function x = RBF_kernel(a,b, sigma2)% Radial Basis Function (RBF) kernel function for implicit higher dimension mapping%%  X = RBF_kernel(a,b,sig2)%% 'sig2' contains the SQUARED variance of the RBF function:%    X = exp(-||a-b||.^2/sig2)%  % 'a' can only contain one datapoint in a row, 'b' can contain N% datapoints of the same dimension as 'a'. If the row-vector 'sig2'% contains i=1 to 'dimension' values, each dimension i has a separate 'sig2(i)'.%% see also:%    poly_kernel, lin_kernel, MLP_kernel, trainlssvm, simlssvm% Copyright (c) 2002,  KULeuven-ESAT-SCD, License & help @ http://www.esat.kuleuven.ac.be/sista/lssvmlabx = zeros(size(b,1),1);% ARD for different dimensions.if size(sigma2,2) == length(a),  % rescaling ~ dimensionality  [n,d] = size(b);  for i=1:size(b,1),      dif = a-b(i,:);      x(i,1) = exp( -(sum((dif.*dif)./(sigma2.*d))) );               endelse  % a single kernel parameter or one for every inputvariable  for i=1:size(b,1),    dif = a-b(i,:);    x(i,1) = exp( -(sum((dif.*dif)./sigma2(1,1))) );  endend