The RBF Kernel

Support Vector Machines in R

Kailash Awati

Instructor

RBF Kernel in a nutshell

Decreasing function of distance between two points in dataset.
Simulates k-NN algorithm.

Chapter 4.3 - RBF kernel - influence as a function of distance between points

Building an SVM using the RBF kernel

Build RBF kernel SVM for complex dataset

svm_model <- svm(y ~ ., 
                data = trainset, 
                type = "C-classification",
                kernel = "radial")

Calculate training/test accuracy and plot against training dataset.

pred_train <- predict(svm_model, trainset)
mean(pred_train == trainset$y)

0.93125

pred_test <- predict(svm_model, testset)
mean(pred_test == testset$y)

0.9416667

#plot decision boundary
plot(svm_model, trainset)

Chapter 4.3 - complex dataset, default RBF kernel, plot using svm.plot

Refining the decision boundary

Tune gamma and cost using tune.svm()

# Tune parameters
tune_out <- tune.svm(x = trainset[,-3],
                     y = trainset[,3],
                     gamma = 5 * 10 ^ (-2:2),
                     cost = c(0.01, 0.1, 1, 10, 100),
                     type = "C-classification",
                     kernel = "radial")

Print best parameters

# Print best values of cost and gamma
tune_out$best.parameters$cost

tune_out$best.parameters$gamma

The tuned model

Build tuned model using best.parameters

svm_model <- svm(y ~ ., data = trainset, 
              type = "C-classification", 
              kernel = "radial",
              cost = tune_out$best.parameters$cost,
              gamma = tune_out$best.parameters$gamma)

Calculate test accuracy

mean(pred_test == testset$y)

0.95

Plot decision boundary

plot(svm_model, trainset)

Chapter 4.3 - complex dataset, tuned RBF kernel, plot using svm.plot

Time to practice!

Support Vector Machines in R