Data 624 Assignment 4
John Kellogg
3/6/2021
Exercise 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)## Warning: package 'mlbench' was built under R version 3.6.3data(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 ...(a)
Using visualizations, explore the predictor variables to understand their distributions as well as the relationships between predictors.
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 1Glass_sub <- subset(Glass, select = -Type)
predictors <- colnames(Glass)
par(mfrow = c(3,3))
for(i in 1:9) {
hist(Glass_sub[,i],main = predictors[i])
}
- There is a lot of variation between the variables.
- Aluminum, Silicon, Sodium being the closest to normal
- Iron, Barium, Potassium appear to be the farthest from normal
- Magnesium is the only bipolar distribution
corrplot.mixed(cor(Glass_sub[,1:9]), lower.col = "black", number.cex = .7)
- There does seem to be relationship between some the variables.
- Calcium and the Refractive Index (RI) have the strongest postive relationship
- Magnesium & Barium, Magnesium & Calcium, Refractive Index & Silicon have the strongest negative relationship
(b)
Do there appear to be any outliers in the data? Are any predictors skewed?
Glass_gather <- Glass %>%
pivot_longer(-Type, names_to = "predictors", values_to = "measurement", values_drop_na = TRUE) %>%
mutate(predictors = as.factor(predictors))
par(mfrow = c(3,3))
for(i in 1:9) {
boxplot(Glass_sub[,i],main = predictors[i], horizontal = TRUE)
}
Glass_gather %>%
filter(predictors == 'Na'|predictors == 'K'|predictors == 'Ba'|predictors == 'Ca')%>%
ggplot(aes(x=Type, y=measurement, color=predictors))+
geom_jitter()+
scale_color_brewer(palette = "Set1") +
theme_light() 
- Seperated out Silicon to see the other elememts clearer
- There does seem to be outliers in most of the elements with the heaviest in Calcium, Potassium, Sodium, and Barium
- Appears most of the outliers are in Type 5 *Except for Calcium where type 2 holds a lot of outliers
par(mfrow = c(3,3))
for(i in 1:9) {
hist(Glass_sub[,i],main = predictors[i])
}
- Most elements have a stong left tails *Barium, Iron, & Potassium are ther strongest
- Magnesium is Bimodal
(c)
Are there any relevant transformations of one or more predictors that might improve the classification model?
glass_process <- preProcess(Glass, method=c('BoxCox', 'center', 'scale'))
glass_update<- predict(glass_process, Glass)
par(mfrow = c(3,3))
for(i in 1:9) {
hist(glass_update[,i],main = predictors[i])
}
par(mfrow = c(3,3))
for(i in 1:9) {
boxplot(glass_update[,i],main = predictors[i], horizontal = TRUE)
}
- BoxCox had the most effect on elements not too far from normal
- For items such as Iron, the skew is too far left tailed for the transform to have major effect.
- Looking at the data for Iron, there is a LOT of zero values which affected the transform.
Exercise 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?
data("Soybean")
Soybean = SoybeannearZeroVar(Soybean)## [1] 19 26 28names(Soybean[,nearZeroVar(Soybean)])## [1] "leaf.mild" "mycelium" "sclerotia"summary(Soybean[19])## leaf.mild
## 0 :535
## 1 : 20
## 2 : 20
## NA's:108summary(Soybean[26])## mycelium
## 0 :639
## 1 : 6
## NA's: 38summary(Soybean[28])## sclerotia
## 0 :625
## 1 : 20
## NA's: 38- all of these values have the ratio of most prevalent to second prevalent value under the 10% ratio.
(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?
Soybean %>%
group_by(Class)%>%
gg_miss_fct(Class)
- The Missing predictors to seem to be in specific variables.
- 2-4-d-injury being the one with the most missing.
(c)
Develop a strategy for handling missing data, either by eliminating predictors or imputation.
