DATA 624 HW4
Christopher Ayre
March 6, 2021
suppressPackageStartupMessages(library(dplyr))
suppressPackageStartupMessages(library(caret))
suppressPackageStartupMessages(library(mlbench))
suppressPackageStartupMessages(library(corrplot))Home Work #4
Question 3.1
3.1. The UC Irvine Machine Learning Repository contains a data set related to glass identification. The data consist of 214 glass samples labeled as one of seven class categories. There are nine predictors, including the refractive index and percentages of eight elements: Na, Mg, Al, Si, K, Ca, Ba, and Fe.
# loading the data
library(mlbench)
data(Glass)
str(Glass)## 'data.frame': 214 obs. of 10 variables:
## $ RI : num 1.52 1.52 1.52 1.52 1.52 ...
## $ Na : num 13.6 13.9 13.5 13.2 13.3 ...
## $ Mg : num 4.49 3.6 3.55 3.69 3.62 3.61 3.6 3.61 3.58 3.6 ...
## $ Al : num 1.1 1.36 1.54 1.29 1.24 1.62 1.14 1.05 1.37 1.36 ...
## $ Si : num 71.8 72.7 73 72.6 73.1 ...
## $ K : num 0.06 0.48 0.39 0.57 0.55 0.64 0.58 0.57 0.56 0.57 ...
## $ Ca : num 8.75 7.83 7.78 8.22 8.07 8.07 8.17 8.24 8.3 8.4 ...
## $ Ba : num 0 0 0 0 0 0 0 0 0 0 ...
## $ Fe : num 0 0 0 0 0 0.26 0 0 0 0.11 ...
## $ Type: Factor w/ 6 levels "1","2","3","5",..: 1 1 1 1 1 1 1 1 1 1 ...- Using visualizations, explore the predictor variables to understand their distributions as well as the relationships between predictors.
- Do there appear to be any outliers in the data? Are any predictors skewed?
- Are there any relevant transformations of one or more predictors that might improve the classification model?
X <- Glass[,1:9]
par(mfrow = c(3, 3))
for (i in 1:ncol(X)) {
hist(X[ ,i], xlab = names(X[i]), main = paste(names(X[i]), "Histogram"), col="steelblue")
}
pairs(X, main="Scatterplot Matrix")
(a) Looking at the Visualizations we can observe the distribution of each of our predicted variables. RI, Na, Al, and Si have relatively normal/symmetric distributions, the others are asymmetric
X <- Glass[,1:9]
par(mfrow = c(3, 3))
for (i in 1:ncol(X)) {
boxplot(X[ ,i], ylab = names(X[i]), horizontal=T,
main = paste(names(X[i]), "Boxplot"), col="steelblue")
}
for (i in 1:ncol(X)) {
d <- density(X[,i], na.rm = TRUE)
plot(d, main = paste(names(X[i]), "Density"))
polygon(d, col="steelblue")
}
(b) There appears to be outliers in all predictor viables except Mg. Mg is left skewed. K, Ba, Ca and Fe are right skewed.
(c)Spatial sign transformation makes all the samples equidistant from the center of the sphere - this solves our problem with outliers. box-cox transformations could also be used on our predictors that are too skewed.
3.2. The soybean data can also be found at the UC Irvine Machine Learning Repository. Data were collected to predict disease in 683 soybeans. The 35 predictors are mostly categorical and include information on the environmen- tal conditions (e.g., temperature, precipitation) and plant conditions (e.g., left spots, mold growth). The outcome labels consist of 19 distinct classes.
