HW 4
Christina Kasman
9/22/2020
- 3.1. The UC Irvine Machine Learning Repository6 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.
- (a) Using visualizations, explore the predictor variables to understand their distributions as well as the relationships between predictors.
- b) Do there appear to be any outliers in the data? Are any predictors skewed?
- (c) Are there any relevant transformations of one or more predictors that might improve the classification model?
- 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 environmental conditions (e.g., temperature, precipitation) and plant conditions (e.g., left spots, mold growth). The outcome labels consist of 19 distinct classes.
- (a) Investigate the frequency distributions for the categorical predictors. Are any of the distributions degenerate in the ways discussed earlier in this chapter?
- (b) 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?
- (c) Develop a strategy for handling missing data, either by eliminating predictors or imputation.
3.1. The UC Irvine Machine Learning Repository6 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.
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 ...head(Glass)## RI Na Mg Al Si K Ca Ba Fe Type
## 1 1.52101 13.64 4.49 1.10 71.78 0.06 8.75 0 0.00 1
## 2 1.51761 13.89 3.60 1.36 72.73 0.48 7.83 0 0.00 1
## 3 1.51618 13.53 3.55 1.54 72.99 0.39 7.78 0 0.00 1
## 4 1.51766 13.21 3.69 1.29 72.61 0.57 8.22 0 0.00 1
## 5 1.51742 13.27 3.62 1.24 73.08 0.55 8.07 0 0.00 1
## 6 1.51596 12.79 3.61 1.62 72.97 0.64 8.07 0 0.26 1predictors <-Glass[,1:9]
head(predictors)## RI Na Mg Al Si K Ca Ba Fe
## 1 1.52101 13.64 4.49 1.10 71.78 0.06 8.75 0 0.00
## 2 1.51761 13.89 3.60 1.36 72.73 0.48 7.83 0 0.00
## 3 1.51618 13.53 3.55 1.54 72.99 0.39 7.78 0 0.00
## 4 1.51766 13.21 3.69 1.29 72.61 0.57 8.22 0 0.00
## 5 1.51742 13.27 3.62 1.24 73.08 0.55 8.07 0 0.00
## 6 1.51596 12.79 3.61 1.62 72.97 0.64 8.07 0 0.26(a) Using visualizations, explore the predictor variables to understand their distributions as well as the relationships between predictors.
r <- cor(predictors, use="complete.obs")
round(r,2)## RI Na Mg Al Si K Ca Ba Fe
## RI 1.00 -0.19 -0.12 -0.41 -0.54 -0.29 0.81 0.00 0.14
## Na -0.19 1.00 -0.27 0.16 -0.07 -0.27 -0.28 0.33 -0.24
## Mg -0.12 -0.27 1.00 -0.48 -0.17 0.01 -0.44 -0.49 0.08
## Al -0.41 0.16 -0.48 1.00 -0.01 0.33 -0.26 0.48 -0.07
## Si -0.54 -0.07 -0.17 -0.01 1.00 -0.19 -0.21 -0.10 -0.09
## K -0.29 -0.27 0.01 0.33 -0.19 1.00 -0.32 -0.04 -0.01
## Ca 0.81 -0.28 -0.44 -0.26 -0.21 -0.32 1.00 -0.11 0.12
## Ba 0.00 0.33 -0.49 0.48 -0.10 -0.04 -0.11 1.00 -0.06
## Fe 0.14 -0.24 0.08 -0.07 -0.09 -0.01 0.12 -0.06 1.00library(ggplot2)
library(corrplot)## corrplot 0.84 loadedlibrary(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(tidyr)
corrplot(r)
boxplot(predictors)
predictors %>%
gather() %>%
ggplot(aes(value)) +
facet_wrap(~ key, scales = "free") +
geom_histogram()## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
b) Do there appear to be any outliers in the data? Are any predictors skewed?
All predictors appear the have outliers except for Mg. K, Ca, Ba, and Fe are all skewed . Mg does not have a normal distribution.
