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PCA2DL1.m
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PCA2DL1.m
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function W=PCA2DL1(x)
% Calculate the first k 2DPCA-L1 components.
% 2DPCA with L1-norm for simultaneously robust and sparse modelling
% Copyright (C) 2013 Jing Wang
%
% This program is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program. If not, see <http://www.gnu.org/licenses/>.
[~,width,p]=size(x);
k=30;
W=zeros(width,k);
% Initialize w as corresponding components of 2DPCA. Other initialization
% could be tried also.
cov=zeros(width);
for i=1:p
cov=cov+x(:,:,i)'*x(:,:,i);
end
[V,D]=eig(cov);
% Sort the eigen values in order.
[~,indx]=sort(diag(D),'descend');
V=V(:,indx);
err_tol=1e-4;
for i=1:k
stop=1;
w=V(:,i);
while stop
varpi=zeros(width,1);
for j=1:p
varpi=varpi+x(:,:,j)'*sign(x(:,:,j)*w);
end
w_new=varpi/norm(varpi);
err=norm(w_new-w);
if err>err_tol
w=w_new;
else
stop=0;
end
end
for j=1:p
x(:,:,j)=x(:,:,j)-x(:,:,j)*w*w';
end
W(:,i)=w;
end