Home > . > prt_centre_kernel.m

prt_centre_kernel

PURPOSE ^

FORMAT [C,C_s,C_ss] = Centre_kernel(K,K_s,K_ss)

SYNOPSIS ^

function [C,C_s,C_ss] = prt_centre_kernel(K,K_s,K_ss)

DESCRIPTION ^

 FORMAT [C,C_s,C_ss] = Centre_kernel(K,K_s,K_ss)

 This function centres the kernel matrix using only the training data
__________________________________________________________________________
 Copyright (C) 2011 Machine Learning & Neuroimaging Laboratory

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 function [C,C_s,C_ss] = prt_centre_kernel(K,K_s,K_ss)
0002 
0003 % FORMAT [C,C_s,C_ss] = Centre_kernel(K,K_s,K_ss)
0004 %
0005 % This function centres the kernel matrix using only the training data
0006 %__________________________________________________________________________
0007 % Copyright (C) 2011 Machine Learning & Neuroimaging Laboratory
0008 
0009 % Written by D. Hardoon, A. Marquand and J. Mourao-Miranda
0010 % Id:$
0011 
0012 if iscell(K), K = K{:}; end
0013 if iscell(K_s), K_s = K_s{:}; end
0014 if iscell(K_ss), K_ss = K_ss{:}; end
0015 
0016 l = size(K,1);
0017 j = ones(l,1);
0018 C = K - (j*j'*K)/l - (K*j*j')/l + ((j'*K*j)*j*j')/(l^2);
0019 
0020 if( nargin > 1 )
0021     tk =  (1/l)*sum(K,1); % (1 x l)
0022     tl = ones(size(K_s,1),1); % (n x 1)
0023     C_s = K_s - ( tl * tk); % ( n x l )
0024     tk2 = (1/(size(K_s,2)))*sum(C_s,2); % ( n x 1 )
0025     C_s = C_s - (tk2 * j'); % ( n x l )
0026     
0027     % Two equivalent ways to achieve the same thing
0028     %C_s = K_s - repmat(sum(K),size(K_s,1),1)/l - repmat(sum(K_s,2),1,size(K_s,2))/size(K_s,2) + repmat(j'*K*j,size(K_s,1),size(K_s,2))/(l^2);
0029     %C_s = K_s - (tl*sum(K))/l - (sum(K_s,2)*j')/size(K_s,2) + ((j'*K*j)*tl*j')/(l^2);
0030     
0031     if nargin > 2
0032         ttj = ones(size(K_ss,1),1);
0033         C_ss = K_ss - (sum(K_s,2)*ttj')/l - (ttj*sum(K_s,2)')/l + ((j'*K*j)*ttj*ttj')/(l^2);
0034     end
0035 end
0036 
0037 C={C};
0038 C_s={C_s};
0039 C_ss={C_ss};

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