KernelMatrix.m

function omega = KernelMatrix(Xtrain,kernel_type, kernel_pars,Xt)
% Construct the positive (semi-) definite and symmetric kernel matrix
%
% >> Omega = kernel_matrix(X, kernel_fct, sig2)
%
% This matrix should be positive definite if the kernel function
% satisfies the Mercer condition. Construct the kernel values for
% all test data points in the rows of Xt, relative to the points of X.
%
% >> Omega_Xt = kernel_matrix(X, kernel_fct, sig2, Xt)
%
%
% Full syntax
%
% >> Omega = kernel_matrix(X, kernel_fct, sig2)
% >> Omega = kernel_matrix(X, kernel_fct, sig2, Xt)
%
% Outputs
%   Omega  : N x N (N x Nt) kernel matrix
% Inputs
%   X      : N x d matrix with the inputs of the training data
%   kernel : Kernel type (by default 'RBF_kernel')
%   sig2   : Kernel parameter (bandwidth in the case of the 'RBF_kernel')
%   Xt(*)  : Nt x d matrix with the inputs of the test data

% Copyright (c) 2012,  Siamak Mehrkanooon 

nb_data = size(Xtrain,1);

if strcmp(kernel_type,'RBF_kernel'),
    if nargin<4,
        XXh = sum(Xtrain.^2,2)*ones(1,nb_data);
        omega = XXh+XXh'-2*(Xtrain*Xtrain');
        omega = exp(-omega./(kernel_pars(1)));
    else
        XXh1 = sum(Xtrain.^2,2)*ones(1,size(Xt,1));
        XXh2 = sum(Xt.^2,2)*ones(1,nb_data);
        omega = XXh1+XXh2' - 2*Xtrain*Xt';
        omega = exp(-omega./(kernel_pars(1)));
    end
         
end