function G = gram(X1, X2, kernel, param1, param2)%GRAM Computes the Gram-matrix of data points X using a kernel function%%   G = gram(X1, X2, kernel, param1, param2)%% Computes the Gram-matrix of data points X1 and X2 using the specified kernel% function. If no kernel is specified, no kernel function is applied. The% function GRAM is than equal to X1*X2'. The use of the function is different% depending on the specified kernel function (because different kernel% functions require different parameters. The possibilities are listed% below.% Linear kernel: G = gram(X1, X2, 'linear')%           which is parameterless% Gaussian kernel: G = gram(X1, X2, 'gauss', s)%           where s is the variance of the used Gaussian function (default = 1).% Polynomial kernel: G = gram(X1, X2, 'poly', R, d)%           where R is the addition value and d the power number (default = 0 and 3)%%% This file is part of the Matlab Toolbox for Dimensionality Reduction v0.4b.% The toolbox can be obtained from http://www.cs.unimaas.nl/l.vandermaaten% You are free to use, change, or redistribute this code in any way you% want for non-commercial purposes. However, it is appreciated if you % maintain the name of the original author.%% (C) Laurens van der Maaten% Maastricht University, 2007    % Check inputs    if size(X1, 2) ~= size(X2, 2)        error('Dimensionality of both datasets should be equal');    end    % If no kernel function is specified    if nargin == 2 || strcmp(kernel, 'none')        kernel = 'linear';    end        switch kernel                % Linear kernel        case 'linear'            G = X1 * X2';                % Gaussian kernel        case 'gauss'            if ~exist('param1', 'var'), param1 = 1; end            G = L2_distance(X1', X2');            G = exp(-(G.^2 / (2 * param1.^2)));                                % Polynomial kernel        case 'poly'            if ~exist('param1', 'var'), param1 = 1; param2 = 3; end            G = ((X1 * X2') + param1) .^ param2;                    otherwise            error('Unknown kernel function.');    end