kernelmatrix.m

% With Fast Computation of the RBF kernel matrix
% To speed up the computation, we exploit a decomposition of the Euclidean distance (norm)
%
% Inputs:
%	ker:    'lin','poly','rbf','sam'
%	X:	data matrix with training samples in rows and features in columns
%	X2:	data matrix with test samples in rows and features in columns
%	sigma: width of the RBF kernel
% 	b:     bias in the linear and polinomial kernel
%	d:     degree in the polynomial kernel
%
% Output:
%	K: kernel matrix
%
% Gustavo Camps-Valls
% 2006(c)
% Jordi (jordi@uv.es), 2007
% 2007-11: if/then -> switch, and fixed RBF kernel

function K = kernelmatrix(ker,X,X2,sigma)

switch ker
    case 'lin'
        if exist('X2','var')
            K = X' * X2;
        else
            K = X' * X;
        end

    case 'poly'
        if exist('X2','var')
            K = (X' * X2 + b).^d;
        else
            K = (X' * X + b).^d;
        end

    case 'rbf'

        n1sq = sum(X.^2,1);
        n1 = size(X,2);

        if isempty(X2);
            D = (ones(n1,1)*n1sq)' + ones(n1,1)*n1sq -2*X'*X;
        else
            n2sq = sum(X2.^2,1);
            n2 = size(X2,2);
            D = (ones(n2,1)*n1sq)' + ones(n1,1)*n2sq -2*X'*X2;
        end;
        K = exp(-D/(2*sigma^2));

    case 'sam'
        if exist('X2','var');
            D = X'*X2;
        else
            D = X'*X;
        end
        K = exp(-acos(D).^2/(2*sigma^2));

    otherwise
        error(['Unsupported kernel ' ker])
end