Implementing SVM dual problem with CVX (polynomial kernel)

1

I’ve been trying to implement the soft-margin, polynomial kernel svm dual problem in svm. As people already know, the dual variable values I should be getting is 0, C (soft margin cost), or sth in between. When I do the original Kernel (x’x) I get these values, however if I use the polynomial or RBF kernel, the alphas are all in the 0 < alpha < C range. None of them are 0 or C. Does anyone know why? I’ve tried alternating the parameters, too. Just in case, here is my code:

cvx_begin
    variables alpha(m);
    minimize (0.5.*alpha'*Q*alpha - ones(m,1)'*alpha);
    subject to 
        alpha >= 0;
        alpha <= C;
        Y'*alpha == 0;
cvx_end

where Q is a matrix I calculate beforehand with the Kernel function.

2

My guess is that none are exactly 0 or C due to numerical inaccuracies. Are any alphas very close to 0 or C (like 1E-10 or C-1E-10)? If so, you should take these to be 0 or C respectively.