R carriages unusually slow when tuning SVM with a linear core

Question

I have observed very strange behavior when configuring SVM parameters with caret. When preparing a single model without tuning SVM with a radial core takes longer than SVM with a linear core, as expected. However, when configuring SVMs with both cores on the same penalty grid, SVMs with a linear kernel take significantly longer than SVMs with a radial core. This behavior can be easily reproduced on both Windows and Linux with R 3.2 and caret6.0-47. Does anyone know why setting up a linear SVM takes much longer than the radial core SVM core?

SVM linear
   user  system elapsed 
   0.51    0.00    0.52 

SVM radial
   user  system elapsed 
   0.85    0.00    0.84 

SVM linear tuning
   user  system elapsed 
 129.98    0.02  130.08 

SVM radial tuning
   user  system elapsed 
   2.44    0.05    2.48 

Toy example code below:

library(data.table)
library(kernlab)
library(caret)

n <- 1000
p <- 10

dat <- data.table(y = as.factor(sample(c('p', 'n'), n, replace = T)))
dat[, (paste0('x', 1:p)) := lapply(1:p, function(x) rnorm(n, 0, 1))]
dat <- as.data.frame(dat)

sigmas <- sigest(as.matrix(dat[, -1]), na.action = na.omit, scaled = TRUE)
sigma  <- mean(as.vector(sigmas[-2]))

cat('\nSVM linear\n')
print(system.time(fit1 <- train(y ~ ., data = dat, method = 'svmLinear', tuneLength = 1,
                                 trControl = trainControl(method = 'cv', number = 3))))

cat('\nSVM radial\n')
print(system.time(fit2 <- train(y ~ ., data = dat, method = 'svmRadial', tuneLength = 1,
                                 trControl = trainControl(method = 'cv', number = 3))))

cat('\nSVM linear tuning\n')
print(system.time(fit3 <- train(y ~ ., data = dat, method = 'svmLinear',
                                 tuneGrid = expand.grid(C = 2 ^ seq(-5, 15, 5)),
                                 trControl = trainControl(method = 'cv', number = 3))))

cat('\nSVM radial tuning\n')
print(system.time(fit4 <- train(y ~ ., data = dat, method = 'svmRadial',
                                 tuneGrid = expand.grid(C = 2 ^ seq(-5, 15, 5), sigma = sigma),
                                 trControl = trainControl(method = 'cv', number = 3))))

Answer 1

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Answer 2

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