mfbox_past.m

toolbox for spm 5 for data, model free analysis

function W=mfbox_past(X,n,beta,numits,verbose)
% Copyright by Peter Gruber, Fabian J. Theis
% Signal Processing & Information Theory group
% Institute of Biophysics, University of Regensburg, Germany
% Homepage: http://research.fabian.theis.name
%           http://www-aglang.uni-regensburg.de
%
% This file is free software, subject to the 
% GNU GENERAL PUBLIC LICENSE, see gpl.txt
%
% mfbox_past - a neural PCA / subspace algorithm
%
% X         data set
% n         reduced dimension
% beta      forgetting factor (1:dont forget, ~0: forget nearly everything before)
% numits    number of iterations (if numits is larger than sample size, the algorithm starts from the beginning again)
%
% W         trained subspace projection matrix
%
% 18.11.2004 Fabian Theis ([e-mail])
%
% Reference:
% B. Yang. Projection approximation subspace tracking. IEEE Trans. on Signal Processing, 43(1):95-107, 1995.

error(nargchk(2,5,nargin))     % check no. of input args

if (nargin<3) beta = 0.5; end
if (nargin<4) numits = 1000; end
if (nargin<5) verbose = 0; end

[m T] = size(X);
W = eye(n,m);
P = eye(n);

cost = [];
for i=1:numits
    b = ((numits-i)*beta+i)/numits;
    x = X(:,mod(i-1,T)+1);
    y = W*x;
    h = P*y;
    m = h/(b+y'*h);
    P = triu(P-m*h');
    P = 1/b*(P+P'-diag(diag(P)));
    e = x-W'*y;
    dW = m*e';
    W = W+dW;
    cost(i) = norm(dW,'fro');
    if ((verbose>0)&&(mod(i,floor(numits/20))==0))
        plot(gca,1:i,cost); set(gca,'YScale','log'); drawnow; title(gca,'Change per iteration');
    end
end

return