSd BrkFace Gd TA PConc Gd TA
## 6 VinylSd None TA TA Wood Gd TA
## BsmtExposure BsmtFinType1 BsmtFinType2 Heating HeatingQC CentralAir
## 1 No GLQ Unf GasA Ex Y
## 2 Gd ALQ Unf GasA Ex Y
## 3 Mn GLQ Unf GasA Ex Y
## 4 No ALQ Unf GasA Gd Y
## 5 Av GLQ Unf GasA Ex Y
## 6 No GLQ Unf GasA Ex Y
## Electrical KitchenQual Functional GarageType GarageFinish GarageQual
## 1 SBrkr Gd Typ Attchd RFn TA
## 2 SBrkr TA Typ Attchd RFn TA
## 3 SBrkr Gd Typ Attchd RFn TA
## 4 SBrkr Gd Typ Detchd Unf TA
## 5 SBrkr Gd Typ Attchd RFn TA
## 6 SBrkr TA Typ Attchd Unf TA
## GarageCond PavedDrive SaleType SaleCondition
## 1 TA Y WD Normal
## 2 TA Y WD Normal
## 3 TA Y WD Normal
## 4 TA Y WD Abnorml
## 5 TA Y WD Normal
## 6 TA Y WD NormalPrint bar plots for categorical data
Generally, most of the residents having following characteristics:
Low density resident
Paved streets
Gravel alley
Regular sized property
Near Flat level
Available with electric power, natural gas, steam supply, water supply, and sewage removal
Inside lot
Gentle slope of property
Single-family Detached
Single storey
Gable roof
Standard (Composite) Shingle roof
Good quality Vinyl Siding exteriors
Slight damped basement
No walkout or garden level walls
Gas forced warm air furnace
Excellent heating quality
Has Air-conditioning
Standard Circuit Breakers & Romex electrical system
Typical kitchen quality
Typical home functionality
Masonry Fireplace in main level
Typical unfinished garage attached to home
Paved driveway
Good pool quality
Minimum Wood/Wire fence
Warranty Deed – Conventional Sales
Normal Sales
# Print bar plots for categorical data for the first 20 attributes
suppressWarnings({
plots_first20attribute <- lapply(colnames(categorical_data)[1:20], function(col) {
ggplot(categorical_data, aes_string(x = col)) +
geom_bar(fill = "steelblue") +
xlab(col) +
ylab("Count") +
ggtitle(paste0("Distribution of", col)) +
scale_x_discrete(guide = guide_axis(check.overlap = TRUE))
})
grid.arrange(grobs = plots_first20attribute, ncol = 5)
})
# Print bar plots for categorical data for the remaining 17 attributes
suppressWarnings({
plots_restattribute <- lapply(colnames(categorical_data)[21:37], function(col) {
ggplot(categorical_data, aes_string(x = col)) +
geom_bar(fill = "steelblue") +
xlab(col) +
ylab("Count") +
ggtitle(paste0("Distribution of", col)) +
scale_x_discrete(guide = guide_axis(check.overlap = TRUE))
})
grid.arrange(grobs = plots_restattribute, ncol = 5)
})
Encode Categorical Data
# Create a copy of the dataset
dataset_encode <- dataset
# Encode Categorical Data
for (col in colnames(dataset_encode)) {
if (is.factor(dataset_encode[[col]]) | is.character(dataset_encode[[col]])) {
encoded_col <- predict(dummyVars(formula = as.formula(paste0("~", col)), data = dataset_encode), newdata = dataset_encode)
dataset_encode[[col]] <- encoded_col
}
}**Crytal & Joer Partt **
library(arules)## Loading required package: Matrix##
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library(catboost)
library(cluster)
library(dplyr)
library(e1071)##
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## imputelibrary(factoextra)## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBalibrary(ggplot2)
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## precision, recalllibrary(Rtsne)
library(DiceKriging)##
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## {
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## <bytecode: 0x7fd2c26e8848>
## <environment: namespace:rlang>#source("data_cleaning.r")Data Transformation/Scaling
Data preprocessing steps such as log transformation, scaling, and one-hot encoding.
Data splitted into train, validation, and test sets and combines the training and validation sets for model training.
Calculates and displays the skewness of the numerical features and target variable before and after the log transformations.
Split the numerical variables into features and the target variable.
X_num <- subset(numerical_data, select = -c(SalePrice))
y <- subset(numerical_data, select = c(SalePrice))$SalePriceLog Transformation for numerical features.
skewness_before <- sapply(X_num, function(x) {
e1071::skewness(x)
})
X_num_skewed <- skewness_before[abs(skewness_before) > 0.75]
for (x in names(X_num_skewed)) {
# bc <- BoxCoxTrans(X_num[[x]], lambda = 0.15)
# X_num[[x]] <- predict(bc, X_num[[x]])
X_num[[x]] <- log1p(X_num[[x]])
}
skewness_after <- sapply(X_num, function(x) {
e1071::skewness(x)
})
data.frame(skewness_before, skewness_after)## skewness_before skewness_after
## MSSubClass 1.40476562 0.248485705
## LotFrontage 2.38005182 -0.890144743
## LotArea 12.18261502 -0.137122272
## OverallQual 0.21649836 0.216498356
## OverallCond 0.69164401 0.691644012
## YearBuilt -0.61220121 -0.612201211
## YearRemodAdd -0.50252776 -0.502527759
## MasVnrArea 2.67091482 0.480131975
## BsmtFinSF1 1.68204129 -0.617139693
## BsmtFinSF2 4.24652141 2.518510460
## BsmtUnfSF 0.91837835 -2.182012816
## TotalBsmtSF 1.52112395 -5.144083032
## X1stFlrSF 1.37392896 0.079949547
## X2ndFlrSF 0.81135997 0.289048572
## LowQualFinSF 8.99283329 7.444994097
## GrLivArea 1.36375364 -0.006127642
## BsmtFullBath 0.59484237 0.594842375
## BsmtHalfBath 4.09497490 3.924985577
## FullBath 0.03648647 0.036486466
## HalfBath 0.67450925 0.674509252
## BedroomAbvGr 0.21135511 0.211355110
## KitchenAbvGr 4.47917826 3.861466484
## Fireplaces 0.64823107 0.648231070
## GarageArea 0.17961125 0.179611252
## WoodDeckSF 1.53820999 0.153221248
## OpenPorchSF 2.35948572 -0.023349240
## EnclosedPorch 3.08352575 2.107936639
## X3SsnPorch 10.28317840 7.719088344
## ScreenPorch 4.11374731 3.143938375
## PoolArea 14.79791829 14.333602712
## MiscVal 24.42652237 5.160083979
## MoSold 0.21161746 0.211617459
## YrSold 0.09607079 0.096070792Log Transformation for the target variable.
skewness_before <- e1071::skewness(y)
y_t <- log1p(y)
skewness_after <- e1071::skewness(y_t)
sprintf("Before: %f, After: %f", skewness_before, skewness_after)## [1] "Before: 1.879009, After: 0.121097"Scaling
X_num <- scale(X_num)One-Hot Encoding for categorical variables.
encoder <- dummyVars(~., data = categorical_data)
X_cat <- predict(encoder, newdata = categorical_data)
X_cat <- data.frame(X_cat)Split into train and validation and test sets.
X <- cbind(X_cat, X_num)
train_idx <- createDataPartition(y_t, p = 0.7, list = F)
X_train <- X[train_idx, ]
y_train <- y_t[train_idx]
X_test <- X[-train_idx, ]
y_test <- y_t[-train_idx]
train_val_idx <- createDataPartition(y_train, p = 0.8, list = FALSE)
X_train <- X_train[train_val_idx, ]
y_train <- y_train[train_val_idx]
X_val <- X_train[-train_val_idx, ]
y_val <- y_train[-train_val_idx]
X_train_val <- rbind(X_train, X_val)
y_train_val <- c(y_train, y_val)dim(X)## [1] 1460 251length(y)## [1] 1460dim(X_train)## [1] 820 251length(y_train)## [1] 820dim(X_val)## [1] 166 251length(y_val)## [1] 166#names(X)Clustering
The code executes PCA (Principal Component Analysis) to reduce the data’s dimensionality and extract the principal components.
Elbow method used to determine the best number of clusters. Result: 3.
K-means clustering is performed on the principal components, assigning each observation to a specific cluster.
The cluster assignments are appended to the principal components data, and a scatter plot is generated to visualize the resulting clusters.
# Load the necessary libraries
library(stats)
library(factoextra)
# Perform PCA on the data matrix
pca_result <- prcomp(X)
# Extract the principal components
principal_components <- as.data.frame(pca_result$x)
# Determine the optimal number of clusters using the elbow method
fviz_nbclust(principal_components, kmeans, method = "wss")
k <- 3
# Perform K-means clustering on the principal components
kmeans_result <- kmeans(principal_components, centers = k)
cluster_assignments <- kmeans_result$cluster
print(cluster_assignments)## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
## 3 2 3 2 3 2 3 3 2 2 2 3 2 3 2 2
## 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
## 2 2 2 2 3 2 3 1 2 3 2 3 2 2 2 2
## 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
## 3 2 3 3 3 2 2 2 2 2 2 2 2 3 3 3
## 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64
## 2 2 3 2 2 3 2 2 1 3 3 2 3 2 1 2
## 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80
## 3 3 3 3 2 2 3 2 3 2 2 1 2 2 2 2
## 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96
## 3 1 3 2 3 3 3 1 2 2 2 2 2 2 3 3
## 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112
## 3 2 2 2 3 3 2 3 2 3 2 2 2 3 2 3
## 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128
## 3 3 2 1 2 2 3 3 2 2 2 1 2 2 1 2
## 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144
## 2 2 3 3 2 3 2 3 2 3 3 3 2 3 2 3
## 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160
## 2 1 2 3 2 2 2 3 3 2 2 2 2 3 3 3
## 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176
## 2 3 3 2 2 2 2 3 3 3 2 3 1 2 3 2
## 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192
## 3 2 3 2 1 2 2 3 2 3 3 2 2 1 3 2
## 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208
## 3 1 2 1 3 3 2 3 2 2 2 1 2 3 2 2
## 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224
## 3 2 2 3 3 2 2 2 3 2 3 1 3 3 3 2
## 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240
## 3 1 3 1 2 1 2 3 1 2 3 1 3 3 3 2
## 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256
## 3 2 2 2 3 3 2 2 3 3 2 1 3 2 2 3
## 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272
## 3 3 3 2 2 3 2 2 2 3 3 2 2 2 3 2
## 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288
## 3 2 2 2 3 2 3 3 3 3 1 3 1 1 2 2
## 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304
## 2 2 3 2 2 3 2 2 2 3 2 2 2 3 3 2
## 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320
## 3 3 3 2 2 3 3 2 2 3 2 3 3 3 3 3
## 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336
## 3 3 3 2 3 2 1 2 2 2 2 2 3 1 3 3
## 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352
## 3 3 3 2 3 2 2 3 1 2 2 2 1 3 3 3
## 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368
## 2 2 2 3 3 1 2 3 2 2 3 1 3 2 3 2
## 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384
## 2 2 3 2 1 2 3 2 2 3 3 3 2 3 3 2
## 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400
## 3 1 2 2 3 3 2 3 2 2 2 2 2 2 2 3
## 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416
## 1 3 2 3 3 2 2 2 3 3 2 2 3 2 3 3
## 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432
## 2 2 2 2 1 3 2 3 2 2 3 2 3 2 1 2
## 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448
## 1 3 1 3 2 2 2 2 3 2 2 1 3 2 3 3
## 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464
## 2 2 2 3 3 3 2 2 2 3 2 2 3 2 2 2
## 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480
## 2 1 2 2 3 3 1 3 1 3 1 2 3 3 3 2
## 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496
## 3 3 2 1 2 2 2 2 2 1 1 2 3 2 2 2
## 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512
## 3 2 2 2 1 3 2 3 1 2 3 3 2 2 2 1
## 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
## 2 2 2 3 3 3 3 2 2 2 2 3 3 3 2 3
## 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544
## 2 3 3 2 2 2 3 2 3 2 2 3 3 3 3 1
## 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560
## 3 3 2 2 2 3 1 2 3 2 3 2 2 2 3 1
## 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576
## 2 2 2 2 3 2 3 3 3 2 2 2 3 3 2 2
## 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592
## 2 2 1 2 2 3 2 3 2 3 2 2 2 2 3 3
## 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608
## 2 1 2 3 2 1 2 1 3 2 3 1 3 3 2 2
## 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624
## 3 2 3 2 3 2 1 2 3 2 3 3 2 3 2 1
## 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640
## 3 2 2 2 3 2 2 1 3 2 2 2 2 2 2 1
## 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656
## 3 3 3 2 3 2 2 2 2 1 3 2 3 2 3 1
## 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672
## 2 2 2 2 3 3 2 2 3 3 3 3 2 2 3 2
## 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688
## 2 3 2 1 2 2 3 2 1 2 1 3 3 3 3 1
## 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704
## 3 3 1 3 3 2 2 2 2 2 2 1 3 2 3 2
## 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720
## 3 2 3 1 3 2 2 2 1 2 3 2 2 2 3 2
## 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736
## 3 1 2 2 3 2 3 3 2 2 1 3 3 2 2 2
## 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752
## 2 3 2 3 2 2 3 2 1 3 3 2 3 2 2 3
## 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768
## 3 3 2 1 3 3 1 3 2 2 3 3 1 3 3 2
## 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784
## 3 3 2 2 2 2 3 1 3 2 2 2 3 3 3 1
## 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800
## 2 2 2 3 2 3 1 2 3 3 3 3 2 2 3 2
## 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816
## 3 2 3 3 2 3 2 3 2 2 2 1 2 2 2 3
## 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832
## 2 3 2 1 3 2 3 2 3 3 2 3 2 1 2 1
## 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848
## 3 2 2 2 2 1 2 2 2 2 2 2 2 2 3 2
## 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864
## 3 3 1 1 2 2 2 2 2 3 2 3 2 2 2 2
## 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880
## 3 2 3 2 2 3 2 3 2 2 2 3 2 3 2 2
## 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896
## 2 3 3 2 2 1 3 2 3 2 2 3 2 2 2 2
## 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912
## 2 2 3 2 2 2 3 3 2 2 3 2 2 3 2 2
## 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928
## 2 2 1 1 2 2 3 2 3 2 3 1 3 2 3 3
## 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944
## 3 3 3 2 3 3 3 2 3 3 3 2 2 3 2 2
## 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960
## 2 2 2 3 3 2 2 2 2 3 1 2 1 2 3 1
## 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976
## 2 3 1 3 3 3 2 2 2 2 2 1 2 3 2 1
## 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992
## 2 1 2 2 2 3 1 3 2 2 2 3 3 3 3 2
## 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008
## 3 3 3 2 2 2 2 3 2 2 3 2 1 2 2 1
## 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024
## 3 2 2 2 2 2 2 3 3 1 3 1 3 3 2 1
## 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040
## 3 2 2 3 2 1 2 3 3 3 2 2 3 3 1 1
## 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056
## 2 2 1 3 3 2 3 2 2 2 3 3 2 2 3 2
## 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072
## 1 3 3 2 1 2 2 2 2 3 3 2 1 2 2 2
## 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088
## 2 2 3 2 2 2 1 2 3 2 3 2 3 2 1 3
## 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104
## 1 1 2 1 2 2 2 3 2 1 2 3 2 2 2 2
## 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120
## 1 3 3 3 3 3 3 3 2 2 2 3 3 2 2 2
## 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136
## 2 3 2 2 3 2 1 3 3 1 2 2 2 3 3 2
## 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152
## 2 2 3 2 2 3 3 2 2 2 3 2 2 2 2 3
## 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168
## 2 2 3 3 2 1 3 3 1 3 2 2 3 3 3 3
## 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184
## 2 3 2 2 1 2 2 3 2 2 2 2 3 3 3 2
## 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200
## 3 2 2 3 3 3 3 1 2 1 2 3 3 2 3 2
## 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216
## 2 3 2 3 2 3 2 3 2 3 3 3 2 2 2 2
## 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232
## 2 3 2 1 2 2 2 2 3 2 3 2 3 2 3 2
## 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248
## 2 2 2 2 1 3 2 3 3 3 3 3 2 3 3 2
## 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264
## 2 2 3 1 2 3 3 2 3 2 3 2 3 2 2 2
## 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280
## 1 1 2 3 3 2 3 2 2 2 2 2 2 3 3 2
## 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296
## 3 3 2 2 2 2 2 2 1 3 2 1 2 3 2 2
## 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312
## 2 1 3 2 3 2 3 3 1 3 1 2 2 3 3 3
## 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328
## 3 3 2 3 3 1 3 2 2 2 3 2 3 2 2 2
## 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344
## 2 3 3 2 2 2 1 2 2 2 3 2 2 2 3 2
## 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360
## 3 2 3 3 3 2 3 2 2 3 3 3 2 2 1 3
## 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376
## 2 3 2 3 1 3 3 1 1 3 2 2 3 3 3 3
## 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392
## 2 2 1 3 2 3 2 2 2 2 3 2 3 2 3 2
## 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408
## 2 2 1 3 2 2 2 2 2 3 3 3 2 1 2 2
## 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424
## 2 3 3 2 2 3 2 1 2 3 2 3 3 1 1 3
## 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440
## 2 2 3 2 2 3 3 1 2 3 2 3 2 3 2 3
## 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456
## 2 1 3 2 3 2 2 3 2 1 2 3 1 2 3 3
## 1457 1458 1459 1460
## 3 3 2 2# Add the cluster assignments to the principal components data
principal_components$cluster <- as.factor(cluster_assignments)
ggplot(principal_components, aes(PC1, PC2, color = cluster)) +
geom_point() +
labs(x = "Principal Component 1", y = "Principal Component 2") +
scale_color_discrete(name = "Cluster") +
theme_minimal()
t-SNE
t-SNE (t-Distributed Stochastic Neighbor Embedding) is perfomed for dimensionality reduction and visualization of the data.
