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PCA.m
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PCA.m
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function [eigvector, eigvalue] = PCA(data, options)
%PCA Principal Component Analysis
%
% Usage:
% [eigvector, eigvalue] = PCA(data, options)
% [eigvector, eigvalue] = PCA(data)
%
% Input:
% data - Data matrix. Each row vector of fea is a data point.
%
% options.ReducedDim - The dimensionality of the reduced subspace. If 0,
% all the dimensions will be kept.
% Default is 0.
%
% Output:
% eigvector - Each column is an embedding function, for a new
% data point (row vector) x, y = x*eigvector
% will be the embedding result of x.
% eigvalue - The sorted eigvalue of PCA eigen-problem.
%
% Examples:
% fea = rand(7,10);
% options=[];
% options.ReducedDim=4;
% [eigvector,eigvalue] = PCA(fea,4);
% Y = fea*eigvector;
%
% version 3.0 --Dec/2011
% version 2.2 --Feb/2009
% version 2.1 --June/2007
% version 2.0 --May/2007
% version 1.1 --Feb/2006
% version 1.0 --April/2004
%
% Written by Deng Cai (dengcai AT gmail.com)
%
if (~exist('options','var'))
options = [];
end
ReducedDim = 0;
if isfield(options,'ReducedDim')
ReducedDim = options.ReducedDim;
end
[nSmp,nFea] = size(data);
if (ReducedDim > nFea) || (ReducedDim <=0)
ReducedDim = nFea;
end
if issparse(data)
data = full(data);
end
sampleMean = mean(data,1);
data = (data - repmat(sampleMean,nSmp,1));
[eigvector, eigvalue] = mySVD(data',ReducedDim);
eigvalue = full(diag(eigvalue)).^2;
if isfield(options,'PCARatio')
sumEig = sum(eigvalue);
sumEig = sumEig*options.PCARatio;
sumNow = 0;
for idx = 1:length(eigvalue)
sumNow = sumNow + eigvalue(idx);
if sumNow >= sumEig
break;
end
end
eigvector = eigvector(:,1:idx);
end