How to Write Own RBF (Gaussian Kernel) For SVM

Hi guys,

To solve a non linear classification problem, I wanted to write my own gaussian kernel (RBF), but i think I did something wrong when I had implemented it in MATLAB.

I implemented the function in the image below:

Using Tylor Series Expansion, it yields:

And, I seperated the Gaussian Kernel like this:

   K(x, x') = phi(x)' * phi(x')

The implementation of this thought is:

function phi = gaussianKernel(x, Sigma2)

gamma   = 1 / (2 * Sigma2);
featDim = 10; % Length of Tylor Series; Gaussian Kernel Converge 0 so It doesn't have to Be Inf Dimension
phi     = []; % Kernel Output, The Dimension will be (#Sample) x (featDim*2)

      for k = 0 : (featDim - 1) 

          % Gaussian Kernel Trick Using Tylor Series Expansion
          phi = [phi, exp( -gamma .* (x(:, 1)).^2) * sqrt(gamma^2 * 2^k / factorial(k)) .* x(:, 1).^k, ...
              exp( -gamma .* (x(:, 2)).^2) * sqrt(gamma^2 * 2^k / factorial(k)) .* x(:, 2).^k];
      end

end

The code doesn' t look like nice due to wrap, so here is as image:

In my implementation, samples are two dim vectors, so the argument "x" is the samples of the classes and N x 2 dim.

The argument "Sigma2" is the variance of the gaussian kernel (RBF).

If you know about RBF (Gaussian Kernel) please let me know how I can make it right..

[Parth Joshi]

Can you post your whole code including kernel call to help us troubleshoot well?Also please post your error

Answer 1

[Mushfique Ahmed]

Hey I was looking to do the same thing? Did you figure it out how to implement the entire thing?