Function:
Calculates the t-SNE coordinates
Creates a dendrogram through hierarchical clustering
Determines the number of clusters visually, assigns data points to clusters
Computes centroids for each cluster
Generates scatter plots to visualize the t-SNE coordinates colored by the original variable and cluster assignments
Includes a bar plot showing the cluster frequencies and evaluates clustering quality using silhouette analysis.
tsne <- Rtsne(X)
tsne_df <- data.frame(tsne)dist_mat <- dist(tsne$Y, method = "euclidean")
hclust_avg <- hclust(dist_mat, method = "average")
dend <- as.dendrogram(hclust_avg)
plot(dend)
k = 15
cut_avg <- cutree(hclust_avg, k)
tsne_df$cluster <- cut_avg
getCentroid <- function(points) {
xy <- numeric(2)
xy[1] = mean(points[, 1])
xy[2] = mean(points[, 2])
return(xy)
}
centroids = matrix(0, k, 2)
for (i in unique(cut_avg)) centroids[i, ] <- getCentroid(tsne$Y[cut_avg == i,])Silhouette Graph: Graph width represents the number of data point; longer length indicates a stronger separation and better-defined clusters.
The lighter the color, the higher the house price.
tsne_df## N Y.1 Y.2 costs itercosts origD perplexity
## 1 1460 1.986541e+01 0.61696248 6.312128e-04 73.771148 50 30
## 2 1460 3.704116e+00 17.12829597 8.232540e-04 71.150987 50 30
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## 1403 1460 -6.030812e+00 -24.70304990 5.400615e-04 71.034367 50 30
## 1404 1460 -1.038455e+00 -19.29325654 9.850615e-05 71.035404 50 30
## 1405 1460 -2.386656e+01 11.36117545 8.398040e-05 71.037731 50 30
## 1406 1460 9.230135e+00 -17.38942026 5.442093e-04 1.555216 50 30
## 1407 1460 -9.327454e-01 -0.14965968 1.155527e-03 1.312321 50 30
## 1408 1460 -8.854525e+00 6.70130812 8.467396e-04 1.228241 50 30
## 1409 1460 -2.899469e+01 -0.85822727 4.657984e-04 1.196858 50 30
## 1410 1460 2.268907e+01 9.64053484 9.739213e-04 1.176920 50 30
## 1411 1460 2.006537e+01 2.54681089 9.351594e-04 1.164909 50 30
## 1412 1460 -2.078524e+01 3.16538571 6.392506e-04 1.155632 50 30
## 1413 1460 -2.179679e+01 30.22033195 1.942632e-04 1.148755 50 30
## 1414 1460 1.277761e+00 -18.70173162 3.241941e-04 1.143827 50 30
## 1415 1460 -2.830772e+01 -0.16233698 1.168225e-03 1.139748 50 30
## 1416 1460 1.580743e+01 -23.78245187 6.510689e-04 1.135437 50 30
## 1417 1460 -2.889879e+01 -10.13346604 7.792210e-04 1.131049 50 30
## 1418 1460 2.096871e+01 -4.48546571 3.990922e-04 1.127886 50 30
## 1419 1460 -2.770916e+00 8.40843064 1.196091e-03 1.125117 50 30
## 1420 1460 -6.531665e+00 -9.51499605 1.223070e-03 1.123256 50 30
## 1421 1460 1.716970e+01 13.71371564 5.184436e-04 73.771148 50 30
## 1422 1460 4.742453e+00 -4.95434696 9.666950e-04 71.150987 50 30
## 1423 1460 1.847358e+01 -19.11311497 3.802887e-04 71.034367 50 30
## 1424 1460 1.124661e+01 -3.27266249 5.747808e-04 71.035404 50 30
## 1425 1460 4.712412e-01 8.16717441 9.501021e-04 71.037731 50 30
## 1426 1460 -1.183659e+01 -1.05178630 4.994076e-04 1.555216 50 30
## 1427 1460 1.975865e+01 -2.33915744 1.054720e-03 1.312321 50 30
## 1428 1460 -2.033919e+01 1.81794261 1.478647e-03 1.228241 50 30
## 1429 1460 -1.087534e+01 11.77413812 6.370088e-04 1.196858 50 30
## 1430 1460 -8.826696e+00 -8.80315052 9.085545e-04 1.176920 50 30
## 1431 1460 2.810761e+01 6.71918546 1.235895e-05 1.164909 50 30
## 1432 1460 3.868118e+00 -5.37952424 6.288693e-04 1.155632 50 30
## 1433 1460 -1.661957e+01 5.17810626 1.096805e-03 1.148755 50 30
## 1434 1460 2.535641e+01 9.06612780 4.559541e-04 1.143827 50 30
## 1435 1460 -4.935467e+00 -4.11613447 1.539246e-03 1.139748 50 30
## 1436 1460 -6.494504e+00 10.44968801 6.199137e-04 1.135437 50 30
## 1437 1460 -1.050849e+01 5.68464705 1.963096e-03 1.131049 50 30
## 1438 1460 7.103009e+00 -11.60549147 2.151471e-04 1.127886 50 30
## 1439 1460 -9.786456e+00 13.71638794 6.997396e-04 1.125117 50 30
## 1440 1460 1.337203e+01 12.78608475 9.893252e-04 1.123256 50 30
## 1441 1460 -3.824934e+01 5.20511904 6.129777e-04 73.771148 50 30
## 1442 1460 1.791757e+01 -18.96874872 4.387507e-04 71.150987 50 30
## 1443 1460 2.088602e+01 -6.26097887 4.572060e-04 71.034367 50 30
## 1444 1460 -1.621145e+01 10.50017360 4.934299e-04 71.035404 50 30
## 1445 1460 -4.787609e+00 -27.51355008 4.254095e-04 71.037731 50 30
## 1446 1460 -1.659919e+00 5.01261706 6.946730e-04 1.555216 50 30
## 1447 1460 -8.850115e+00 0.23989059 3.445671e-04 1.312321 50 30
## 1448 1460 2.029528e+01 -1.74577380 4.550161e-04 1.228241 50 30
## 1449 1460 -2.112497e+01 7.39873074 8.625991e-04 1.196858 50 30
## 1450 1460 4.543679e+01 4.46023390 6.728958e-04 1.176920 50 30
## 1451 1460 -1.623457e+01 21.62679191 1.708126e-03 1.164909 50 30
## 1452 1460 -2.317150e+00 -25.15562445 3.244397e-04 1.155632 50 30
## 1453 1460 2.044313e+01 -20.20933600 9.929341e-04 1.148755 50 30
## 1454 1460 -1.486533e+01 -10.55844168 6.205043e-04 1.143827 50 30
## 1455 1460 -5.134882e+00 -19.33441084 9.290986e-04 1.139748 50 30
## 1456 1460 2.816420e+01 8.06133960 1.117811e-03 1.135437 50 30
## 1457 1460 -1.921733e+00 -12.02716207 8.692068e-04 1.131049 50 30
## 1458 1460 5.645777e+00 26.29267797 1.536823e-03 1.127886 50 30
## 1459 1460 -5.443215e-01 6.01642272 4.247624e-04 1.125117 50 30
## 1460 1460 5.800857e-01 7.68324594 8.081546e-04 1.123256 50 30
## theta max_iter stop_lying_iter mom_switch_iter momentum final_momentum eta
## 1 0.5 1000 250 250 0.5 0.8 200
## 2 0.5 1000 250 250 0.5 0.8 200
## 3 0.5 1000 250 250 0.5 0.8 200
## 4 0.5 1000 250 250 0.5 0.8 200
## 5 0.5 1000 250 250 0.5 0.8 200
## 6 0.5 1000 250 250 0.5 0.8 200
## 7 0.5 1000 250 250 0.5 0.8 200
## 8 0.5 1000 250 250 0.5 0.8 200
## 9 0.5 1000 250 250 0.5 0.8 200
## 10 0.5 1000 250 250 0.5 0.8 200
## 11 0.5 1000 250 250 0.5 0.8 200
## 12 0.5 1000 250 250 0.5 0.8 200
## 13 0.5 1000 250 250 0.5 0.8 200
## 14 0.5 1000 250 250 0.5 0.8 200
## 15 0.5 1000 250 250 0.5 0.8 200
## 16 0.5 1000 250 250 0.5 0.8 200
## 17 0.5 1000 250 250 0.5 0.8 200
## 18 0.5 1000 250 250 0.5 0.8 200
## 19 0.5 1000 250 250 0.5 0.8 200
## 20 0.5 1000 250 250 0.5 0.8 200
## 21 0.5 1000 250 250 0.5 0.8 200
## 22 0.5 1000 250 250 0.5 0.8 200
## 23 0.5 1000 250 250 0.5 0.8 200
## 24 0.5 1000 250 250 0.5 0.8 200
## 25 0.5 1000 250 250 0.5 0.8 200
## 26 0.5 1000 250 250 0.5 0.8 200
## 27 0.5 1000 250 250 0.5 0.8 200
## 28 0.5 1000 250 250 0.5 0.8 200
## 29 0.5 1000 250 250 0.5 0.8 200
## 30 0.5 1000 250 250 0.5 0.8 200
## 31 0.5 1000 250 250 0.5 0.8 200
## 32 0.5 1000 250 250 0.5 0.8 200
## 33 0.5 1000 250 250 0.5 0.8 200
## 34 0.5 1000 250 250 0.5 0.8 200
## 35 0.5 1000 250 250 0.5 0.8 200
## 36 0.5 1000 250 250 0.5 0.8 200
## 37 0.5 1000 250 250 0.5 0.8 200
## 38 0.5 1000 250 250 0.5 0.8 200
## 39 0.5 1000 250 250 0.5 0.8 200
## 40 0.5 1000 250 250 0.5 0.8 200
## 41 0.5 1000 250 250 0.5 0.8 200
## 42 0.5 1000 250 250 0.5 0.8 200
## 43 0.5 1000 250 250 0.5 0.8 200
## 44 0.5 1000 250 250 0.5 0.8 200
## 45 0.5 1000 250 250 0.5 0.8 200
## 46 0.5 1000 250 250 0.5 0.8 200
## 47 0.5 1000 250 250 0.5 0.8 200
## 48 0.5 1000 250 250 0.5 0.8 200
## 49 0.5 1000 250 250 0.5 0.8 200
## 50 0.5 1000 250 250 0.5 0.8 200
## 51 0.5 1000 250 250 0.5 0.8 200
## 52 0.5 1000 250 250 0.5 0.8 200
## 53 0.5 1000 250 250 0.5 0.8 200
## 54 0.5 1000 250 250 0.5 0.8 200
## 55 0.5 1000 250 250 0.5 0.8 200
## 56 0.5 1000 250 250 0.5 0.8 200
## 57 0.5 1000 250 250 0.5 0.8 200
## 58 0.5 1000 250 250 0.5 0.8 200
## 59 0.5 1000 250 250 0.5 0.8 200
## 60 0.5 1000 250 250 0.5 0.8 200
## 61 0.5 1000 250 250 0.5 0.8 200
## 62 0.5 1000 250 250 0.5 0.8 200
## 63 0.5 1000 250 250 0.5 0.8 200
## 64 0.5 1000 250 250 0.5 0.8 200
## 65 0.5 1000 250 250 0.5 0.8 200
## 66 0.5 1000 250 250 0.5 0.8 200
## 67 0.5 1000 250 250 0.5 0.8 200
## 68 0.5 1000 250 250 0.5 0.8 200
## 69 0.5 1000 250 250 0.5 0.8 200
## 70 0.5 1000 250 250 0.5 0.8 200
## 71 0.5 1000 250 250 0.5 0.8 200
## 72 0.5 1000 250 250 0.5 0.8 200
## 73 0.5 1000 250 250 0.5 0.8 200
## 74 0.5 1000 250 250 0.5 0.8 200
## 75 0.5 1000 250 250 0.5 0.8 200
## 76 0.5 1000 250 250 0.5 0.8 200
## 77 0.5 1000 250 250 0.5 0.8 200
## 78 0.5 1000 250 250 0.5 0.8 200
## 79 0.5 1000 250 250 0.5 0.8 200
## 80 0.5 1000 250 250 0.5 0.8 200
## 81 0.5 1000 250 250 0.5 0.8 200
## 82 0.5 1000 250 250 0.5 0.8 200
## 83 0.5 1000 250 250 0.5 0.8 200
## 84 0.5 1000 250 250 0.5 0.8 200
## 85 0.5 1000 250 250 0.5 0.8 200
## 86 0.5 1000 250 250 0.5 0.8 200
## 87 0.5 1000 250 250 0.5 0.8 200
## 88 0.5 1000 250 250 0.5 0.8 200
## 89 0.5 1000 250 250 0.5 0.8 200
## 90 0.5 1000 250 250 0.5 0.8 200
## 91 0.5 1000 250 250 0.5 0.8 200
## 92 0.5 1000 250 250 0.5 0.8 200
## 93 0.5 1000 250 250 0.5 0.8 200
## 94 0.5 1000 250 250 0.5 0.8 200
## 95 0.5 1000 250 250 0.5 0.8 200
## 96 0.5 1000 250 250 0.5 0.8 200
## 97 0.5 1000 250 250 0.5 0.8 200
## 98 0.5 1000 250 250 0.5 0.8 200
## 99 0.5 1000 250 250 0.5 0.8 200
## 100 0.5 1000 250 250 0.5 0.8 200
## 101 0.5 1000 250 250 0.5 0.8 200
## 102 0.5 1000 250 250 0.5 0.8 200
## 103 0.5 1000 250 250 0.5 0.8 200
## 104 0.5 1000 250 250 0.5 0.8 200
## 105 0.5 1000 250 250 0.5 0.8 200
## 106 0.5 1000 250 250 0.5 0.8 200
## 107 0.5 1000 250 250 0.5 0.8 200
## 108 0.5 1000 250 250 0.5 0.8 200
## 109 0.5 1000 250 250 0.5 0.8 200
## 110 0.5 1000 250 250 0.5 0.8 200
## 111 0.5 1000 250 250 0.5 0.8 200
## 112 0.5 1000 250 250 0.5 0.8 200
## 113 0.5 1000 250 250 0.5 0.8 200
## 114 0.5 1000 250 250 0.5 0.8 200
## 115 0.5 1000 250 250 0.5 0.8 200
## 116 0.5 1000 250 250 0.5 0.8 200
## 117 0.5 1000 250 250 0.5 0.8 200
## 118 0.5 1000 250 250 0.5 0.8 200
## 119 0.5 1000 250 250 0.5 0.8 200
## 120 0.5 1000 250 250 0.5 0.8 200
## 121 0.5 1000 250 250 0.5 0.8 200
## 122 0.5 1000 250 250 0.5 0.8 200
## 123 0.5 1000 250 250 0.5 0.8 200
## 124 0.5 1000 250 250 0.5 0.8 200
## 125 0.5 1000 250 250 0.5 0.8 200
## 126 0.5 1000 250 250 0.5 0.8 200
## 127 0.5 1000 250 250 0.5 0.8 200
## 128 0.5 1000 250 250 0.5 0.8 200
## 129 0.5 1000 250 250 0.5 0.8 200
## 130 0.5 1000 250 250 0.5 0.8 200
## 131 0.5 1000 250 250 0.5 0.8 200
## 132 0.5 1000 250 250 0.5 0.8 200
## 133 0.5 1000 250 250 0.5 0.8 200
## 134 0.5 1000 250 250 0.5 0.8 200
## 135 0.5 1000 250 250 0.5 0.8 200
## 136 0.5 1000 250 250 0.5 0.8 200
## 137 0.5 1000 250 250 0.5 0.8 200
## 138 0.5 1000 250 250 0.5 0.8 200
## 139 0.5 1000 250 250 0.5 0.8 200
## 140 0.5 1000 250 250 0.5 0.8 200
## 141 