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 ...
#separate predictors from response
glassX <- Glass[, -10]
#histograms
library(lattice)
for(i in 1:ncol(glassX)){
print(histogram(glassX[,i], xlab = names(glassX)[i], type = "count", main = paste("Histogram of", names(glassX)[i])))
}
#boxplots
par(mfrow = c(1, 3))
for(i in 1:ncol(glassX)){
boxplot(glassX[,i], main = names(glassX)[i], col = "blue")
}
par(mfrow = c(1, 1))
#correlation plot to understand relationships among predictors
library(corrplot)
## corrplot 0.95 loaded
glassCorr <- cor(glassX)
corrplot(glassCorr, order = "hclust", tl.cex = .75)
#It looks like most of the predictors have low correlation there are some pairs
#that do correlate though, such as Si-RI which have negative correlation, RI-Ca
#with positive correlation, and Mg-Al and Mg-Ba with negative correlation.
#
#There are even some with no correlation whatsoever such as Al-Si, RI-Ba, and K-Fe.
#scatter plot matrix colored by glass type
splom(glassX, groups = Glass$Type, auto.key = list(columns = 3), type = c("p", "g"))
#calculate skewness for each predictor
library(e1071)
skewValues <- apply(glassX, 2, skewness)
skewValues
## RI Na Mg Al Si K Ca
## 1.6027151 0.4478343 -1.1364523 0.8946104 -0.7202392 6.4600889 2.0184463
## Ba Fe
## 3.3686800 1.7298107
cat("\n")
#if max/min > 20 means it is likely, but not certainly skewed.
for(i in 1:ncol(glassX)){
if(min(glassX[,i])>0){ #division by zero
ratio <- max(glassX[,i])/min(glassX[,i])
cat(names(glassX)[i], ": max/min ratio =", round(ratio, 2), "\n")
} else{
cat(names(glassX)[i], ": contains zero as values\n")
}
}
## RI : max/min ratio = 1.02
## Na : max/min ratio = 1.62
## Mg : contains zero as values
## Al : max/min ratio = 12.07
## Si : max/min ratio = 1.08
## K : contains zero as values
## Ca : max/min ratio = 2.98
## Ba : contains zero as values
## Fe : contains zero as values
#None of the min/max ratios exceed 20, however we can see that Al has the highest min/max ration which means that the range
#of values is larger than the rest, alongside it being relatively uniform over that range.
#
#It seems that most of the elements are right skewed with the exception of Mg, which is left skewed.
#
#Elements which are significantly skewed are RI, Mg, K, Ca, Ba, and Fe. Where K is the most skewed with a skewness of 6.46.
#
#Elements which are relatively uniform are Na, Al, and Si. Where Na is the least skewed.
library(caret)
## Loading required package: ggplot2
##
## Attaching package: 'ggplot2'
## The following object is masked from 'package:e1071':
##
## element
#box-Cox transformations for predictors with strictly positive values
for(i in 1:ncol(glassX)){
if(min(glassX[,i]) > 0){ #all values must be > 0
cat("\n-----------------------------------------")
cat("\nBox-Cox for", names(glassX)[i], "\n")
bc <- BoxCoxTrans(glassX[,i])
print(bc)
transformed <- predict(bc, glassX[,i])
cat("Skewness before:", round(skewness(glassX[,i]), 3), "\n")
cat("Skewness after:", round(skewness(transformed), 3), "\n")
#histogram comparisons before and after transformation
print(histogram(glassX[,i], xlab = "Natural Units", type = "count",
main = paste("Original:", names(glassX)[i])))
print(histogram(transformed, xlab = "Box-Cox Units", type = "count",
main = paste("Box-Cox:", names(glassX)[i])))
} else {
cat("\n-----------------------------------------")
cat("\n", names(glassX)[i],
"contains zero or negative values\n")
}
}
