bsvkernel.m

Matlab codes for Hidden Sapce Support vector machines

function k = bsvkernel(u,v,kernel,kernelparam)
%  BSVKERNEL kernel for Support Vector Methods
%
%  Usage: k = svkernel(u,v,kernel kernelparam)
%
%  Parameters:       u,v -           - input parameters
%                    kernel          - kernel type
%                    kernelparam     - kernel parameter
%              
%
%  Values for ker: 'linear'  -
%                  'poly'    - kenelparam(1) is degree of polynomial
%                  'rbf'     - kenelparam(1) is width of rbfs (sigma)
%                  'sigmoid' - kenelparam(1) is scale, p2 is offset
%                  'spline'  -
%                  'bspline' - kenelparam(1) is degree of bspline
%                  'fourier' - kenelparam(1) is degree
%                  'erfb'    - kenelparam(1) is width of rbfs (sigma)
%                  'anova'   - kenelparam(1) is max order of terms
%              

  if (nargin < 1) % check correct number of arguments
     help svkernel
  else
     p2=-1;
    % could check for correct number of args in here
    % but will slow things down further
    switch lower(kernel)
      case 'linear'
        k = sum(u.*v,2) +1;
      case 'poly'
        k = (sum(u.*v,2) + 1).^kernelparam(1);
      case 'rbf'
        k = exp(-sum((u-v).^2,2)/2/(kernelparam(1)^2));
       case 'crbf'
        k = exp(-sum(conj(u-v).*(u-v),2)/2/(kernelparam(1)^2));
      case 'coswave'
        k = exp(-sum((u-v).^2,2)/2/(kernelparam(1)^2)).*prod(cos((u-v)/kernelparam),2);
      case 'wave2'
        tempx=sum((u-v).^2,2);
        k = exp(-tempx/kernelparam(1)^2).*prod(1-2*((u-v)/kernelparam(1)).^2,2);
      case 'wave4'
        tempx=sum((u-v).^2,2);
        k = exp(-tempx/kernelparam(1)^2).*prod(1-4*((u-v)/kernelparam(1)).^2+4/3*((u-v)/kernelparam(1)).^4,2);
      case 'wave6'
        tempx=sum((u-v).^2,2);
        k = exp(-tempx/kernelparam(1)^2).*prod(1-6*((u-v)/kernelparam(1)).^2+4*((u-v)/kernelparam(1)).^4-8/15*((u-v)/kernelparam(1)).^6,2);
      case 'cauchy'
          k = kernelparam(1).^2./( kernelparam(1).^2 + sum((u-v).^2,2));
      case 'erbf'
        k = exp(-sqrt(sum((u-v).^2,2))/kernelparam(1));
      case 'sinc'
        k = sinc((u-v)/pi/kernelparam(1));
      case 'cos'
        temp = sum(u.*v,2)./kernelparam(1);
        k = cos(temp);
      case 'sigmoid'
        k = tanh(kernelparam(1)*u*v'/length(u) + p2);
      case 'fourier'
        z = sin(kernelparam(1) + 1/2)*2*ones(length(u),1);
        i = find(u-v);
        z(i) = sin(kernelparam(1) + 1/2)*(u(i)-v(i))./sin((u(i)-v(i))/2);
        k = prod(z);
      case 'spline'
        z = 1 + u.*v + (1/2)*u.*v.*min(u,v) - (1/6)*(min(u,v)).^3;
        k = prod(z);
      case 'bspline'
        z = 0;
        for r = 0: 2*(kernelparam(1)+1)
          z = z + (-1)^r*binomial(2*(kernelparam(1)+1),r)*(max(0,u-v + kernelparam(1)+1 - r)).^(2*kernelparam(1) + 1);
        end
        k = prod(z);
      case 'anovaspline1'
        z = 1 + u.*v + u.*v.*min(u,v) - ((u+v)/2).*(min(u,v)).^2 + (1/3)*(min(u,v)).^3;
        k = prod(z); 
      case 'anovaspline2'
        z = 1 + u.*v + (u.*v).^2 + (u.*v).^2.*min(u,v) - u.*v.*(u+v).*(min(u,v)).^2 + (1/3)*(u.^2 + 4*u.*v + v.^2).*(min(u,v)).^3 - (1/2)*(u+v).*(min(u,v)).^4 + (1/5)*(min(u,v)).^5;
        k = prod(z);
      case 'anovaspline3'
        z = 1 + u.*v + (u.*v).^2 + (u.*v).^3 + (u.*v).^3.*min(u,v) - (3/2)*(u.*v).^2.*(u+v).*(min(u,v)).^2 + u.*v.*(u.^2 + 3*u.*v + v.^2).*(min(u,v)).^3 - (1/4)*(u.^3 + 9*u.^2.*v + 9*u.*v.^2 + v.^3).*(min(u,v)).^4 + (3/5)*(u.^2 + 3*u.*v + v.^2).*(min(u,v)).^5 - (1/2)*(u+v).*(min(u,v)).^6 + (1/7)*(min(u,v)).^7;
        k = prod(z);
      case 'anovabspline'
        z = 0;
        for r = 0: 2*(kernelparam(1)+1)
          z = z + (-1)^r*binomial(2*(kernelparam(1)+1),r)*(max(0,u-v + kernelparam(1)+1 - r)).^(2*kernelparam(1) + 1);
        end
        k = prod(1 + z);
      otherwise
        k = u*v';
    end

  end