0.5 1000 250 250 0.5 0.8 200
## 142 0.5 1000 250 250 0.5 0.8 200
## 143 0.5 1000 250 250 0.5 0.8 200
## 144 0.5 1000 250 250 0.5 0.8 200
## 145 0.5 1000 250 250 0.5 0.8 200
## 146 0.5 1000 250 250 0.5 0.8 200
## 147 0.5 1000 250 250 0.5 0.8 200
## 148 0.5 1000 250 250 0.5 0.8 200
## 149 0.5 1000 250 250 0.5 0.8 200
## 150 0.5 1000 250 250 0.5 0.8 200
## 151 0.5 1000 250 250 0.5 0.8 200
## 152 0.5 1000 250 250 0.5 0.8 200
## 153 0.5 1000 250 250 0.5 0.8 200
## 154 0.5 1000 250 250 0.5 0.8 200
## 155 0.5 1000 250 250 0.5 0.8 200
## 156 0.5 1000 250 250 0.5 0.8 200
## 157 0.5 1000 250 250 0.5 0.8 200
## 158 0.5 1000 250 250 0.5 0.8 200
## 159 0.5 1000 250 250 0.5 0.8 200
## 160 0.5 1000 250 250 0.5 0.8 200
## 161 0.5 1000 250 250 0.5 0.8 200
## 162 0.5 1000 250 250 0.5 0.8 200
## 163 0.5 1000 250 250 0.5 0.8 200
## 164 0.5 1000 250 250 0.5 0.8 200
## 165 0.5 1000 250 250 0.5 0.8 200
## 166 0.5 1000 250 250 0.5 0.8 200
## 167 0.5 1000 250 250 0.5 0.8 200
## 168 0.5 1000 250 250 0.5 0.8 200
## 169 0.5 1000 250 250 0.5 0.8 200
## 170 0.5 1000 250 250 0.5 0.8 200
## 171 0.5 1000 250 250 0.5 0.8 200
## 172 0.5 1000 250 250 0.5 0.8 200
## 173 0.5 1000 250 250 0.5 0.8 200
## 174 0.5 1000 250 250 0.5 0.8 200
## 175 0.5 1000 250 250 0.5 0.8 200
## 176 0.5 1000 250 250 0.5 0.8 200
## 177 0.5 1000 250 250 0.5 0.8 200
## 178 0.5 1000 250 250 0.5 0.8 200
## 179 0.5 1000 250 250 0.5 0.8 200
## 180 0.5 1000 250 250 0.5 0.8 200
## 181 0.5 1000 250 250 0.5 0.8 200
## 182 0.5 1000 250 250 0.5 0.8 200
## 183 0.5 1000 250 250 0.5 0.8 200
## 184 0.5 1000 250 250 0.5 0.8 200
## 185 0.5 1000 250 250 0.5 0.8 200
## 186 0.5 1000 250 250 0.5 0.8 200
## 187 0.5 1000 250 250 0.5 0.8 200
## 188 0.5 1000 250 250 0.5 0.8 200
## 189 0.5 1000 250 250 0.5 0.8 200
## 190 0.5 1000 250 250 0.5 0.8 200
## 191 0.5 1000 250 250 0.5 0.8 200
## 192 0.5 1000 250 250 0.5 0.8 200
## 193 0.5 1000 250 250 0.5 0.8 200
## 194 0.5 1000 250 250 0.5 0.8 200
## 195 0.5 1000 250 250 0.5 0.8 200
## 196 0.5 1000 250 250 0.5 0.8 200
## 197 0.5 1000 250 250 0.5 0.8 200
## 198 0.5 1000 250 250 0.5 0.8 200
## 199 0.5 1000 250 250 0.5 0.8 200
## 200 0.5 1000 250 250 0.5 0.8 200
## 201 0.5 1000 250 250 0.5 0.8 200
## 202 0.5 1000 250 250 0.5 0.8 200
## 203 0.5 1000 250 250 0.5 0.8 200
## 204 0.5 1000 250 250 0.5 0.8 200
## 205 0.5 1000 250 250 0.5 0.8 200
## 206 0.5 1000 250 250 0.5 0.8 200
## 207 0.5 1000 250 250 0.5 0.8 200
## 208 0.5 1000 250 250 0.5 0.8 200
## 209 0.5 1000 250 250 0.5 0.8 200
## 210 0.5 1000 250 250 0.5 0.8 200
## 211 0.5 1000 250 250 0.5 0.8 200
## 212 0.5 1000 250 250 0.5 0.8 200
## 213 0.5 1000 250 250 0.5 0.8 200
## 214 0.5 1000 250 250 0.5 0.8 200
## 215 0.5 1000 250 250 0.5 0.8 200
## 216 0.5 1000 250 250 0.5 0.8 200
## 217 0.5 1000 250 250 0.5 0.8 200
## 218 0.5 1000 250 250 0.5 0.8 200
## 219 0.5 1000 250 250 0.5 0.8 200
## 220 0.5 1000 250 250 0.5 0.8 200
## 221 0.5 1000 250 250 0.5 0.8 200
## 222 0.5 1000 250 250 0.5 0.8 200
## 223 0.5 1000 250 250 0.5 0.8 200
## 224 0.5 1000 250 250 0.5 0.8 200
## 225 0.5 1000 250 250 0.5 0.8 200
## 226 0.5 1000 250 250 0.5 0.8 200
## 227 0.5 1000 250 250 0.5 0.8 200
## 228 0.5 1000 250 250 0.5 0.8 200
## 229 0.5 1000 250 250 0.5 0.8 200
## 230 0.5 1000 250 250 0.5 0.8 200
## 231 0.5 1000 250 250 0.5 0.8 200
## 232 0.5 1000 250 250 0.5 0.8 200
## 233 0.5 1000 250 250 0.5 0.8 200
## 234 0.5 1000 250 250 0.5 0.8 200
## 235 0.5 1000 250 250 0.5 0.8 200
## 236 0.5 1000 250 250 0.5 0.8 200
## 237 0.5 1000 250 250 0.5 0.8 200
## 238 0.5 1000 250 250 0.5 0.8 200
## 239 0.5 1000 250 250 0.5 0.8 200
## 240 0.5 1000 250 250 0.5 0.8 200
## 241 0.5 1000 250 250 0.5 0.8 200
## 242 0.5 1000 250 250 0.5 0.8 200
## 243 0.5 1000 250 250 0.5 0.8 200
## 244 0.5 1000 250 250 0.5 0.8 200
## 245 0.5 1000 250 250 0.5 0.8 200
## 246 0.5 1000 250 250 0.5 0.8 200
## 247 0.5 1000 250 250 0.5 0.8 200
## 248 0.5 1000 250 250 0.5 0.8 200
## 249 0.5 1000 250 250 0.5 0.8 200
## 250 0.5 1000 250 250 0.5 0.8 200
## 251 0.5 1000 250 250 0.5 0.8 200
## 252 0.5 1000 250 250 0.5 0.8 200
## 253 0.5 1000 250 250 0.5 0.8 200
## 254 0.5 1000 250 250 0.5 0.8 200
## 255 0.5 1000 250 250 0.5 0.8 200
## 256 0.5 1000 250 250 0.5 0.8 200
## 257 0.5 1000 250 250 0.5 0.8 200
## 258 0.5 1000 250 250 0.5 0.8 200
## 259 0.5 1000 250 250 0.5 0.8 200
## 260 0.5 1000 250 250 0.5 0.8 200
## 261 0.5 1000 250 250 0.5 0.8 200
## 262 0.5 1000 250 250 0.5 0.8 200
## 263 0.5 1000 250 250 0.5 0.8 200
## 264 0.5 1000 250 250 0.5 0.8 200
## 265 0.5 1000 250 250 0.5 0.8 200
## 266 0.5 1000 250 250 0.5 0.8 200
## 267 0.5 1000 250 250 0.5 0.8 200
## 268 0.5 1000 250 250 0.5 0.8 200
## 269 0.5 1000 250 250 0.5 0.8 200
## 270 0.5 1000 250 250 0.5 0.8 200
## 271 0.5 1000 250 250 0.5 0.8 200
## 272 0.5 1000 250 250 0.5 0.8 200
## 273 0.5 1000 250 250 0.5 0.8 200
## 274 0.5 1000 250 250 0.5 0.8 200
## 275 0.5 1000 250 250 0.5 0.8 200
## 276 0.5 1000 250 250 0.5 0.8 200
## 277 0.5 1000 250 250 0.5 0.8 200
## 278 0.5 1000 250 250 0.5 0.8 200
## 279 0.5 1000 250 250 0.5 0.8 200
## 280 0.5 1000 250 250 0.5 0.8 200
## 281 0.5 1000 250 250 0.5 0.8 200
## 282 0.5 1000 250 250 0.5 0.8 200
## 283 0.5 1000 250 250 0.5 0.8 200
## 284 0.5 1000 250 250 0.5 0.8 200
## 285 0.5 1000 250 250 0.5 0.8 200
## 286 0.5 1000 250 250 0.5 0.8 200
## 287 0.5 1000 250 250 0.5 0.8 200
## 288 0.5 1000 250 250 0.5 0.8 200
## 289 0.5 1000 250 250 0.5 0.8 200
## 290 0.5 1000 250 250 0.5 0.8 200
## 291 0.5 1000 250 250 0.5 0.8 200
## 292 0.5 1000 250 250 0.5 0.8 200
## 293 0.5 1000 250 250 0.5 0.8 200
## 294 0.5 1000 250 250 0.5 0.8 200
## 295 0.5 1000 250 250 0.5 0.8 200
## 296 0.5 1000 250 250 0.5 0.8 200
## 297 0.5 1000 250 250 0.5 0.8 200
## 298 0.5 1000 250 250 0.5 0.8 200
## 299 0.5 1000 250 250 0.5 0.8 200
## 300 0.5 1000 250 250 0.5 0.8 200
## 301 0.5 1000 250 250 0.5 0.8 200
## 302 0.5 1000 250 250 0.5 0.8 200
## 303 0.5 1000 250 250 0.5 0.8 200
## 304 0.5 1000 250 250 0.5 0.8 200
## 305 0.5 1000 250 250 0.5 0.8 200
## 306 0.5 1000 250 250 0.5 0.8 200
## 307 0.5 1000 250 250 0.5 0.8 200
## 308 0.5 1000 250 250 0.5 0.8 200
## 309 0.5 1000 250 250 0.5 0.8 200
## 310 0.5 1000 250 250 0.5 0.8 200
## 311 0.5 1000 250 250 0.5 0.8 200
## 312 0.5 1000 250 250 0.5 0.8 200
## 313 0.5 1000 250 250 0.5 0.8 200
## 314 0.5 1000 250 250 0.5 0.8 200
## 315 0.5 1000 250 250 0.5 0.8 200
## 316 0.5 1000 250 250 0.5 0.8 200
## 317 0.5 1000 250 250 0.5 0.8 200
## 318 0.5 1000 250 250 0.5 0.8 200
## 319 0.5 1000 250 250 0.5 0.8 200
## 320 0.5 1000 250 250 0.5 0.8 200
## 321 0.5 1000 250 250 0.5 0.8 200
## 322 0.5 1000 250 250 0.5 0.8 200
## 323 0.5 1000 250 250 0.5 0.8 200
## 324 0.5 1000 250 250 0.5 0.8 200
## 325 0.5 1000 250 250 0.5 0.8 200
## 326 0.5 1000 250 250 0.5 0.8 200
## 327 0.5 1000 250 250 0.5 0.8 200
## 328 0.5 1000 250 250 0.5 0.8 200
## 329 0.5 1000 250 250 0.5 0.8 200
## 330 0.5 1000 250 250 0.5 0.8 200
## 331 0.5 1000 250 250 0.5 0.8 200
## 332 0.5 1000 250 250 0.5 0.8 200
## 333 0.5 1000 250 250 0.5 0.8 200
## 334 0.5 1000 250 250 0.5 0.8 200
## 335 0.5 1000 250 250 0.5 0.8 200
## 336 0.5 1000 250 250 0.5 0.8 200
## 337 0.5 1000 250 250 0.5 0.8 200
## 338 0.5 1000 250 250 0.5 0.8 200
## 339 0.5 1000 250 250 0.5 0.8 200
## 340 0.5 1000 250 250 0.5 0.8 200
## 341 0.5 1000 250 250 0.5 0.8 200
## 342 0.5 1000 250 250 0.5 0.8 200
## 343 0.5 1000 250 250 0.5 0.8 200
## 344 0.5 1000 250 250 0.5 0.8 200
## 345 0.5 1000 250 250 0.5 0.8 200
## 346 0.5 1000 250 250 0.5 0.8 200
## 347 0.5 1000 250 250 0.5 0.8 200
## 348 0.5 1000 250 250 0.5 0.8 200
## 349 0.5 1000 250 250 0.5 0.8 200
## 350 0.5 1000 250 250 0.5 0.8 200
## 351 0.5 1000 250 250 0.5 0.8 200
## 352 0.5 1000 250 250 0.5 0.8 200
## 353 0.5 1000 250 250 0.5 0.8 200
## 354 0.5 1000 250 250 0.5 0.8 200
## 355 0.5 1000 250 250 0.5 0.8 200
## 356 0.5 1000 250 250 0.5 0.8 200
## 357 0.5 1000 250 250 0.5 0.8 200
## 358 0.5 1000 250 250 0.5 0.8 200
## 359 0.5 1000 250 250 0.5 0.8 200
## 360 0.5 1000 250 250 0.5 0.8 200
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## 1282 0.5 1000 250 250 0.5 0.8 200
## 1283 0.5 1000 250 250 0.5 0.8 200
## 1284 0.5 1000 250 250 0.5 0.8 200
## 1285 0.5 1000 250 250 0.5 0.8 200
## 1286 0.5 1000 250 250 0.5 0.8 200
## 1287 0.5 1000 250 250 0.5 0.8 200
## 1288 0.5 1000 250 250 0.5 0.8 200
## 1289 0.5 1000 250 250 0.5 0.8 200
## 1290 0.5 1000 250 250 0.5 0.8 200
## 1291 0.5 1000 250 250 0.5 0.8 200
## 1292 0.5 1000 250 250 0.5 0.8 200
## 1293 0.5 1000 250 250 0.5 0.8 200
## 1294 0.5 1000 250 250 0.5 0.8 200
## 1295 0.5 1000 250 250 0.5 0.8 200
## 1296 0.5 1000 250 250 0.5 0.8 200
## 1297 0.5 1000 250 250 0.5 0.8 200
## 1298 0.5 1000 250 250 0.5 0.8 200
## 1299 0.5 1000 250 250 0.5 0.8 200
## 1300 0.5 1000 250 250 0.5 0.8 200
## 1301 0.5 1000 250 250 0.5 0.8 200
## 1302 0.5 1000 250 250 0.5 0.8 200
## 1303 0.5 1000 250 250 0.5 0.8 200
## 1304 0.5 1000 250 250 0.5 0.8 200
## 1305 0.5 1000 250 250 0.5 0.8 200
## 1306 0.5 1000 250 250 0.5 0.8 200
## 1307 0.5 1000 250 250 0.5 0.8 200
## 1308 0.5 1000 250 250 0.5 0.8 200
## 1309 0.5 1000 250 250 0.5 0.8 200
## 1310 0.5 1000 250 250 0.5 0.8 200
## 1311 0.5 1000 250 250 0.5 0.8 200
## 1312 0.5 1000 250 250 0.5 0.8 200
## 1313 0.5 1000 250 250 0.5 0.8 200
## 1314 0.5 1000 250 250 0.5 0.8 200
## 1315 0.5 1000 250 250 0.5 0.8 200
## 1316 0.5 1000 250 250 0.5 0.8 200
## 1317 0.5 1000 250 250 0.5 0.8 200
## 1318 0.5 1000 250 250 0.5 0.8 200
## 1319 0.5 1000 250 250 0.5 0.8 200
## 1320 0.5 1000 250 250 0.5 0.8 200
## 1321 0.5 1000 250 250 0.5 0.8 200
## 1322 0.5 1000 250 250 0.5 0.8 200
## 1323 0.5 1000 250 250 0.5 0.8 200
## 1324 0.5 1000 250 250 0.5 0.8 200
## 1325 0.5 1000 250 250 0.5 0.8 200
## 1326 0.5 1000 250 250 0.5 0.8 200
## 1327 0.5 1000 250 250 0.5 0.8 200
## 1328 0.5 1000 250 250 0.5 0.8 200
## 1329 0.5 1000 250 250 0.5 0.8 200
## 1330 0.5 1000 250 250 0.5 0.8 200
## 1331 0.5 1000 250 250 0.5 0.8 200
## 1332 0.5 1000 250 250 0.5 0.8 200
## 1333 0.5 1000 250 250 0.5 0.8 200
## 1334 0.5 1000 250 250 0.5 0.8 200
## 1335 0.5 1000 250 250 0.5 0.8 200
## 1336 0.5 1000 250 250 0.5 0.8 200
## 1337 0.5 1000 250 250 0.5 0.8 200
## 1338 0.5 1000 250 250 0.5 0.8 200
## 1339 0.5 1000 250 250 0.5 0.8 200
## 1340 0.5 1000 250 250 0.5 0.8 200
## 1341 0.5 1000 250 250 0.5 0.8 200
## 1342 0.5 1000 250 250 0.5 0.8 200