##
## -----------------------------------------
## Box-Cox for RI
## Box-Cox Transformation
##
## 214 data points used to estimate Lambda
##
## Input data summary:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.511 1.517 1.518 1.518 1.519 1.534
##
## Largest/Smallest: 1.02
## Sample Skewness: 1.6
##
## Estimated Lambda: -2
##
## Skewness before: 1.603
## Skewness after: 1.566
##
## -----------------------------------------
## Box-Cox for Na
## Box-Cox Transformation
##
## 214 data points used to estimate Lambda
##
## Input data summary:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 10.73 12.91 13.30 13.41 13.82 17.38
##
## Largest/Smallest: 1.62
## Sample Skewness: 0.448
##
## Estimated Lambda: -0.1
## With fudge factor, Lambda = 0 will be used for transformations
##
## Skewness before: 0.448
## Skewness after: 0.034
##
## -----------------------------------------
## Mg contains zero or negative values
##
## -----------------------------------------
## Box-Cox for Al
## Box-Cox Transformation
##
## 214 data points used to estimate Lambda
##
## Input data summary:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.290 1.190 1.360 1.445 1.630 3.500
##
## Largest/Smallest: 12.1
## Sample Skewness: 0.895
##
## Estimated Lambda: 0.5
##
## Skewness before: 0.895
## Skewness after: 0.091
##
## -----------------------------------------
## Box-Cox for Si
## Box-Cox Transformation
##
## 214 data points used to estimate Lambda
##
## Input data summary:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 69.81 72.28 72.79 72.65 73.09 75.41
##
## Largest/Smallest: 1.08
## Sample Skewness: -0.72
##
## Estimated Lambda: 2
##
## Skewness before: -0.72
## Skewness after: -0.651
##
## -----------------------------------------
## K contains zero or negative values
##
## -----------------------------------------
## Box-Cox for Ca
## Box-Cox Transformation
##
## 214 data points used to estimate Lambda
##
## Input data summary:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 5.430 8.240 8.600 8.957 9.172 16.190
##
## Largest/Smallest: 2.98
## Sample Skewness: 2.02
##
## Estimated Lambda: -1.1
##
## Skewness before: 2.018
## Skewness after: -0.194
##
## -----------------------------------------
## Ba contains zero or negative values
##
## -----------------------------------------
## Fe contains zero or negative values
#As you can see in the output. BoxCox decreases the skewness of every element. Some decreases are very large,
#even overshooting as seen where Ca skewness goes from 2.018 (right) to -0.194 (left)
#
#Then some are barely changed at all, still improved but extremely minor. Such as RI and Si.
#
#
cat("\n-----------------------------------------\n")
##
## -----------------------------------------
#preprocess BoxCox, center, and scale to all predictors
glassPP <- preProcess(glassX, method = c("BoxCox", "center", "scale"))
glassPP
## Created from 214 samples and 9 variables
##
## Pre-processing:
## - Box-Cox transformation (5)
## - centered (9)
## - ignored (0)
## - scaled (9)
##
## Lambda estimates for Box-Cox transformation:
## -2, -0.1, 0.5, 2, -1.1
glassTransformed <- predict(glassPP, glassX)
#check near zero variance predictors
nearZeroVar(glassTransformed)
## integer(0)
#check highly correlated predictors
glassCorr2 <- cor(glassTransformed)
highCorr <- findCorrelation(glassCorr2, .75)
highCorr
## [1] 7
if(length(highCorr) > 0){
names(glassTransformed)[highCorr]
}
## [1] "Ca"
#correlation plot after transformation
corrplot(glassCorr2, order = "hclust", tl.cex = .75)
library(kernlab)
##
## Attaching package: 'kernlab'
## The following object is masked from 'package:ggplot2':
##
## alpha
set.seed(67)
sigDist <- sigest(Type~ ., data = Glass, frac = 1)
sigDist
## 90% 50% 10%
## 0.02176819 0.06906005 0.83586779
svmTuneGrid <- data.frame(sigma = as.vector(sigDist)[1], C = 2^(-2:10))
svmTuneGrid
## sigma C
## 1 0.02176819 0.25
## 2 0.02176819 0.50
## 3 0.02176819 1.00
## 4 0.02176819 2.00
## 5 0.02176819 4.00
## 6 0.02176819 8.00
## 7 0.02176819 16.00
## 8 0.02176819 32.00
## 9 0.02176819 64.00
## 10 0.02176819 128.00
## 11 0.02176819 256.00
## 12 0.02176819 512.00
## 13 0.02176819 1024.00
library(AppliedPredictiveModeling)
library(caret)
set.seed(67)
svmFit <- train(Type~ ., data = Glass, method = "svmRadial",
preProc = c("center", "scale"),tuneGrid = svmTuneGrid,
trControl = trainControl(method = "repeatedcv", repeats = 5))
plot(svmFit, scales = list(x = list(log = 2)))
