Ex.1

Use the svm() algorithm of the e1071 package to carry out the support vector machine for the PlantGrowth data set. Then, discuss the number of support vectors/samples. [Install the e1071 package in R if needed.]

Solution:

library(e1071)
## Warning: package 'e1071' was built under R version 4.0.5
plant_svm <- svm(group ~ ., data = PlantGrowth)
summary(plant_svm)
## 
## Call:
## svm(formula = group ~ ., data = PlantGrowth)
## 
## 
## Parameters:
##    SVM-Type:  C-classification 
##  SVM-Kernel:  radial 
##        cost:  1 
## 
## Number of Support Vectors:  29
## 
##  ( 10 9 10 )
## 
## 
## Number of Classes:  3 
## 
## Levels: 
##  ctrl trt1 trt2

When using the svm() algorithm on the PlantGrowth data set it shows that there are 29 support vectors.

Ex.2

Do a similar SVM analysis as that in the previous question using the iris data set. Discuss the number of support vectors/samples.

Solution:

iris_svm <- svm(Species ~ ., data = iris)
summary(iris_svm)
## 
## Call:
## svm(formula = Species ~ ., data = iris)
## 
## 
## Parameters:
##    SVM-Type:  C-classification 
##  SVM-Kernel:  radial 
##        cost:  1 
## 
## Number of Support Vectors:  51
## 
##  ( 8 22 21 )
## 
## 
## Number of Classes:  3 
## 
## Levels: 
##  setosa versicolor virginica

When using the svm() algorithm on the iris data set it shows that there are 51 support vectors.

Ex.3

Use the iris data set (or any other data set) to select 80% of the samples for the training svm(), then use the rest 20% for validation. Discuss your results.

Solution:

library(caret)
## Loading required package: lattice
## Loading required package: ggplot2
train <- createDataPartition(iris$Species, p = 0.80, list = FALSE)
validation <- iris[-train]
iris_dataset <- data.frame(iris[train])
svm(train ~ ., data = iris_dataset)
## 
## Call:
## svm(formula = train ~ ., data = iris_dataset)
## 
## 
## Parameters:
##    SVM-Type:  eps-regression 
##  SVM-Kernel:  radial 
##        cost:  1 
##       gamma:  0.02941176 
##     epsilon:  0.1 
## 
## 
## Number of Support Vectors:  120

Selecting 80% of the samples to train svm() gives us 120 support vectors.