# Loading the data
data(Soybean)
summary(Soybean)## Class date plant.stand precip temp
## brown-spot : 92 5 :149 0 :354 0 : 74 0 : 80
## alternarialeaf-spot: 91 4 :131 1 :293 1 :112 1 :374
## frog-eye-leaf-spot : 91 3 :118 NA's: 36 2 :459 2 :199
## phytophthora-rot : 88 2 : 93 NA's: 38 NA's: 30
## anthracnose : 44 6 : 90
## brown-stem-rot : 44 (Other):101
## (Other) :233 NA's : 1
## hail crop.hist area.dam sever seed.tmt germ plant.growth
## 0 :435 0 : 65 0 :123 0 :195 0 :305 0 :165 0 :441
## 1 :127 1 :165 1 :227 1 :322 1 :222 1 :213 1 :226
## NA's:121 2 :219 2 :145 2 : 45 2 : 35 2 :193 NA's: 16
## 3 :218 3 :187 NA's:121 NA's:121 NA's:112
## NA's: 16 NA's: 1
##
##
## leaves leaf.halo leaf.marg leaf.size leaf.shread leaf.malf leaf.mild
## 0: 77 0 :221 0 :357 0 : 51 0 :487 0 :554 0 :535
## 1:606 1 : 36 1 : 21 1 :327 1 : 96 1 : 45 1 : 20
## 2 :342 2 :221 2 :221 NA's:100 NA's: 84 2 : 20
## NA's: 84 NA's: 84 NA's: 84 NA's:108
##
##
##
## stem lodging stem.cankers canker.lesion fruiting.bodies ext.decay
## 0 :296 0 :520 0 :379 0 :320 0 :473 0 :497
## 1 :371 1 : 42 1 : 39 1 : 83 1 :104 1 :135
## NA's: 16 NA's:121 2 : 36 2 :177 NA's:106 2 : 13
## 3 :191 3 : 65 NA's: 38
## NA's: 38 NA's: 38
##
##
## mycelium int.discolor sclerotia fruit.pods fruit.spots seed
## 0 :639 0 :581 0 :625 0 :407 0 :345 0 :476
## 1 : 6 1 : 44 1 : 20 1 :130 1 : 75 1 :115
## NA's: 38 2 : 20 NA's: 38 2 : 14 2 : 57 NA's: 92
## NA's: 38 3 : 48 4 :100
## NA's: 84 NA's:106
##
##
## mold.growth seed.discolor seed.size shriveling roots
## 0 :524 0 :513 0 :532 0 :539 0 :551
## 1 : 67 1 : 64 1 : 59 1 : 38 1 : 86
## NA's: 92 NA's:106 NA's: 92 NA's:106 2 : 15
## NA's: 31
##
##
## - Investigate the frequency distributions for the categorical predictors. Are any of the distributions degenerate in the ways discussed earlier in this chapter?
- Roughly 18 % of the data are missing. Are there particular predictors that are more likely to be missing? Is the pattern of missing data related to the classes?
- Develop a strategy for handling missing data, either by eliminating predictors or imputation.
X <- Soybean[,2:36]
par(mfrow = c(3, 6))
for (i in 1:ncol(X)) {
smoothScatter(X[ ,i], ylab = names(X[i]))
}
(a) mycelium and sclerotia reflect low frequencies - we see a solid color across each chart
library(VIM)## Loading required package: colorspace## Loading required package: grid## Loading required package: data.table##
## Attaching package: 'data.table'## The following objects are masked from 'package:dplyr':
##
## between, first, last## VIM is ready to use.
## Since version 4.0.0 the GUI is in its own package VIMGUI.
##
## Please use the package to use the new (and old) GUI.## Suggestions and bug-reports can be submitted at: https://github.com/alexkowa/VIM/issues##
## Attaching package: 'VIM'## The following object is masked from 'package:datasets':
##
## sleepaggr(Soybean, prop = c(T, T), bars=T, numbers=T, sortVars=T)
##
## Variables sorted by number of missings:
## Variable Count
## hail 0.177159590
## sever 0.177159590
## seed.tmt 0.177159590
## lodging 0.177159590
## germ 0.163982430
## leaf.mild 0.158125915
## fruiting.bodies 0.155197657
## fruit.spots 0.155197657
## seed.discolor 0.155197657
## shriveling 0.155197657
## leaf.shread 0.146412884
## seed 0.134699854
## mold.growth 0.134699854
## seed.size 0.134699854
## leaf.halo 0.122986823
## leaf.marg 0.122986823
## leaf.size 0.122986823
## leaf.malf 0.122986823
## fruit.pods 0.122986823
## precip 0.055636896
## stem.cankers 0.055636896
## canker.lesion 0.055636896
## ext.decay 0.055636896
## mycelium 0.055636896
## int.discolor 0.055636896
## sclerotia 0.055636896
## plant.stand 0.052708638
## roots 0.045387994
## temp 0.043923865
## crop.hist 0.023426061
## plant.growth 0.023426061
## stem 0.023426061
## date 0.001464129
## area.dam 0.001464129
## Class 0.000000000
## leaves 0.000000000library(dplyr)
Soybean %>%
mutate(Total = n()) %>%
filter(!complete.cases(.)) %>%
group_by(Class) %>%
mutate(Missing = n(), Proportion=Missing/Total) %>%
select(Class, Missing, Proportion) %>%
unique()## # A tibble: 5 × 3
## # Groups: Class [5]
## Class Missing Proportion
## <fct> <int> <dbl>
## 1 phytophthora-rot 68 0.0996
## 2 diaporthe-pod-&-stem-blight 15 0.0220
## 3 cyst-nematode 14 0.0205
## 4 2-4-d-injury 16 0.0234
## 5 herbicide-injury 8 0.0117(b) Several predictors variables have over 10% of their values missing. I believe the missing data is related to the classes - This is supported by the data mutation above reflecting classes that hold the most missing cases.
(c) For each variable missing less than 10% of data I would use KNN or mode imputation approaches. However, for the other variables I would use a tree-based modeling approach which is designed to handle such high levels of missing data, unlike other types of regression models.