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RSPCA.m
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RSPCA.m
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function W=RSPCA(x,rho,nPV)
% calculate projection vectors for RSPCA
% Input:
% x, data
% rho, tuning parameter
% nPV, number of projection vectors
% Output:
% W, the obtained projection vectors
%
% 2018-4-23 18:33:56
lam=10^(-rho);
s=1; % set s as 1 since the script is adopted from GPCA
x=x'; % so that the following lines could be consistent with the 2DPCAL1-S
x0=x;
d=size(x,2);
% SVD/PCA as the initialization
[~,~,W0]=svd(x,0);
% calculate multiple projection vectors
W=zeros(d,nPV);
for iPV=1:nPV
w=W0(:,iPV);
rsd=1;
while rsd>1e-4
fp=pnorm(x*w,s);
v=s*x'*((abs(x*w).^(s-1)).*sign(x*w));
% update rule
w=v.*abs(w)./(lam+abs(w));
w=w/norm(w);
f=pnorm(x*w,s);
rsd=abs(f-fp)/fp;
end
W(:,iPV)=w;
x=x0*(eye(d)-W*W'); % deflating
end