## 1343 0.5 1000 250 250 0.5 0.8 200
## 1344 0.5 1000 250 250 0.5 0.8 200
## 1345 0.5 1000 250 250 0.5 0.8 200
## 1346 0.5 1000 250 250 0.5 0.8 200
## 1347 0.5 1000 250 250 0.5 0.8 200
## 1348 0.5 1000 250 250 0.5 0.8 200
## 1349 0.5 1000 250 250 0.5 0.8 200
## 1350 0.5 1000 250 250 0.5 0.8 200
## 1351 0.5 1000 250 250 0.5 0.8 200
## 1352 0.5 1000 250 250 0.5 0.8 200
## 1353 0.5 1000 250 250 0.5 0.8 200
## 1354 0.5 1000 250 250 0.5 0.8 200
## 1355 0.5 1000 250 250 0.5 0.8 200
## 1356 0.5 1000 250 250 0.5 0.8 200
## 1357 0.5 1000 250 250 0.5 0.8 200
## 1358 0.5 1000 250 250 0.5 0.8 200
## 1359 0.5 1000 250 250 0.5 0.8 200
## 1360 0.5 1000 250 250 0.5 0.8 200
## 1361 0.5 1000 250 250 0.5 0.8 200
## 1362 0.5 1000 250 250 0.5 0.8 200
## 1363 0.5 1000 250 250 0.5 0.8 200
## 1364 0.5 1000 250 250 0.5 0.8 200
## 1365 0.5 1000 250 250 0.5 0.8 200
## 1366 0.5 1000 250 250 0.5 0.8 200
## 1367 0.5 1000 250 250 0.5 0.8 200
## 1368 0.5 1000 250 250 0.5 0.8 200
## 1369 0.5 1000 250 250 0.5 0.8 200
## 1370 0.5 1000 250 250 0.5 0.8 200
## 1371 0.5 1000 250 250 0.5 0.8 200
## 1372 0.5 1000 250 250 0.5 0.8 200
## 1373 0.5 1000 250 250 0.5 0.8 200
## 1374 0.5 1000 250 250 0.5 0.8 200
## 1375 0.5 1000 250 250 0.5 0.8 200
## 1376 0.5 1000 250 250 0.5 0.8 200
## 1377 0.5 1000 250 250 0.5 0.8 200
## 1378 0.5 1000 250 250 0.5 0.8 200
## 1379 0.5 1000 250 250 0.5 0.8 200
## 1380 0.5 1000 250 250 0.5 0.8 200
## 1381 0.5 1000 250 250 0.5 0.8 200
## 1382 0.5 1000 250 250 0.5 0.8 200
## 1383 0.5 1000 250 250 0.5 0.8 200
## 1384 0.5 1000 250 250 0.5 0.8 200
## 1385 0.5 1000 250 250 0.5 0.8 200
## 1386 0.5 1000 250 250 0.5 0.8 200
## 1387 0.5 1000 250 250 0.5 0.8 200
## 1388 0.5 1000 250 250 0.5 0.8 200
## 1389 0.5 1000 250 250 0.5 0.8 200
## 1390 0.5 1000 250 250 0.5 0.8 200
## 1391 0.5 1000 250 250 0.5 0.8 200
## 1392 0.5 1000 250 250 0.5 0.8 200
## 1393 0.5 1000 250 250 0.5 0.8 200
## 1394 0.5 1000 250 250 0.5 0.8 200
## 1395 0.5 1000 250 250 0.5 0.8 200
## 1396 0.5 1000 250 250 0.5 0.8 200
## 1397 0.5 1000 250 250 0.5 0.8 200
## 1398 0.5 1000 250 250 0.5 0.8 200
## 1399 0.5 1000 250 250 0.5 0.8 200
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## 1401 0.5 1000 250 250 0.5 0.8 200
## 1402 0.5 1000 250 250 0.5 0.8 200
## 1403 0.5 1000 250 250 0.5 0.8 200
## 1404 0.5 1000 250 250 0.5 0.8 200
## 1405 0.5 1000 250 250 0.5 0.8 200
## 1406 0.5 1000 250 250 0.5 0.8 200
## 1407 0.5 1000 250 250 0.5 0.8 200
## 1408 0.5 1000 250 250 0.5 0.8 200
## 1409 0.5 1000 250 250 0.5 0.8 200
## 1410 0.5 1000 250 250 0.5 0.8 200
## 1411 0.5 1000 250 250 0.5 0.8 200
## 1412 0.5 1000 250 250 0.5 0.8 200
## 1413 0.5 1000 250 250 0.5 0.8 200
## 1414 0.5 1000 250 250 0.5 0.8 200
## 1415 0.5 1000 250 250 0.5 0.8 200
## 1416 0.5 1000 250 250 0.5 0.8 200
## 1417 0.5 1000 250 250 0.5 0.8 200
## 1418 0.5 1000 250 250 0.5 0.8 200
## 1419 0.5 1000 250 250 0.5 0.8 200
## 1420 0.5 1000 250 250 0.5 0.8 200
## 1421 0.5 1000 250 250 0.5 0.8 200
## 1422 0.5 1000 250 250 0.5 0.8 200
## 1423 0.5 1000 250 250 0.5 0.8 200
## 1424 0.5 1000 250 250 0.5 0.8 200
## 1425 0.5 1000 250 250 0.5 0.8 200
## 1426 0.5 1000 250 250 0.5 0.8 200
## 1427 0.5 1000 250 250 0.5 0.8 200
## 1428 0.5 1000 250 250 0.5 0.8 200
## 1429 0.5 1000 250 250 0.5 0.8 200
## 1430 0.5 1000 250 250 0.5 0.8 200
## 1431 0.5 1000 250 250 0.5 0.8 200
## 1432 0.5 1000 250 250 0.5 0.8 200
## 1433 0.5 1000 250 250 0.5 0.8 200
## 1434 0.5 1000 250 250 0.5 0.8 200
## 1435 0.5 1000 250 250 0.5 0.8 200
## 1436 0.5 1000 250 250 0.5 0.8 200
## 1437 0.5 1000 250 250 0.5 0.8 200
## 1438 0.5 1000 250 250 0.5 0.8 200
## 1439 0.5 1000 250 250 0.5 0.8 200
## 1440 0.5 1000 250 250 0.5 0.8 200
## 1441 0.5 1000 250 250 0.5 0.8 200
## 1442 0.5 1000 250 250 0.5 0.8 200
## 1443 0.5 1000 250 250 0.5 0.8 200
## 1444 0.5 1000 250 250 0.5 0.8 200
## 1445 0.5 1000 250 250 0.5 0.8 200
## 1446 0.5 1000 250 250 0.5 0.8 200
## 1447 0.5 1000 250 250 0.5 0.8 200
## 1448 0.5 1000 250 250 0.5 0.8 200
## 1449 0.5 1000 250 250 0.5 0.8 200
## 1450 0.5 1000 250 250 0.5 0.8 200
## 1451 0.5 1000 250 250 0.5 0.8 200
## 1452 0.5 1000 250 250 0.5 0.8 200
## 1453 0.5 1000 250 250 0.5 0.8 200
## 1454 0.5 1000 250 250 0.5 0.8 200
## 1455 0.5 1000 250 250 0.5 0.8 200
## 1456 0.5 1000 250 250 0.5 0.8 200
## 1457 0.5 1000 250 250 0.5 0.8 200
## 1458 0.5 1000 250 250 0.5 0.8 200
## 1459 0.5 1000 250 250 0.5 0.8 200
## 1460 0.5 1000 250 250 0.5 0.8 200
## exaggeration_factor cluster
## 1 12 1
## 2 12 2
## 3 12 1
## 4 12 3
## 5 12 1
## 6 12 4
## 7 12 5
## 8 12 2
## 9 12 6
## 10 12 7
## 11 12 8
## 12 12 1
## 13 12 9
## 14 12 5
## 15 12 7
## 16 12 3
## 17 12 10
## 18 12 11
## 19 12 7
## 20 12 8
## 21 12 1
## 22 12 3
## 23 12 5
## 24 12 4
## 25 12 9
## 26 12 5
## 27 12 2
## 28 12 5
## 29 12 7
## 30 12 3
## 31 12 3
## 32 12 7
## 33 12 5
## 34 12 2
## 35 12 12
## 36 12 1
## 37 12 7
## 38 12 2
## 39 12 8
## 40 12 11
## 41 12 7
## 42 12 2
## 43 12 9
## 44 12 9
## 45 12 9
## 46 12 12
## 47 12 4
## 48 12 5
## 49 12 6
## 50 12 8
## 51 12 2
## 52 12 13
## 53 12 9
## 54 12 4
## 55 12 7
## 56 12 4
## 57 12 14
## 58 12 1
## 59 12 1
## 60 12 8
## 61 12 7
## 62 12 3
## 63 12 12
## 64 12 3
## 65 12 1
## 66 12 1
## 67 12 7
## 68 12 5
## 69 12 3
## 70 12 3
## 71 12 7
## 72 12 8
## 73 12 15
## 74 12 9
## 75 12 6
## 76 12 14
## 77 12 8
## 78 12 3
## 79 12 6
## 80 12 3
## 81 12 15
## 82 12 12
## 83 12 5
## 84 12 7
## 85 12 2
## 86 12 1
## 87 12 1
## 88 12 14
## 89 12 13
## 90 12 7
## 91 12 11
## 92 12 7
## 93 12 3
## 94 12 6
## 95 12 1
## 96 12 2
## 97 12 5
## 98 12 7
## 99 12 10
## 100 12 10
## 101 12 5
## 102 12 1
## 103 12 11
## 104 12 5
## 105 12 3
## 106 12 1
## 107 12 10
## 108 12 9
## 109 12 3
## 110 12 7
## 111 12 3
## 112 12 1
## 113 12 1
## 114 12 7
## 115 12 15
## 116 12 14
## 117 12 2
## 118 12 7
## 119 12 1
## 120 12 1
## 121 12 4
## 122 12 3
## 123 12 9
## 124 12 12
## 125 12 7
## 126 12 13
## 127 12 4
## 128 12 3
## 129 12 15
## 130 12 4
## 131 12 15
## 132 12 1
## 133 12 8
## 134 12 5
## 135 12 7
## 136 12 7
## 137 12 7
## 138 12 6
## 139 12 1
## 140 12 1
## 141 12 8
## 142 12 5
## 143 12 3
## 144 12 5
## 145 12 6
## 146 12 14
## 147 12 3
## 148 12 1
## 149 12 7
## 150 12 3
## 151 12 8
## 152 12 5
## 153 12 15
## 154 12 9
## 155 12 3
## 156 12 3
## 157 12 11
## 158 12 1
## 159 12 1
## 160 12 4
## 161 12 7
## 162 12 1
## 163 12 5
## 164 12 3
## 165 12 3
## 166 12 6
## 167 12 9
## 168 12 1
## 169 12 1
## 170 12 5
## 171 12 13
## 172 12 7
## 173 12 1
## 174 12 9
## 175 12 7
## 176 12 7
## 177 12 2
## 178 12 3
## 179 12 5
## 180 12 3
## 181 12 14
## 182 12 3
## 183 12 11
## 184 12 1
## 185 12 3
## 186 12 13
## 187 12 7
## 188 12 13
## 189 12 10
## 190 12 4
## 191 12 10
## 192 12 15
## 193 12 5
## 194 12 14
## 195 12 8
## 196 12 14
## 197 12 5
## 198 12 9
## 199 12 13
## 200 12 5
## 201 12 5
## 202 12 2
## 203 12 3
## 204 12 12
## 205 12 3
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## 207 12 7
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## 209 12 1
## 210 12 7
## 211 12 3
## 212 12 5
## 213 12 1
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## 215 12 2
## 216 12 2
## 217 12 5
## 218 12 3
## 219 12 2
## 220 12 12
## 221 12 5
## 222 12 1
## 223 12 1
## 224 12 9
## 225 12 5
## 226 12 14
## 227 12 1
## 228 12 14
## 229 12 8
## 230 12 12
## 231 12 9
## 232 12 1
## 233 12 14
## 234 12 9
## 235 12 1
## 236 12 14
## 237 12 5
## 238 12 4
## 239 12 5
## 240 12 3
## 241 12 5
## 242 12 3
## 243 12 3
## 244 12 1
## 245 12 1
## 246 12 2
## 247 12 6
## 248 12 7
## 249 12 1
## 250 12 2
## 251 12 10
## 252 12 12
## 253 12 1
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## 255 12 8
## 256 12 1
## 257 12 1
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## 259 12 4
## 260 12 11
## 261 12 9
## 262 12 1
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## 273 12 1
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## 276 12 3
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## 279 12 5
## 280 12 15
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## 283 12 12
## 284 12 5
## 285 12 12
## 286 12 14
## 287 12 3
## 288 12 8
## 289 12 8
## 290 12 3
## 291 12 1
## 292 12 3
## 293 12 3
## 294 12 15
## 295 12 7
## 296 12 7
## 297 12 3
## 298 12 15
## 299 12 2
## 300 12 2
## 301 12 7
## 302 12 1
## 303 12 5
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## 315 12 3
## 316 12 1
## 317 12 15
## 318 12 1
## 319 12 1
## 320 12 7
## 321 12 1
## 322 12 1
## 323 12 15
## 324 12 3
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## 339 12 7
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## 345 12 14
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## 348 12 7
## 349 12 14
## 350 12 1
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## 352 12 4
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## 422 12 2
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## 426 12 3
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## 428 12 8
## 429 12 5
## 430 12 7
## 431 12 14
## 432 12 3
## 433 12 14
## 434 12 1
## 435 12 14
## 436 12 1
## 437 12 3
## 438 12 3
## 439 12 3
## 440 12 10
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## 442 12 6
## 443 12 3
## 444 12 12
## 445 12 1
## 446 12 7
## 447 12 7
## 448 12 1
## 449 12 3
## 450 12 3
## 451 12 3
## 452 12 7
## 453 12 1
## 454 12 1
## 455 12 6
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## 457 12 3
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## 459 12 3
## 460 12 3
## 461 12 1
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## 463 12 9
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## 465 12 7
## 466 12 12
## 467 12 9
## 468 12 15
## 469 12 5
## 470 12 1
## 471 12 4
## 472 12 15
## 473 12 12
## 474 12 5
## 475 12 12
## 476 12 9
## 477 12 5
## 478 12 1
## 479 12 5
## 480 12 8
## 481 12 5
## 482 12 5
## 483 12 3
## 484 12 12
## 485 12 8
## 486 12 8
## 487 12 7
## 488 12 9
## 489 12 6
## 490 12 14
## 491 12 14
## 492 12 3
## 493 12 1
## 494 12 9
## 495 12 3
## 496 12 3
## 497 12 5
## 498 12 3
## 499 12 7
## 500 12 2
## 501 12 14
## 502 12 1
## 503 12 10
## 504 12 9
## 505 12 14
## 506 12 6
## 507 12 1
## 508 12 5
## 509 12 3
## 510 12 7
## 511 12 10
## 512 12 12
## 513 12 9
## 514 12 8
## 515 12 3
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## 517 12 15
