# Libraries
library(e1071)
library(caret)## Loading required package: lattice## Loading required package: ggplot2Use 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
# PlantGrowth datset
data(PlantGrowth)
head(PlantGrowth)## weight group
## 1 4.17 ctrl
## 2 5.58 ctrl
## 3 5.18 ctrl
## 4 6.11 ctrl
## 5 4.50 ctrl
## 6 4.61 ctrlsvm_pg <- svm(group ~ ., data = PlantGrowth)
summary(svm_pg)##
## 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 trt2It comes out that there are 29 support vectors out of 30 samples that are closer to the hyperplane and influence the orientation and position of the hyperplane. There are 3 classes.
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 datset
data("iris")
head(iris)## Sepal.Length Sepal.Width Petal.Length Petal.Width Species
## 1 5.1 3.5 1.4 0.2 setosa
## 2 4.9 3.0 1.4 0.2 setosa
## 3 4.7 3.2 1.3 0.2 setosa
## 4 4.6 3.1 1.5 0.2 setosa
## 5 5.0 3.6 1.4 0.2 setosa
## 6 5.4 3.9 1.7 0.4 setosasvm_iris <- svm(Species ~ ., data = iris)
summary(svm_iris)##
## 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 virginicaThere are 51 support vectors and 3 classes in this case out of 150 samples in the dataset. In this case there is very less data for support vectors as compared to PlantGrowth dataset.
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
set.seed(609)
# partitioning for training and validation
partition <- createDataPartition(iris$Species, p=0.80, list = FALSE)
training <- iris[partition,]
validation <- iris[-partition,]
svm_train_iris <- svm(Species ~ ., data = training)
summary(svm_train_iris)##
## Call:
## svm(formula = Species ~ ., data = training)
##
##
## Parameters:
## SVM-Type: C-classification
## SVM-Kernel: radial
## cost: 1
##
## Number of Support Vectors: 45
##
## ( 8 18 19 )
##
##
## Number of Classes: 3
##
## Levels:
## setosa versicolor virginicapred_valid <- predict(svm_train_iris, validation)
confusionMatrix(validation$Species, pred_valid)## Confusion Matrix and Statistics
##
## Reference
## Prediction setosa versicolor virginica
## setosa 10 0 0
## versicolor 0 9 1
## virginica 0 0 10
##
## Overall Statistics
##
## Accuracy : 0.9667
## 95% CI : (0.8278, 0.9992)
## No Information Rate : 0.3667
## P-Value [Acc > NIR] : 4.476e-12
##
## Kappa : 0.95
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: setosa Class: versicolor Class: virginica
## Sensitivity 1.0000 1.0000 0.9091
## Specificity 1.0000 0.9524 1.0000
## Pos Pred Value 1.0000 0.9000 1.0000
## Neg Pred Value 1.0000 1.0000 0.9500
## Prevalence 0.3333 0.3000 0.3667
## Detection Rate 0.3333 0.3000 0.3333
## Detection Prevalence 0.3333 0.3333 0.3333
## Balanced Accuracy 1.0000 0.9762 0.9545The accuracy of the model has comeout as 96.67%.Here the training model shows 45 support vectors.