Parameter selection for RBF and polynomial kernel of SVM - Is the best 'c' (Cost parameter) same for both kernels?

Question

I have read that Cost parameter is independent of kernel used and depends on training data. After performing parameter selection for RBF, I get the best combination of 'c' and Gamma 'g'. So can I use the same 'c' for Polynomial kernel and identify a good degree 'd' ? Or can I do better if I start a fresh grid search for 'c' and 'd' ?

Answer 1

You can do better. Changing the kernel is changing the type of solution and SVM can find and how well it might overfit your data, so you need a new C. Though keeping the old C might be an acceptable guess if you use a high degree polynomial.