## 518 12 1
## 519 12 1
## 520 12 3
## 521 12 11
## 522 12 7
## 523 12 3
## 524 12 1
## 525 12 1
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## 527 12 8
## 528 12 1
## 529 12 3
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## 531 12 7
## 532 12 3
## 533 12 11
## 534 12 11
## 535 12 1
## 536 12 3
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## 539 12 7
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## 542 12 1
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## 546 12 1
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## 549 12 9
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## 555 12 1
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## 563 12 8
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## 617 12 1
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## 633 12 7
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## 651 12 1
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## 669 12 8
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## 673 12 7
## 674 12 9
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## 676 12 14
## 677 12 6
## 678 12 3
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## 680 12 7
## 681 12 4
## 682 12 3
## 683 12 12
## 684 12 5
## 685 12 1
## 686 12 1
## 687 12 1
## 688 12 14
## 689 12 5
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## 691 12 12
## 692 12 1
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## 696 12 7
## 697 12 3
## 698 12 2
## 699 12 9
## 700 12 12
## 701 12 5
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## 703 12 1
## 704 12 6
## 705 12 4
## 706 12 11
## 707 12 7
## 708 12 12
## 709 12 1
## 710 12 7
## 711 12 3
## 712 12 3
## 713 12 12
## 714 12 7
## 715 12 15
## 716 12 7
## 717 12 3
## 718 12 2
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## 720 12 8
## 721 12 12
## 722 12 12
## 723 12 8
## 724 12 3
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## 729 12 6
## 730 12 13
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## 785 12 3
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## 790 12 15
## 791 12 12
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## 1460 12 9ggplot(tsne_df, aes(x=Y.1, y=Y.2, color=y)) +
geom_point() +
scale_color_gradientn(colours = heat.colors(10))
ggplot(data.frame(table(tsne_df$cluster)), aes(x=Var1, y=Freq)) +
geom_bar(stat = "identity") +
coord_flip()
ggplot(tsne_df, aes(x=Y.1, y=Y.2, color=cluster)) +
geom_point() +
scale_color_viridis() +
scale_fill_viridis(discrete = T) +
geom_point(data = data.frame(centroids), aes(x=X1, y=X2), color="black", fill="white", shape=21, size=8) +
geom_text(data = data.frame(centroids), aes(x=X1, y=X2, label=1:k), color="black")
fviz_silhouette(silhouette(cutree(hclust_avg, k = k), dist_mat))## cluster size ave.sil.width
## 1 1 241 0.32
## 2 2 71 0.48
## 3 3 240 0.19
## 4 4 39 0.50
## 5 5 175 0.52
## 6 6 42 0.83
## 7 7 152 0.17
## 8 8 104 0.52
## 9 9 105 0.32
## 10 10 35 0.57
## 11 11 37 0.85
## 12 12 77 0.60
## 13 13 21 0.90
## 14 14 66 0.72
## 15 15 55 0.56
Baselines
Sets up empty lists to store RMSE values for baseline models on the training and testing datasets.
Calculate performance metrics (MAE, MAPE, RMSE, MSE, R2) by converting predicted and actual values from transformed to original scale.
Focus on data structures and the metrics calculation function.
baselines_rmse <- list()
baselines_rmse_test <- list()
actual_metrics_test <- list()
metrics_fusion <- function(y_pred, y) {
y_pred_inv <- expm1(y_pred)
y_inv <- expm1(y)
a <- mae(y_pred_inv, y_inv)
b <- mape(y_pred_inv, y_inv)
c <- rmse(y_pred_inv, y_inv)
d <- mse(y_pred_inv, y_inv)
e <- R2(y_pred_inv, y_inv)
return(c("mae" = a, "mape" = b, "rmse" = c, "mse" = d, "r2" = e))
}Linear Regression
Evaluates the performance of a linear regression model for a regression problem.
Cross-validation used to train the model on the training and validation data.
Resulting model is applied to make predictions on the validation dataset.
Root mean squared error (RMSE) is calculated as a measure of prediction accuracy for the model on the validation data.
Trained linear regression model used to make predictions on the test dataset.
###3 RMSE is calculated by comparing the predicted values with the actual test values. #### Stores additional performance metrics (MAE, MAPE, RMSE, MSE, R2) for the linear regression model on the test data.
linreg_tc <- trainControl(method = "cv", number = 5)
linreg_cv <- caret::train(
SalePrice ~ .,
data = cbind(X_train_val, SalePrice = y_train_val),
trControl = linreg_tc,
method = "lm"
)## Warning in predict.lm(modelFit, newdata): prediction from a rank-deficient fit
## may be misleading
## Warning in predict.lm(modelFit, newdata): prediction from a rank-deficient fit
## may be misleading
## Warning in predict.lm(modelFit, newdata): prediction from a rank-deficient fit
## may be misleading
## Warning in predict.lm(modelFit, newdata): prediction from a rank-deficient fit
## may be misleading
## Warning in predict.lm(modelFit, newdata): prediction from a rank-deficient fit
## may be misleading# Validation predictions and metrics
score_val <- linreg_cv$results$RMSE
baselines_rmse$linear_regression <- score_val
# Test predictions and metrics
linreg <- lm(SalePrice ~ ., data = cbind(X_train_val, SalePrice = y_train_val))
y_pred_test <- predict(linreg, newdata = X_test)## Warning in predict.lm(linreg, newdata = X_test): prediction from a
## rank-deficient fit may be misleadingscore_test <- rmse(y_pred_test, y_test)
baselines_rmse_test$linear_regression <- score_test
actual_metrics_test$linear_regression <- metrics_fusion(y_pred_test, y_test)
# Display scores
score_val## [1] 0.119461score_test## [1] 0.161295Lasso Regression
Lasso Regression applied to a regression problem.
Model trained by using cross-validation and selects the optimal regularization parameter.
Root mean squared error (RMSE) calculated for the validation set.
For the test set, target variable predicted by using the trained model, calculates the RMSE
Actual performance metrics (MAE, MAPE, RMSE, MSE, R2) computed for the Lasso Regression model on the test set
Displays the validation RMSE and test RMSE.
lasso <- cv.glmnet(x = as.matrix(X_train_val), y = y_train_val, alpha = 1)
# Validation predictions and metrics
score_val <- mean(sqrt(lasso$cvm))
baselines_rmse$lasso <- score_val
# Test predictions and metrics
y_pred_test <- predict(lasso, newx = as.matrix(X_test))
score_test <- rmse(y_pred_test, y_test)
baselines_rmse_test$lasso <- score_test
actual_metrics_test$lasso <- metrics_fusion(y_pred_test, y_test)
# Display scores
score_val## [1] 0.1493742score_test## [1] 0.1480355Ridge Regression
Ridge Regression applied to a regression problem.
Model trained by using cross-validation and selects the optimal regularization parameter.
Root mean squared error (RMSE) calculated for the validation set.
For the test set, it predicts the target variable using the trained model, calculates the RMSE.
Actual performance metrics (MAE, MAPE, RMSE, MSE, R2) computed for the Ridge Regression model on the test set.
Validation RMSE and test RMSE dsiplayed.
ridge <- cv.glmnet(x = as.matrix(X_train_val), y = y_train_val, alpha = 0)
# Validation predictions and metrics
score_val <- mean(sqrt(ridge$cvm))
baselines_rmse$ridge <- score_val
# Test predictions and metrics
y_pred_test <- predict(ridge, newx = as.matrix(X_test))
score_test <- rmse(y_pred_test, y_test)
baselines_rmse_test$ridge <- score_test
actual_metrics_test$ridge <- metrics_fusion(y_pred_test, y_test)
# Display scores
score_val## [1] 0.2335508score_test## [1] 0.1440556Elastic Net
Elastic Net Regression applied to a regression problem.
Cross-validation peformed to select the optimal alpha parameter, which controls the balance between L1 (Lasso) and L2 (Ridge) regularization.
The root mean squared error (RMSE) calculated for the validation set.
For the test set, it predicts the target variable using the trained Elastic Net model with the selected alpha value, calculates the RMSE.
Actual performance metrics (MAE, MAPE, RMSE, MSE, R2) computed for the Elastic Net model on the test set.
Selected alpha, validation RMSE, and test RMSE.
results <- data.frame()
for (i in 0:20) {
elasticnet <- cv.glmnet(x = as.matrix(X_train_val), y = y_train_val, alpha = i/20)
row <- data.frame(alpha = i/20, rmse_val = mean(sqrt(elasticnet$cvm)))
results <- rbind(results, row)
}
best_alpha <- results$alpha[which.min(results$rmse_val)]
# Validation predictions and metrics
score_val <- min(results$rmse_val)
baselines_rmse$elasticnet <- score_val
# Test predictions and metrics
elasticnet <- cv.glmnet(x = as.matrix(X_train_val), y = y_train_val, alpha = best_alpha)
y_pred_test <- predict(elasticnet, newx = as.matrix(X_test))
score_test <- rmse(y_pred_test, y_test)
baselines_rmse_test$elasticnet <- score_test
actual_metrics_test$elasticnet <- metrics_fusion(y_pred_test, y_test)
# Display scores
best_alpha## [1] 1score_val## [1] 0.1478863score_test## [1] 0.1471193K-Nearest Neighbors Regression
K-Nearest Neighbors Regression applied to the data
Calculates the RMSE for validation and test sets, and stores the results.
Additional performance metrics computed and displays the RMSE values.
knn_tc <- trainControl(method = "cv", number = 5)
knn_cv <- caret::train(
SalePrice ~ .,
data = cbind(X_train_val, SalePrice = y_train_val),
trControl = knn_tc,
method = "knn"
)
# Validation predictions and metrics
score_val <- mean(knn_cv$results$RMSE)
baselines_rmse$knn <- score_val
# Test predictions and metrics
knn <- knnreg(x = X_train_val, y = y_train_val)
y_pred_test <- predict(knn, newdata = X_test)
score_test <- rmse(y_pred_test, y_test)
baselines_rmse_test$knn <- score_test
actual_metrics_test$knn <- metrics_fusion(y_pred_test, y_test)
# Display scores
score_val## [1] 0.1777406score_test## [1] 0.1793364Support Vector Regression
Support Vector Regression (SVR) applied to the data
Calculates the RMSE for validation and test sets, and stores the results.
Additional performance metrics computed and displays the RMSE values.
svr_tc <- trainControl(method = "cv", number = 5)
svr_cv <- caret::train(
SalePrice ~ .,
data = cbind(X_train_val, SalePrice = y_train_val),
trControl = svr_tc,
method = "svmLinear2"
