Training an SVM with an RBF kernel model with
c = 5.5 and
gamma = 1.06, for a 5-class classification problem on the NSL-KDD train data-set with 122 features using one vs rest strategy takes $2162$ seconds. Also, considering binary classification (
c = 10,
gamma = 4), it takes $520.56$ seconds.
After dimensionality reduction, from 122 to 30, using a sparse auto-encoder, the training time falls dramatically, from $2162$ to $240$ and $520$ to $170$, while using the same hyperparameters for the RBF-kernel.
What is the reason for that? Is it not true that using kernel neutralized the effect of high dimensions?