#copy dataframe
Soybean_update <- Soybean
#rewrite dataframe so I control the formating
fwrite(Soybean,"soybean.temp")
Soybean_update <- fread("soybean.temp",colClasses = "character")
#updating all columns but class to numberic
Soybean_update <- Soybean_update %>%
mutate_at(vars("date","plant.stand","precip","temp","hail","crop.hist","area.dam","sever","seed.tmt","germ","plant.growth","leaves","leaf.halo","leaf.marg","leaf.size","leaf.shread","leaf.malf","leaf.mild","stem","lodging","stem.cankers","canker.lesion","fruiting.bodies","ext.decay","mycelium","int.discolor","sclerotia","fruit.pods","fruit.spots","seed","mold.growth","seed.discolor","seed.size","shriveling","roots" ),as.numeric)
#setting all NA's to mean of column
Soybean_update <-Soybean_update %>%
mutate_all(~ifelse(is.na(.x), mean(.x, na.rm = TRUE), .x))
summary(Soybean_update)## Class date plant.stand precip
## Length:683 Min. :0.000 Min. :0.0000 Min. :0.000
## Class :character 1st Qu.:2.000 1st Qu.:0.0000 1st Qu.:1.000
## Mode :character Median :4.000 Median :0.0000 Median :2.000
## Mean :3.554 Mean :0.4529 Mean :1.597
## 3rd Qu.:5.000 3rd Qu.:1.0000 3rd Qu.:2.000
## Max. :6.000 Max. :1.0000 Max. :2.000
## temp hail crop.hist area.dam
## Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:1.000 1st Qu.:0.000 1st Qu.:1.000 1st Qu.:1.000
## Median :1.000 Median :0.000 Median :2.000 Median :1.000
## Mean :1.182 Mean :0.226 Mean :1.885 Mean :1.581
## 3rd Qu.:2.000 3rd Qu.:0.226 3rd Qu.:3.000 3rd Qu.:3.000
## Max. :2.000 Max. :1.000 Max. :3.000 Max. :3.000
## sever seed.tmt germ plant.growth
## Min. :0.0000 Min. :0.0000 Min. :0.000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:1.000 1st Qu.:0.0000
## Median :1.0000 Median :0.5196 Median :1.000 Median :0.0000
## Mean :0.7331 Mean :0.5196 Mean :1.049 Mean :0.3388
## 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:2.000 3rd Qu.:1.0000
## Max. :2.0000 Max. :2.0000 Max. :2.000 Max. :1.0000
## leaves leaf.halo leaf.marg leaf.size
## Min. :0.0000 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:1.0000 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:1.000
## Median :1.0000 Median :2.000 Median :0.000 Median :1.000
## Mean :0.8873 Mean :1.202 Mean :0.773 Mean :1.284
## 3rd Qu.:1.0000 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:2.000
## Max. :1.0000 Max. :2.000 Max. :2.000 Max. :2.000
## leaf.shread leaf.malf leaf.mild stem
## Min. :0.0000 Min. :0.00000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.00000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.00000 Median :0.0000 Median :1.0000
## Mean :0.1647 Mean :0.07513 Mean :0.1043 Mean :0.5562
## 3rd Qu.:0.1647 3rd Qu.:0.00000 3rd Qu.:0.0000 3rd Qu.:1.0000
## Max. :1.0000 Max. :1.00000 Max. :2.0000 Max. :1.0000
## lodging stem.cankers canker.lesion fruiting.bodies
## Min. :0.00000 Min. :0.00 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.00000 1st Qu.:0.00 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.00000 Median :0.00 Median :0.9798 Median :0.0000
## Mean :0.07473 Mean :1.06 Mean :0.9798 Mean :0.1802
## 3rd Qu.:0.00000 3rd Qu.:3.00 3rd Qu.:2.0000 3rd Qu.:0.1802
## Max. :1.00000 Max. :3.00 Max. :3.0000 Max. :1.0000
## ext.decay mycelium int.discolor sclerotia
## Min. :0.0000 Min. :0.000000 Min. :0.0000 Min. :0.00000
## 1st Qu.:0.0000 1st Qu.:0.000000 1st Qu.:0.0000 1st Qu.:0.00000
## Median :0.0000 Median :0.000000 Median :0.0000 Median :0.00000
## Mean :0.2496 Mean :0.009302 Mean :0.1302 Mean :0.03101
## 3rd Qu.:0.2496 3rd Qu.:0.000000 3rd Qu.:0.0000 3rd Qu.:0.00000
## Max. :2.0000 Max. :1.000000 Max. :2.0000 Max. :1.00000
## fruit.pods fruit.spots seed mold.growth
## Min. :0.0000 Min. :0.000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.000 Median :0.0000 Median :0.0000
## Mean :0.5042 Mean :1.021 Mean :0.1946 Mean :0.1134
## 3rd Qu.:1.0000 3rd Qu.:1.021 3rd Qu.:0.1946 3rd Qu.:0.0000
## Max. :3.0000 Max. :4.000 Max. :1.0000 Max. :1.0000
## seed.discolor seed.size shriveling roots
## Min. :0.0000 Min. :0.00000 Min. :0.00000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.0000
## Median :0.0000 Median :0.00000 Median :0.00000 Median :0.0000
## Mean :0.1109 Mean :0.09983 Mean :0.06586 Mean :0.1779
## 3rd Qu.:0.0000 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.00000 Max. :1.00000 Max. :2.0000