)## Warning in svm.default(x = as.matrix(x), y = y, kernel = "linear", cost =
## param$cost, : Variable(s) 'Condition2PosA' and 'Condition2PosN' and
## 'Condition2RRAe' and 'Condition2RRNn' and 'RoofStyleShed' and 'RoofMatlClyTile'
## and 'Exterior1stAsphShn' and 'Exterior1stImStucc' and 'Exterior1stStone' and
## 'BsmtCondPo' and 'HeatingQCPo' and 'ElectricalMix' and 'FunctionalSev' and
## 'GarageQualPo' and 'SaleTypeConLw' and 'SaleTypeOth' constant. Cannot scale
## data.
## Warning in svm.default(x = as.matrix(x), y = y, kernel = "linear", cost =
## param$cost, : Variable(s) 'Condition2PosA' and 'Condition2PosN' and
## 'Condition2RRAe' and 'Condition2RRNn' and 'RoofStyleShed' and 'RoofMatlClyTile'
## and 'Exterior1stAsphShn' and 'Exterior1stImStucc' and 'Exterior1stStone' and
## 'BsmtCondPo' and 'HeatingQCPo' and 'ElectricalMix' and 'FunctionalSev' and
## 'GarageQualPo' and 'SaleTypeConLw' and 'SaleTypeOth' constant. Cannot scale
## data.
## Warning in svm.default(x = as.matrix(x), y = y, kernel = "linear", cost =
## param$cost, : Variable(s) 'Condition2PosA' and 'Condition2PosN' and
## 'Condition2RRAe' and 'Condition2RRNn' and 'RoofStyleShed' and 'RoofMatlClyTile'
## and 'Exterior1stAsphShn' and 'Exterior1stImStucc' and 'Exterior1stStone' and
## 'BsmtCondPo' and 'HeatingQCPo' and 'ElectricalMix' and 'FunctionalSev' and
## 'GarageQualPo' and 'SaleTypeConLw' and 'SaleTypeOth' constant. Cannot scale
## data.## Warning in svm.default(x = as.matrix(x), y = y, kernel = "linear", cost =
## param$cost, : Variable(s) 'Condition2Artery' and 'Condition2PosA' and
## 'Condition2PosN' and 'Condition2RRAe' and 'Condition2RRNn' and 'RoofStyleShed'
## and 'RoofMatlClyTile' and 'RoofMatlRoll' and 'Exterior1stAsphShn' and
## 'ExterCondEx' and 'BsmtCondPo' and 'HeatingQCPo' and 'ElectricalFuseP' and
## 'ElectricalMix' and 'FunctionalSev' and 'SaleTypeConLw' and 'SaleTypeOth'
## constant. Cannot scale data.
## Warning in svm.default(x = as.matrix(x), y = y, kernel = "linear", cost =
## param$cost, : Variable(s) 'Condition2Artery' and 'Condition2PosA' and
## 'Condition2PosN' and 'Condition2RRAe' and 'Condition2RRNn' and 'RoofStyleShed'
## and 'RoofMatlClyTile' and 'RoofMatlRoll' and 'Exterior1stAsphShn' and
## 'ExterCondEx' and 'BsmtCondPo' and 'HeatingQCPo' and 'ElectricalFuseP' and
## 'ElectricalMix' and 'FunctionalSev' and 'SaleTypeConLw' and 'SaleTypeOth'
## constant. Cannot scale data.
## Warning in svm.default(x = as.matrix(x), y = y, kernel = "linear", cost =
## param$cost, : Variable(s) 'Condition2Artery' and 'Condition2PosA' and
## 'Condition2PosN' and 'Condition2RRAe' and 'Condition2RRNn' and 'RoofStyleShed'
## and 'RoofMatlClyTile' and 'RoofMatlRoll' and 'Exterior1stAsphShn' and
## 'ExterCondEx' and 'BsmtCondPo' and 'HeatingQCPo' and 'ElectricalFuseP' and
## 'ElectricalMix' and 'FunctionalSev' and 'SaleTypeConLw' and 'SaleTypeOth'
## constant. Cannot scale data.## Warning in svm.default(x = as.matrix(x), y = y, kernel = "linear", cost =
## param$cost, : Variable(s) 'Condition2PosA' and 'Condition2PosN' and
## 'Condition2RRAe' and 'Condition2RRNn' and 'RoofStyleShed' and 'RoofMatlClyTile'
## and 'Exterior1stAsphShn' and 'ExterCondPo' and 'BsmtCondPo' and 'HeatingQCPo'
## and 'ElectricalMix' and 'FunctionalSev' and 'SaleTypeConLw' and 'SaleTypeOth'
## constant. Cannot scale data.
## Warning in svm.default(x = as.matrix(x), y = y, kernel = "linear", cost =
## param$cost, : Variable(s) 'Condition2PosA' and 'Condition2PosN' and
## 'Condition2RRAe' and 'Condition2RRNn' and 'RoofStyleShed' and 'RoofMatlClyTile'
## and 'Exterior1stAsphShn' and 'ExterCondPo' and 'BsmtCondPo' and 'HeatingQCPo'
## and 'ElectricalMix' and 'FunctionalSev' and 'SaleTypeConLw' and 'SaleTypeOth'
## constant. Cannot scale data.
## Warning in svm.default(x = as.matrix(x), y = y, kernel = "linear", cost =
## param$cost, : Variable(s) 'Condition2PosA' and 'Condition2PosN' and
## 'Condition2RRAe' and 'Condition2RRNn' and 'RoofStyleShed' and 'RoofMatlClyTile'
## and 'Exterior1stAsphShn' and 'ExterCondPo' and 'BsmtCondPo' and 'HeatingQCPo'
## and 'ElectricalMix' and 'FunctionalSev' and 'SaleTypeConLw' and 'SaleTypeOth'
## constant. Cannot scale data.## Warning in svm.default(x = as.matrix(x), y = y, kernel = "linear", cost =
## param$cost, : Variable(s) 'UtilitiesAllPub' and 'UtilitiesNoSeWa' and
## 'Condition2PosA' and 'Condition2PosN' and 'Condition2RRAe' and 'Condition2RRNn'
## and 'RoofStyleShed' and 'RoofMatlClyTile' and 'RoofMatlMetal' and
## 'Exterior1stAsphShn' and 'BsmtCondPo' and 'HeatingQCPo' and 'ElectricalMix' and
## 'FunctionalSev' and 'SaleTypeConLw' and 'SaleTypeCWD' and 'SaleTypeOth'
## constant. Cannot scale data.
## Warning in svm.default(x = as.matrix(x), y = y, kernel = "linear", cost =
## param$cost, : Variable(s) 'UtilitiesAllPub' and 'UtilitiesNoSeWa' and
## 'Condition2PosA' and 'Condition2PosN' and 'Condition2RRAe' and 'Condition2RRNn'
## and 'RoofStyleShed' and 'RoofMatlClyTile' and 'RoofMatlMetal' and
## 'Exterior1stAsphShn' and 'BsmtCondPo' and 'HeatingQCPo' and 'ElectricalMix' and
## 'FunctionalSev' and 'SaleTypeConLw' and 'SaleTypeCWD' and 'SaleTypeOth'
## constant. Cannot scale data.
## Warning in svm.default(x = as.matrix(x), y = y, kernel = "linear", cost =
## param$cost, : Variable(s) 'UtilitiesAllPub' and 'UtilitiesNoSeWa' and
## 'Condition2PosA' and 'Condition2PosN' and 'Condition2RRAe' and 'Condition2RRNn'
## and 'RoofStyleShed' and 'RoofMatlClyTile' and 'RoofMatlMetal' and
## 'Exterior1stAsphShn' and 'BsmtCondPo' and 'HeatingQCPo' and 'ElectricalMix' and
## 'FunctionalSev' and 'SaleTypeConLw' and 'SaleTypeCWD' and 'SaleTypeOth'
## constant. Cannot scale data.## Warning in svm.default(x = as.matrix(x), y = y, kernel = "linear", cost =
## param$cost, : Variable(s) 'Condition1RRNe' and 'Condition2PosA' and
## 'Condition2PosN' and 'Condition2RRAe' and 'Condition2RRNn' and 'RoofStyleShed'
## and 'RoofMatlClyTile' and 'Exterior1stAsphShn' and 'FoundationWood' and
## 'BsmtCondPo' and 'HeatingFloor' and 'HeatingQCPo' and 'ElectricalMix' and
## 'FunctionalSev' and 'SaleTypeConLw' and 'SaleTypeOth' and 'PoolArea' constant.
## Cannot scale data.
## Warning in svm.default(x = as.matrix(x), y = y, kernel = "linear", cost =
## param$cost, : Variable(s) 'Condition1RRNe' and 'Condition2PosA' and
## 'Condition2PosN' and 'Condition2RRAe' and 'Condition2RRNn' and 'RoofStyleShed'
## and 'RoofMatlClyTile' and 'Exterior1stAsphShn' and 'FoundationWood' and
## 'BsmtCondPo' and 'HeatingFloor' and 'HeatingQCPo' and 'ElectricalMix' and
## 'FunctionalSev' and 'SaleTypeConLw' and 'SaleTypeOth' and 'PoolArea' constant.
## Cannot scale data.
## Warning in svm.default(x = as.matrix(x), y = y, kernel = "linear", cost =
## param$cost, : Variable(s) 'Condition1RRNe' and 'Condition2PosA' and
## 'Condition2PosN' and 'Condition2RRAe' and 'Condition2RRNn' and 'RoofStyleShed'
## and 'RoofMatlClyTile' and 'Exterior1stAsphShn' and 'FoundationWood' and
## 'BsmtCondPo' and 'HeatingFloor' and 'HeatingQCPo' and 'ElectricalMix' and
## 'FunctionalSev' and 'SaleTypeConLw' and 'SaleTypeOth' and 'PoolArea' constant.
## Cannot scale data.## Warning in svm.default(x = as.matrix(x), y = y, kernel = "linear", cost =
## param$cost, : Variable(s) 'Condition2PosA' and 'Condition2PosN' and
## 'Condition2RRAe' and 'Condition2RRNn' and 'RoofStyleShed' and 'RoofMatlClyTile'
## and 'Exterior1stAsphShn' and 'BsmtCondPo' and 'HeatingQCPo' and 'ElectricalMix'
## and 'FunctionalSev' and 'SaleTypeConLw' and 'SaleTypeOth' constant. Cannot
## scale data.# Validation predictions and metrics
score_val <- mean(svr_cv$results$RMSE)
baselines_rmse$svr <- score_val
# Test predictions and metrics
svr <- e1071::svm(SalePrice ~ ., data = cbind(X_train_val, SalePrice = y_train_val))## Warning in svm.default(x, y, scale = scale, ..., na.action = na.action):
## Variable(s) 'Condition2PosA' and 'Condition2PosN' and 'Condition2RRAe' and
## 'Condition2RRNn' and 'RoofStyleShed' and 'RoofMatlClyTile' and
## 'Exterior1stAsphShn' and 'BsmtCondPo' and 'HeatingQCPo' and 'ElectricalMix' and
## 'FunctionalSev' and 'SaleTypeConLw' and 'SaleTypeOth' constant. Cannot scale
## data.y_pred_test <- predict(svr, newdata = X_test)
score_test <- rmse(y_pred_test, y_test)
baselines_rmse_test$svr <- score_test
actual_metrics_test$svr <- metrics_fusion(y_pred_test, y_test)
# Display scores
score_val## [1] 0.124865score_test## [1] 0.1267516Decision Tree
Decision Tree regression applied to the data.
Calculates the RMSE for validation and test sets, and stores the results.
Additional performance metrics computed and displays the RMSE values.
dt_tc <- trainControl(method = "cv", number = 5)
dt_cv <- caret::train(
SalePrice ~ .,
data = cbind(X_train_val, SalePrice = y_train_val),
trControl = dt_tc,
method = "rpart"
)## Warning in nominalTrainWorkflow(x = x, y = y, wts = weights, info = trainInfo,
## : There were missing values in resampled performance measures.# Validation predictions and metrics
score_val <- mean(dt_cv$results$RMSE, na.rm = TRUE)
baselines_rmse$decision_tree <- score_val
# Test predictions and metrics
dt <- caret::train(x = X_train_val, y = y_train_val, method = "rpart")## Warning in nominalTrainWorkflow(x = x, y = y, wts = weights, info = trainInfo,
## : There were missing values in resampled performance measures.y_pred_test <- predict(dt, newdata = X_test)
score_test <- rmse(y_pred_test, y_test)
baselines_rmse_test$decision_tree <- score_test
actual_metrics_test$decision_tree <- metrics_fusion(y_pred_test, y_test)
# Display scores
score_val## [1] 0.289205score_test## [1] 0.2626485Ensemble Learning
Empty lists initialized that will be used to store the RMSE values and actual performance metrics for ensemble learning models.
Empty lists will be populated with values in subsequent steps of the code.
ensemble_rmse <- list()
ensemble_actual_metrics <- list()
ensemble_rmse_test <- list()
ensemble_actual_metrics_test <- list()Random Forest
Random forest algorithm implemented for regression tasks using ensemble learning.
Rrandom forest model trained on the training and validation data.
Its performance is evaluated using root mean squared error (RMSE) on the validation and test datasets.
Calculate feature importance using the random forest model and creates a bar plot to visualize the top 30 important features.
rf_tc <- trainControl(method = "cv", number = 5)
rf_cv <- caret::train(
SalePrice ~ .,
data = cbind(X_train_val, SalePrice = y_train_val),
trControl = rf_tc,
method = "rf"
)
# Validation predictions and metrics
score_val <- mean(rf_cv$results$RMSE)
ensemble_rmse$random_forest <- score_val
# Test predictions and metrics
rf <- randomForest(x = X_train_val, y = y_train_val, proximity = T)
y_pred_test_rf <- predict(rf, newdata = X_test)
score_test <- rmse(y_pred_test_rf, y_test)
ensemble_rmse_test$random_forest <- score_test
ensemble_actual_metrics_test$random_forest <- metrics_fusion(y_pred_test_rf, y_test)
y_pred_train_rf <- predict(rf, newdata = X_train_val)
# Display scores
score_val## [1] 0.1627213score_test## [1] 0.1435882rf_df <- data.frame(rf$importance) %>%
mutate(Feature = rownames(rf$importance)) %>%
arrange(desc(IncNodePurity)) %>%
head(30)
rf_df## IncNodePurity Feature
## OverallQual 35.8200230 OverallQual
## GrLivArea 22.5369310 GrLivArea
## YearBuilt 15.5175623 YearBuilt
## TotalBsmtSF 9.2277186 TotalBsmtSF
## X1stFlrSF 7.5228946 X1stFlrSF
## GarageArea 7.1683823 GarageArea
## ExterQualTA 6.3994395 ExterQualTA
## FullBath 4.4304280 FullBath
## LotArea 3.8857608 LotArea
## BsmtFinSF1 3.2226996 BsmtFinSF1
## KitchenQualTA 3.0886205 KitchenQualTA
## GarageFinishUnf 2.6874279 GarageFinishUnf
## X2ndFlrSF 2.3344098 X2ndFlrSF
## YearRemodAdd 2.0607904 YearRemodAdd
## BsmtQualEx 1.8732206 BsmtQualEx
## LotFrontage 1.7545423 LotFrontage
## BsmtQualTA 1.4949112 BsmtQualTA
## Fireplaces 1.2870101 Fireplaces
## OverallCond 1.1575509 OverallCond
## BsmtUnfSF 1.0456659 BsmtUnfSF
## FoundationPConc 0.7169229 FoundationPConc
## KitchenQualEx 0.6838094 KitchenQualEx
## MSZoningRM 0.6426478 MSZoningRM
## MasVnrArea 0.6137453 MasVnrArea
## OpenPorchSF 0.5774658 OpenPorchSF
## BsmtFinType1Unf 0.5552275 BsmtFinType1Unf
## BsmtQualGd 0.5473481 BsmtQualGd
## MoSold 0.4738863 MoSold
## MSSubClass 0.4545181 MSSubClass
## KitchenQualGd 0.4520441 KitchenQualGdggplot(data = rf_df, aes(x = reorder(Feature, IncNodePurity), y = IncNodePurity)) +
geom_bar(stat = "identity") +
coord_flip()
Gradient-Boosted Trees
Gradient-Boosted Trees (GBT) using XGBoost, LightGBM, and CatBoost libraries implemented for regression tasks.
The models are trained on the training and validation data, and their performance is evaluated using RMSE on the validation and test datasets.
The best hyperparameters are determined through cross-validation, and the models are then used to make predictions on the test data.
The RMSE scores and other evaluation metrics are recorded for each model.
The feature importance of the GBT model is visualized using a bar chart.