(c) Are there any relevant transformations of one or more predictors that might improve the classification model?
Using a log transformation or box cox transformation on the skewed and not normal distribution should improve the classification model, while removing or imputing values for outliers may help with values that are above or below the normal distribution.
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 environmental conditions (e.g., temperature, precipitation) and plant conditions (e.g., left spots, mold growth). The outcome labels consist of 19 distinct classes.
library(mlbench)
data("Soybean")
head(Soybean)## Class date plant.stand precip temp hail crop.hist area.dam
## 1 diaporthe-stem-canker 6 0 2 1 0 1 1
## 2 diaporthe-stem-canker 4 0 2 1 0 2 0
## 3 diaporthe-stem-canker 3 0 2 1 0 1 0
## 4 diaporthe-stem-canker 3 0 2 1 0 1 0
## 5 diaporthe-stem-canker 6 0 2 1 0 2 0
## 6 diaporthe-stem-canker 5 0 2 1 0 3 0
## sever seed.tmt germ plant.growth leaves leaf.halo leaf.marg leaf.size
## 1 1 0 0 1 1 0 2 2
## 2 2 1 1 1 1 0 2 2
## 3 2 1 2 1 1 0 2 2
## 4 2 0 1 1 1 0 2 2
## 5 1 0 2 1 1 0 2 2
## 6 1 0 1 1 1 0 2 2
## leaf.shread leaf.malf leaf.mild stem lodging stem.cankers canker.lesion
## 1 0 0 0 1 1 3 1
## 2 0 0 0 1 0 3 1
## 3 0 0 0 1 0 3 0
## 4 0 0 0 1 0 3 0
## 5 0 0 0 1 0 3 1
## 6 0 0 0 1 0 3 0
## fruiting.bodies ext.decay mycelium int.discolor sclerotia fruit.pods
## 1 1 1 0 0 0 0
## 2 1 1 0 0 0 0
## 3 1 1 0 0 0 0
## 4 1 1 0 0 0 0
## 5 1 1 0 0 0 0
## 6 1 1 0 0 0 0
## fruit.spots seed mold.growth seed.discolor seed.size shriveling roots
## 1 4 0 0 0 0 0 0
## 2 4 0 0 0 0 0 0
## 3 4 0 0 0 0 0 0
## 4 4 0 0 0 0 0 0
## 5 4 0 0 0 0 0 0
## 6 4 0 0 0 0 0 0(a) Investigate the frequency distributions for the categorical predictors. Are any of the distributions degenerate in the ways discussed earlier in this chapter?
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
##
##
## Soybean%>%
gather() %>%
ggplot(aes(value)) +
facet_wrap(~ key, scales = "free") +
geom_histogram(stat = "count")## Warning: attributes are not identical across measure variables;
## they will be dropped## Warning: Ignoring unknown parameters: binwidth, bins, pad
There are a few variables that are degenerate (skewed, outliers, etc…) including Shriveling, Sclerotia, roots, hail, mycelium, and int.discolor
table(Soybean$Class)##
## 2-4-d-injury alternarialeaf-spot
## 16 91
## anthracnose bacterial-blight
## 44 20
## bacterial-pustule brown-spot
## 20 92
## brown-stem-rot charcoal-rot
## 44 20
## cyst-nematode diaporthe-pod-&-stem-blight
## 14 15
## diaporthe-stem-canker downy-mildew
## 20 20
## frog-eye-leaf-spot herbicide-injury
## 91 8
## phyllosticta-leaf-spot phytophthora-rot
## 20 88
## powdery-mildew purple-seed-stain
## 20 20
## rhizoctonia-root-rot
## 20(c) Develop a strategy for handling missing data, either by eliminating predictors or imputation.
Since there is a large % of missing values, I would not opt to remove the data. In additiona the data appears to be missing not at random and is correlated with specific predictors. Instead I would recommend using a method to impute the missing values such as KNN. k neighbors are chosen based on some distance measure and their average is used as an imputation estimate.