# If the linear kernel function is the same as RBF with sigma = inf, then what is happening when the kernel scale is changed with a linear SVM?

So to clarify, I think that the linear cannot be better than rbf if you have the right parameters and that linear is just a worse version of rbf. Linear comes from rbf. Is this correct? Also, in Matlab I see sigma for kernel scale but not gamma. Are gamma and sigma the same?

I think that the linear cannot be better than rbf if you have the right parameters

Yes, that is shown in the linked paper.

and that linear is just a worse version of rbf. Linear comes from rbf. Is this correct?

Linear kernel is the simple case of not using the kernel trick and you can get to it as a special case of the RBF kernel.

Also, in Matlab I see sigma for kernel scale but not gamma. Are gamma and sigma the same?

The Gaussian (RBF) kernel should have 1 parameter (called gamma or scale). The linear kernel has no parameters.

• Re: the last point, there are unfortunately many parameterizations of the Gaussian RBF kernel in relatively widespread use: the ones I know of are all of the form $\exp( - A \lVert x - y \rVert^2 )$ where $A$ can be $\gamma$, $\frac{1}{2 \sigma^2}$, $\frac{1}{\sigma^2}$, $\frac{1}{\tau}$, among other variations. – Danica Aug 31 '17 at 20:29
• Thanks! Can we say that there is 1 real-valued parameter? – Matteo T. Aug 31 '17 at 20:51