Code snippet showcases the application of ensemble learning techniques for regression tasks using boosting algorithms.
dtrain_val <- xgb.DMatrix(data = as.matrix(X_train_val), label = y_train_val)
dtest <- xgb.DMatrix(data = as.matrix(X_test), label = y_test)
xgb_params = list(
eta = 0.01,
gamma = 0.0468,
max_depth = 6,
min_child_weight = 1.41,
subsample = 0.769,
colsample_bytree = 0.283
)
xgb_cv <- xgb.cv(
params = xgb_params,
data = dtrain_val,
nround = 10000,
nfold = 5,
prediction = F,
showsd = T,
metrics = "rmse",
verbose = 1,
print_every_n = 500,
early_stopping_rounds = 25
)## [1] train-rmse:11.418173+0.009312 test-rmse:11.418032+0.037707
## Multiple eval metrics are present. Will use test_rmse for early stopping.
## Will train until test_rmse hasn't improved in 25 rounds.
##
## [501] train-rmse:0.122416+0.000718 test-rmse:0.151194+0.011679
## [1001] train-rmse:0.067115+0.000792 test-rmse:0.111984+0.015818
## [1501] train-rmse:0.063952+0.000693 test-rmse:0.110568+0.015565
## [2001] train-rmse:0.062368+0.000594 test-rmse:0.109887+0.015488
## [2501] train-rmse:0.061336+0.000637 test-rmse:0.109424+0.015445
## [3001] train-rmse:0.060585+0.000637 test-rmse:0.109157+0.015395
## Stopping. Best iteration:
## [3100] train-rmse:0.060437+0.000639 test-rmse:0.109116+0.015395# Validation predictions and metrics
score_val <- xgb_cv$evaluation_log$test_rmse_mean %>% min
ensemble_rmse$xgboost <- score_val
# Test predictions and metrics
xgb <- xgboost(
params = xgb_params,
data = dtrain_val,
nround = 10000,
eval_metric = "rmse",
verbose = 1,
print_every_n = 500,
early_stopping_rounds = 25
)## [1] train-rmse:11.418175
## Will train until train_rmse hasn't improved in 25 rounds.
##
## [501] train-rmse:0.121366
## [1001] train-rmse:0.066540
## [1501] train-rmse:0.063327
## [2001] train-rmse:0.061612
## Stopping. Best iteration:
## [2380] train-rmse:0.060862y_pred_test_xgb <- predict(xgb, newdata = dtest)
score_test <- rmse(y_pred_test_xgb, y_test)
ensemble_rmse_test$xgboost_test <- score_test
ensemble_actual_metrics_test$xgboost_test <- metrics_fusion(y_pred_test_xgb, y_test)
y_pred_train_xgb <- predict(xgb, newdata = dtrain_val)
# Display scores
score_val## [1] 0.1091156score_test## [1] 0.1351047xgb_df <- xgb.importance(model = xgb) %>% head(30)
xgb_df## Feature Gain Cover Frequency
## 1: OverallQual 0.204357375 0.048455667 0.036605446
## 2: GrLivArea 0.187873639 0.092621352 0.071564281
## 3: TotalBsmtSF 0.071215137 0.044733177 0.045471818
## 4: X1stFlrSF 0.066424282 0.025027221 0.037998733
## 5: GarageArea 0.061748139 0.035421587 0.039138695
## 6: YearBuilt 0.058576716 0.035625412 0.035718809
## 7: LotArea 0.039380593 0.070606809 0.060417986
## 8: Fireplaces 0.024034670 0.013081639 0.011652945
## 9: BsmtFinSF1 0.020379570 0.037358283 0.029259025
## 10: FullBath 0.018980583 0.007904839 0.005699810
## 11: YearRemodAdd 0.017155113 0.030636703 0.030398987
## 12: OverallCond 0.015373809 0.064598616 0.045851805
## 13: GarageFinishUnf 0.015123053 0.003157144 0.002659911
## 14: ExterQualTA 0.014625351 0.002904329 0.002659911
## 15: KitchenQualTA 0.013043303 0.003082766 0.003419886
## 16: BsmtQualEx 0.011601321 0.006710853 0.005446485
## 17: X2ndFlrSF 0.010247440 0.034935983 0.030778974
## 18: KitchenQualEx 0.007935387 0.010449434 0.006839772
## 19: BsmtUnfSF 0.007359055 0.019644450 0.030905636
## 20: LotFrontage 0.007015886 0.016424371 0.020012666
## 21: BsmtQualTA 0.006682741 0.001496148 0.001646612
## 22: CentralAirN 0.006523123 0.003310191 0.004939835
## 23: NeighborhoodOldTown 0.005628740 0.008750892 0.011019633
## 24: MSZoningRM 0.004493076 0.002718383 0.003799873
## 25: BsmtFinType1Unf 0.004017082 0.004583204 0.006333122
## 26: HalfBath 0.003984329 0.010759106 0.008866371
## 27: PavedDriveN 0.003835572 0.002180571 0.004053198
## 28: SaleConditionAbnorml 0.003579281 0.018882788 0.015072831
## 29: BsmtFullBath 0.003330441 0.008910376 0.006586447
## 30: OpenPorchSF 0.003188367 0.013043735 0.014946168
## Feature Gain Cover Frequencyggplot(data = xgb_df, aes(x = reorder(Feature, Gain), y = Gain)) +
geom_bar(stat = "identity") +
coord_flip()
objective_fn <- makeSingleObjectiveFunction(
fn = function(x) {
params = list(
booster = "gbtree",
eta = x["eta"],
gamma = x["gamma"],
max_depth = x["max_depth"],
min_child_weight = x["min_child_weight"],
subsample = x["subsample"],
colsample_bytree = x["colsample_bytree"],
max_delta_step = x["max_delta_step"]
)
cv <- xgb.cv(
params = params,
data = dtrain_val,
nround = 10000,
nfold = 5,
prediction = F,
showsd = T,
metrics = "rmse",
verbose = 1,
print_every_n = 500,
early_stopping_rounds = 25
)
cv$evaluation_log$test_rmse_mean %>% min
},
par.set = makeParamSet(
makeNumericParam("eta", lower = 0.005, upper = 0.01),
makeNumericParam("gamma", lower = 0.01, upper = 5),
makeIntegerParam("max_depth", lower = 2, upper = 10),
makeIntegerParam("min_child_weight", lower = 1, upper = 2000),
makeNumericParam("subsample", lower = 0.20, upper = 0.8),
makeNumericParam("colsample_bytree", lower = 0.20, upper = 0.8),
makeNumericParam("max_delta_step", lower = 0, upper = 5)
),
minimize = TRUE
)
#Train model
design <- generateDesign(n = 1000, par.set = getParamSet(objective_fn), fun = lhs::randomLHS)
control <- makeMBOControl() %>% setMBOControlTermination(., iters = 10)
#run <- mbo(
# fun = objective_fn,
# design = design,
# learner = makeLearner("regr.km", predict.type = "se", covtype = "matern3_2", control = list(trace = FALSE)),
# control = control,
# show.info = TRUE
#)# Best parameters
#run$xlgb_train_val <- lgb.Dataset(data = as.matrix(X_train_val), label = y_train_val)
lgb_test <- lgb.Dataset(data = as.matrix(X_test), label = y_test)
params <- list(
objective = "regression",
metric = "rmse",
boosting_type = "gbdt",
num_boost_round = 100,
num_leaves = 15,
learning_rate = 0.1,
feature_fraction = 0.9,
bagging_fraction = 0.8,
bagging_freq = 5
)
lgb_cv <- lgb.cv(
params = params,
data = lgb_train_val,
early_stopping_rounds = 25,
verbose = 0
)## [LightGBM] [Warning] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000624 seconds.
## You can set `force_row_wise=true` to remove the overhead.
## And if memory is not enough, you can set `force_col_wise=true`.
## [LightGBM] [Warning] Auto-choosing col-wise multi-threading, the overhead of testing was 0.001020 seconds.
## You can set `force_col_wise=true` to remove the overhead.
## [LightGBM] [Warning] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000579 seconds.
## You can set `force_row_wise=true` to remove the overhead.
## And if memory is not enough, you can set `force_col_wise=true`.
## [LightGBM] [Info] Start training from score 12.010789
## [LightGBM] [Info] Start training from score 12.038003
## [LightGBM] [Info] Start training from score 12.030342# Validation predictions and metrics
score_val <- min(unlist(lgb_cv$record_evals$valid$rmse$eval))
ensemble_rmse$lightgbm <- score_val
# Test predictions and metrics
lgb <- lgb.train(
params = params,
data = lgb_train_val,
verbose = 0
)## [LightGBM] [Warning] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000880 seconds.
## You can set `force_row_wise=true` to remove the overhead.
## And if memory is not enough, you can set `force_col_wise=true`.y_pred_test_lgb <- predict(lgb, data = as.matrix(X_test))
score_test <- rmse(y_pred_test_lgb, y_test)
ensemble_rmse_test$lightgbm <- score_test
ensemble_actual_metrics_test$lightgbm <- metrics_fusion(y_pred_test_lgb, y_test)
y_pred_train_lgb <- predict(lgb, data = as.matrix(X_train_val))
# Display scores
score_val## [1] 0.126261score_test## [1] 0.1336074lgb_df <- lgb.importance(model = lgb) %>% head(30)
lgb_df## Feature Gain Cover Frequency
## 1: OverallQual 0.454226756 0.050860957 0.039285714
## 2: GrLivArea 0.128875044 0.081404078 0.084285714
## 3: YearBuilt 0.080733547 0.046497964 0.047142857
## 4: X1stFlrSF 0.043955023 0.064228468 0.058571429
## 5: TotalBsmtSF 0.042628788 0.035034501 0.040714286
## 6: GarageArea 0.039530885 0.065209870 0.065714286
## 7: LotArea 0.024602838 0.057027899 0.066428571
## 8: BsmtFinSF1 0.022149980 0.029657467 0.040714286
## 9: OverallCond 0.018937937 0.043331803 0.040000000
## 10: YearRemodAdd 0.016657560 0.033957354 0.037857143
## 11: BsmtQualEx 0.012289128 0.004082281 0.004285714
## 12: Fireplaces 0.009999300 0.007211450 0.010000000
## 13: FullBath 0.008424059 0.003993063 0.002857143
## 14: KitchenQualTA 0.007947941 0.002942028 0.004285714
## 15: CentralAirN 0.007330142 0.006012443 0.006428571
## 16: MSZoningRM 0.006194982 0.002476352 0.004285714
## 17: BsmtFullBath 0.005677041 0.006273569 0.007857143
## 18: GarageFinishUnf 0.004913020 0.002987725 0.004285714
## 19: MSZoningRL 0.004418270 0.004265070 0.008571429
## 20: BsmtQualTA 0.003857842 0.003372887 0.001428571
## 21: X2ndFlrSF 0.003744204 0.018489948 0.015000000
## 22: MoSold 0.003404445 0.029378932 0.035000000
## 23: WoodDeckSF 0.002879812 0.014979969 0.025000000
## 24: NeighborhoodOldTown 0.002848057 0.008597597 0.007857143
## 25: BsmtFinType1GLQ 0.002843099 0.005618577 0.004285714
## 26: LotFrontage 0.002629261 0.016083230 0.025000000
## 27: BsmtUnfSF 0.002615394 0.019194990 0.030714286
## 28: HalfBath 0.002407552 0.005052802 0.004285714
## 29: BsmtFinType1Unf 0.002141156 0.002661316 0.003571429
## 30: OpenPorchSF 0.002121693 0.024289137 0.025000000
## Feature Gain Cover Frequencyggplot(data = xgb_df, aes(x = reorder(Feature, Gain), y = Gain)) +
geom_bar(stat = "identity") +
coord_flip()
train_val_pool <- catboost.load_pool(data = X_train_val, label = y_train_val)
test_pool <- catboost.load_pool(data = X_test, label = y_test)
params <- list(
loss_function = "RMSE",
iterations = 10000,
learning_rate = 0.01,
metric_period = 1000
)
catb_cv <- catboost.cv(
train_val_pool,
params = params,
fold_count = 5,
early_stopping_rounds = 25
)## Warning: Overfitting detector is active, thus evaluation metric is calculated on every iteration. 'metric_period' is ignored for evaluation metric.
## 0: learn: 11.9172012 test: 11.9175202 best: 11.9175202 (0) total: 105ms remaining: 17m 26s
## 1000: learn: 0.1295348 test: 0.2370490 best: 0.2370490 (1000) total: 32.4s remaining: 4m 51s
## 2000: learn: 0.0707314 test: 0.2081933 best: 0.2081933 (2000) total: 1m 4s remaining: 4m 15s
## 3000: learn: 0.0468866 test: 0.2008346 best: 0.2008346 (3000) total: 1m 39s remaining: 3m 52s
## 4000: learn: 0.0326615 test: 0.1978133 best: 0.1978133 (4000) total: 2m 12s remaining: 3m 18s
## 5000: learn: 0.0237753 test: 0.1965102 best: 0.1965102 (5000) total: 2m 52s remaining: 2m 51s
## 6000: learn: 0.0177702 test: 0.1958595 best: 0.1958590 (5994) total: 3m 33s remaining: 2m 22s
## 7000: learn: 0.0132868 test: 0.1955237 best: 0.1955213 (6994) total: 4m 9s remaining: 1m 46s
## Stopped by overfitting detector (25 iterations wait)# Validation predictions and metrics
score_val <- min(catb_cv$test.RMSE.mean)
ensemble_rmse$catboost <- score_val
# Test predictions and metrics
catb <- catboost.train(
params = params,
learn_pool = train_val_pool
)## 0: learn: 0.3940438 total: 4.23ms remaining: 42.3s
## 1000: learn: 0.0739695 total: 3.37s remaining: 30.3s
## 2000: learn: 0.0495301 total: 7.3s remaining: 29.2s
## 3000: learn: 0.0347174 total: 11.3s remaining: 26.4s
## 4000: learn: 0.0259864 total: 15s remaining: 22.5s
## 5000: learn: 0.0199218 total: 18.9s remaining: 18.9s
## 6000: learn: 0.0156171 total: 22.9s remaining: 15.3s
## 7000: learn: 0.0121744 total: 26.7s remaining: 11.4s
## 8000: learn: 0.0095347 total: 31.2s remaining: 7.79s
## 9000: learn: 0.0075367 total: 36s remaining: 3.99s
## 9999: learn: 0.0059626 total: 40.4s remaining: 0usy_pred_test_catboost <- catboost.predict(catb, test_pool)
score_test <- rmse(y_pred_test_catboost, y_test)
ensemble_rmse_test$catboost <- score_test
ensemble_actual_metrics_test$catboost <- metrics_fusion(y_pred_test_catboost, y_test)
y_pred_train_catboost <- catboost.predict(catb, train_val_pool)
# Display scores
score_val## [1] 0.1955237score_test## [1] 0.1307994catb_df <- data.frame(catboost.get_feature_importance(catb))
catb_df <- catb_df %>%
mutate(Feature = rownames(catb_df)) %>%
rename(Importance = catboost.get_feature_importance.catb.) %>%
arrange(desc(Importance)) %>%
head(30)
catb_df## Importance Feature
## OverallQual 18.6865285 OverallQual
## GrLivArea 15.9957967 GrLivArea
## YearBuilt 6.0437026 YearBuilt
## TotalBsmtSF 5.9438516 TotalBsmtSF
## LotArea 4.6002718 LotArea
## GarageArea 4.4567953 GarageArea
## X1stFlrSF 3.9975964 X1stFlrSF
## BsmtFinSF1 2.9055472 BsmtFinSF1
## Fireplaces 2.7871758 Fireplaces
## OverallCond 2.5896726 OverallCond
## YearRemodAdd 2.2410595 YearRemodAdd
## FullBath 1.9223412 FullBath
## X2ndFlrSF 1.2148459 X2ndFlrSF
## BsmtFullBath 1.1134079 BsmtFullBath
## LotFrontage 1.0256831 LotFrontage
## HalfBath 0.9762099 HalfBath
## ExterQualTA 0.9216750 ExterQualTA
## BsmtUnfSF 0.8596448 BsmtUnfSF
## BsmtQualEx 0.8233995 BsmtQualEx
## BsmtFinType1Unf 0.8202585 BsmtFinType1Unf
## WoodDeckSF 0.7339830 WoodDeckSF
## MoSold 0.6885107 MoSold
## KitchenQualGd 0.6724627 KitchenQualGd
## GarageFinishUnf 0.6692537 GarageFinishUnf
## SaleConditionAbnorml 0.6094765 SaleConditionAbnorml
## BsmtQualTA 0.5756826 BsmtQualTA
## HeatingQCEx 0.5728080 HeatingQCEx
## CentralAirY 0.5548040 CentralAirY
## KitchenQualEx 0.5465232 KitchenQualEx
## BsmtQualGd 0.5227769 BsmtQualGdggplot(data = catb_df, aes(x = reorder(Feature, Importance), y = Importance)) +
geom_bar(stat = "identity") +
coord_flip()
Association Rule Mining on Housing Characteristics
Code snippet performs association rule mining on housing characteristics using the Apriori algorithm.
Converts categorical data into transactions and applies the Apriori algorithm to find frequent itemsets.
Generate association rules using given support and confidence thresholds.
The code includes a dictionary to map column names and values to their corresponding descriptions for better rule interpretation.
Top ten association rules with their corresponding explanations displayed, including the antecedent (IF) and consequent (THEN) parts along with their descriptions and confidence percentages.
transactions <- transactions(categorical_data)## Warning: Column(s) 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,
## 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37
## not logical or factor. Applying default discretization (see '? discretizeDF').summary(transactions)## transactions as itemMatrix in sparse format with
## 1460 rows (elements/itemsets/transactions) and
## 218 columns (items) and a density of 0.1697248
##
## most frequent items:
## Utilities=AllPub Street=Pave Condition2=Norm RoofMatl=CompShg
## 1459 1454 1445 1434
## Heating=GasA (Other)
## 1428 46800
##
## element (itemset/transaction) length distribution:
## sizes
## 37
## 1460
##
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 37 37 37 37 37 37
##
## includes extended item information - examples:
## labels variables levels
## 1 MSZoning=C (all) MSZoning C (all)
## 2 MSZoning=FV MSZoning FV
## 3 MSZoning=RH MSZoning RH
##
## includes extended transaction information - examples:
## transactionID
## 1 1
## 2 2
## 3 3inspect(head(transactions, n = 1))## items transactionID
## [1] {MSZoning=RL,
## Street=Pave,
## LotShape=Reg,
## LandContour=Lvl,
## Utilities=AllPub,
## LotConfig=Inside,
## LandSlope=Gtl,
## Neighborhood=CollgCr,
## Condition1=Norm,
## Condition2=Norm,
## BldgType=1Fam,
## HouseStyle=2Story,
## RoofStyle=Gable,
## RoofMatl=CompShg,
## Exterior1st=VinylSd,
## MasVnrType=BrkFace,
## ExterQual=Gd,
## ExterCond=TA,
## Foundation=PConc,
## BsmtQual=Gd,
## BsmtCond=TA,
## BsmtExposure=No,
## BsmtFinType1=GLQ,
## BsmtFinType2=Unf,
## Heating=GasA,
## HeatingQC=Ex,
## CentralAir=Y,
## Electrical=SBrkr,
## KitchenQual=Gd,
## Functional=Typ,
## GarageType=Attchd,
## GarageFinish=RFn,
## GarageQual=TA,
## GarageCond=TA,
## PavedDrive=Y,
## SaleType=WD,
## SaleCondition=Normal} 1rules <- apriori(transactions, parameter = list(support = 0.95, confidence = 0.95))## Apriori
##
## Parameter specification:
## confidence minval smax arem aval originalSupport maxtime support minlen
## 0.95 0.1 1 none FALSE TRUE 5 0.95 1
## maxlen target ext
## 10 rules TRUE
##
## Algorithmic control:
## filter tree heap memopt load sort verbose
## 0.1 TRUE TRUE FALSE TRUE 2 TRUE
##
## Absolute minimum support count: 1387
##
## set item appearances ...[0 item(s)] done [0.00s].
## set transactions ...[218 item(s), 1460 transaction(s)] done [0.01s].
## sorting and recoding items ... [7 item(s)] done [0.00s].
## creating transaction tree ... done [0.00s].
## checking subsets of size 1 2 3 4 done [0.00s].
## writing ... [94 rule(s)] done [0.00s].
## creating S4 object ... done [0.00s].summary(rules)## set of 94 rules
##
## rule length distribution (lhs + rhs):sizes
## 1 2 3 4
## 7 28 39 20
##
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.000 2.000 3.000 2.766 3.000 4.000
##
## summary of quality measures:
## support confidence coverage lift
## Min. :0.9500 Min. :0.9534 Min. :0.9507 Min. :0.9996
## 1st Qu.:0.9562 1st Qu.:0.9793 1st Qu.:0.9678 1st Qu.:0.9998
## Median :0.9637 Median :0.9895 Median :0.9781 Median :1.0000
## Mean :0.9664 Mean :0.9871 Mean :0.9791 Mean :1.0000
## 3rd Qu.:0.9740 3rd Qu.:0.9958 3rd Qu.:0.9897 3rd Qu.:1.0000
## Max. :0.9993 Max. :0.9993 Max. :1.0000 Max. :1.0010
## count
## Min. :1387
## 1st Qu.:1396
## Median :1407
## Mean :1411
## 3rd Qu.:1422
## Max. :1459
##
## mining info:
## data ntransactions support confidence
## transactions 1460 0.95 0.95
## call
## apriori(data = transactions, parameter = list(support = 0.95, confidence = 0.95))con <- file("data_description.txt", open = "r")
column_dictionary <- list()
value_dictionary <- list()
repeat {
line <- readLines(con, n = 1)
if (length(line) == 0) {
break
}
first_character <- substr(line, 1, 1)
if (first_character == "") {
next
}
if (first_character != " ") {
column_name <- sub(":.*", "", line)
column_description <- trimws(sub(".*:", "", line))
column_dictionary[[column_name]] <- column_description
value_dictionary[[column_name]] <- list()
} else {
pairs <- unlist(strsplit(line, "\t"))
key <- trimws(pairs[1])
value <- trimws(pairs[2])
value_dictionary[[column_name]][[key]] <- value
}
}
close(con)rules_top_ten_df <- data.frame(
lhs = labels(lhs(rules)),
rhs = labels(rhs(rules)),
rules@quality
) %>% arrange(desc(lift)) %>% head(n = 20)for (i in 1:nrow(rules_top_ten_df)) {
row <- rules_top_ten_df[i, ]
explanation <- ""
lhs <- unlist(strsplit(gsub('^.|.$', '', row["lhs"]), ","))
for (i in 1:length(lhs)) {
pair <- unlist(strsplit(lhs[i], "="))
key <- pair[1]
value <- pair[2]
key_t <- column_dictionary[[key]]
value_t <- value_dictionary[[key]][[value]]
if (i == 1) {
explanation <- paste("IF", key_t, "=", value_t)
} else {
explanation <- paste(explanation, "AND", key_t, "=", value_t)
}
}
rhs <- unlist(strsplit(gsub('^.|.$', '', row["rhs"]), "="))
key <- rhs[1]
value <- rhs[2]
key_t <- column_dictionary[[key]]
value_t <- value_dictionary[[key]][[value]]
confidence_pct <- format(round(row["confidence"] * 100, 2), 2)
explanation <- paste(explanation, "THEN", key_t, "=", value_t, "(Confidence:", paste0(confidence_pct, "%)"))
print(explanation)
cat("\n")
}## [1] "IF Proximity to various conditions (if more than one is present) = Normal THEN Garage condition = Typical/Average (Confidence: 96.47%)"
##
## [1] "IF Garage condition = Typical/Average THEN Proximity to various conditions (if more than one is present) = Normal (Confidence: 99.08%)"
##
## [1] "IF Type of utilities available = All public Utilities (E,G,W,& S) AND Garage condition = Typical/Average THEN Proximity to various conditions (if more than one is present) = Normal (Confidence: 99.08%)"
##
## [1] "IF Type of utilities available = All public Utilities (E,G,W,& S) AND Proximity to various conditions (if more than one is present) = Normal THEN Garage condition = Typical/Average (Confidence: 96.47%)"
##
## [1] "IF Type of road access to property = Paved AND Garage condition = Typical/Average THEN Proximity to various conditions (if more than one is present) = Normal (Confidence: 99.07%)"
##
## [1] "IF Type of road access to property = Paved AND Type of utilities available = All public Utilities (E,G,W,& S) AND Garage condition = Typical/Average THEN Proximity to various conditions (if more than one is present) = Normal (Confidence: 99.07%)"
##
## [1] "IF Type of road access to property = Paved AND Proximity to various conditions (if more than one is present) = Normal THEN Garage condition = Typical/Average (Confidence: 96.46%)"
##
## [1] "IF Type of road access to property = Paved AND Type of utilities available = All public Utilities (E,G,W,& S) AND Proximity to various conditions (if more than one is present) = Normal THEN Garage condition = Typical/Average (Confidence: 96.45%)"
##
## [1] "IF Type of heating = Gas forced warm air furnace THEN Roof material = Standard (Composite) Shingle (Confidence: 98.25%)"
##
## [1] "IF Roof material = Standard (Composite) Shingle THEN Type of heating = Gas forced warm air furnace (Confidence: 97.84%)"
##
## [1] "IF Type of utilities available = All public Utilities (E,G,W,& S) AND Type of heating = Gas forced warm air furnace THEN Roof material = Standard (Composite) Shingle (Confidence: 98.25%)"
##
## [1] "IF Type of utilities available = All public Utilities (E,G,W,& S) AND Roof material = Standard (Composite) Shingle THEN Type of heating = Gas forced warm air furnace (Confidence: 97.84%)"
##
## [1] "IF Type of road access to property = Paved AND Type of heating = Gas forced warm air furnace THEN Roof material = Standard (Composite) Shingle (Confidence: 98.24%)"
##
## [1] "IF Type of road access to property = Paved AND Type of utilities available = All public Utilities (E,G,W,& S) AND Type of heating = Gas forced warm air furnace THEN Roof material = Standard (Composite) Shingle (Confidence: 98.24%)"
##
## [1] "IF Type of road access to property = Paved AND Roof material = Standard (Composite) Shingle THEN Type of heating = Gas forced warm air furnace (Confidence: 97.83%)"
##
## [1] "IF Type of road access to property = Paved AND Type of utilities available = All public Utilities (E,G,W,& S) AND Roof material = Standard (Composite) Shingle THEN Type of heating = Gas forced warm air furnace (Confidence: 97.83%)"
##
## [1] "IF Proximity to various conditions (if more than one is present) = Normal AND Type of heating = Gas forced warm air furnace THEN Roof material = Standard (Composite) Shingle (Confidence: 98.23%)"
##
## [1] "IF Type of utilities available = All public Utilities (E,G,W,& S) AND Proximity to various conditions (if more than one is present) = Normal AND Type of heating = Gas forced warm air furnace THEN Roof material = Standard (Composite) Shingle (Confidence: 98.23%)"
##
## [1] "IF Proximity to various conditions (if more than one is present) = Normal AND Roof material = Standard (Composite) Shingle THEN Type of heating = Gas forced warm air furnace (Confidence: 97.82%)"
##
## [1] "IF Type of utilities available = All public Utilities (E,G,W,& S) AND Proximity to various conditions (if more than one is present) = Normal AND Roof material = Standard (Composite) Shingle THEN Type of heating = Gas forced warm air furnace (Confidence: 97.81%)"Stacking
Stacking is performed by combining the predictions from different models (Random Forest, XGBoost, LightGBM, CatBoost) into a new dataset.
Linear regression model is trained on the stacked dataset to learn the relationship between ensemble predictions and the actual target values.
Model’s predictions on the test dataset are evaluated using root mean squared error (RMSE).
Metrics fusion function is applied to assess the performance of the stacking ensemble.
stacked_data <- data.frame(y = y_train_val, prediction_rf = y_pred_train_rf, prediction_xgb = y_pred_train_xgb, prediction_lgb = y_pred_train_lgb, prediction_catboost = y_pred_train_catboost)
stacked_data_test <- data.frame(y = y_test, prediction_rf = y_pred_test_rf, prediction_xgb = y_pred_test_xgb, prediction_lgb = y_pred_test_lgb, prediction_catboost = y_pred_test_catboost)
model_meta <- caret::train(y ~ ., data = stacked_data, method = "lm")
predictions_meta <- predict(model_meta, newdata = stacked_data_test)
ensemble_rmse_test$stacking_score <- rmse(predictions_meta, y_test)
ensemble_actual_metrics_test$stacking <- metrics_fusion(predictions_meta, y_test)Comparison
Compares the performance of different models and ensembles using the root mean squared error (RMSE) metric.
Bar charts created to display the RMSE values, with the x-axis representing the models and the y-axis representing the RMSE.
First set of plots focuses on the baseline models on both the training and test sets.
Second set focuses on the ensemble models on both the training and test sets.
Purpose is to compare the models’ performance and determine which ones have the lowest RMSE, indicating better predictive accuracy.
# Plot RMSE for baseline models
df <- data.frame(models = names(baselines_rmse), rmse = unlist(baselines_rmse))
df## models rmse
## linear_regression linear_regression 0.1194610
## lasso lasso 0.1493742
## ridge ridge 0.2335508
## elasticnet elasticnet 0.1478863
## knn knn 0.1777406
## svr svr 0.1248650
## decision_tree decision_tree 0.2892050ggplot(df, aes(x = models, y = rmse)) +
geom_bar(stat = "identity", fill = "steelblue") +
xlab("Models") +
ylab("RMSE") +
ylim(0, 0.35) +
ggtitle("Baseline RMSE") +
theme_minimal()
# Plot RMSE for ensemble models
df <- data.frame(models = names(ensemble_rmse), rmse = unlist(ensemble_rmse))
df## models rmse
## random_forest random_forest 0.1627213
## xgboost xgboost 0.1091156
## lightgbm lightgbm 0.1262610
## catboost catboost 0.1955237ggplot(df, aes(x = models, y = rmse)) +
geom_bar(stat = "identity", fill = "steelblue") +
xlab("Models") +
ylab("RMSE") +
ylim(0, 0.35) +
ggtitle("Ensemble RMSE") +
theme_minimal()
# Plot RMSE for baseline models on the test set
df <- data.frame(models = names(baselines_rmse_test), rmse = unlist(baselines_rmse_test))
df## models rmse
## linear_regression linear_regression 0.1612950
## lasso lasso 0.1480355
## ridge ridge 0.1440556
## elasticnet elasticnet 0.1471193
## knn knn 0.1793364
## svr svr 0.1267516
## decision_tree decision_tree 0.2626485ggplot(df, aes(x = models, y = rmse)) +
geom_bar(stat = "identity", fill = "steelblue") +
xlab("Models") +
ylab("RMSE") +
ylim(0, 0.35) +
ggtitle("Baseline RMSE") +
theme_minimal()
# Plot RMSE for ensemble models on the test set
df <- data.frame(models = names(ensemble_rmse_test), rmse = unlist(ensemble_rmse_test))
df## models rmse
## random_forest random_forest 0.1435882
## xgboost_test xgboost_test 0.1351047
## lightgbm lightgbm 0.1336074
## catboost catboost 0.1307994
## stacking_score stacking_score 0.1310475ggplot(df, aes(x = models, y = rmse)) +
geom_bar(stat = "identity", fill = "steelblue") +
xlab("Models") +
ylab("RMSE") +
ylim(0, 0.35) +
ggtitle("Ensemble RMSE") +
theme_minimal()
data.frame(t(data.frame(actual_metrics_test))) %>% arrange(desc(r2))## mae mape rmse mse r2
## svr 15705.43 0.08222700 31085.89 966332571 0.8407060
## knn 22612.07 0.12419763 38225.12 1461159938 0.7550270
## ridge 16739.70 0.08369617 41046.13 1684784791 0.7381262
## linear_regression 18470.01 0.09486984 48124.01 2315920621 0.7006933
## elasticnet 17306.11 0.08499196 45218.01 2044668646 0.6917430
## lasso 17431.81 0.08576208 45247.96 2047377440 0.6896186
## decision_tree 37446.16 0.20550054 55798.36 3113457487 0.4761366data.frame(t(data.frame(ensemble_actual_metrics_test))) %>% arrange(desc(r2))## mae mape rmse mse r2
## stacking 15761.98 0.08050219 32177.71 1035404809 0.8303333
## catboost 15735.51 0.08036705 32272.69 1041526458 0.8298829
## lightgbm 16416.50 0.08410440 32215.00 1037806124 0.8292566
## random_forest 17398.61 0.09047328 33335.24 1111238512 0.8116846
## xgboost_test 16823.60 0.08491487 34785.18 1210008624 0.8064798save(list=ls(), file="assignment_model")