%PCA Principal component analysis (PCA or MCA on overall covariance matrix)% %   [W,FRAC] = PCA(A,N)%   [W,N]    = PCA(A,FRAC)%% INPUT%   A           Dataset%   N  or FRAC  Number of dimensions (>= 1) or fraction of variance (< 1) %               to retain; if > 0, perform PCA; otherwise MCA. Default: N = inf.%% OUTPUT%   W           Affine PCA mapping%   FRAC or N   Fraction of variance or number of dimensions retained.%% DESCRIPTION% This routine performs a principal component analysis (PCA) or minor% component analysis (MCA) on the overall covariance matrix (weighted% by the class prior probabilities). It finds a rotation of the dataset A to % an N-dimensional linear subspace such that at least (for PCA) or at most % (for MCA) a fraction FRAC of the total variance is preserved.%% PCA is applied when N (or FRAC) >= 0; MCA when N (or FRAC) < 0. If N is % given (abs(N) >= 1), FRAC is optimised. If FRAC is given (abs(FRAC) < 1), % N is optimised. %% Objects in a new dataset B can be mapped by B*W, W*B or by A*PCA([],N)*B.% Default (N = inf): the features are decorrelated and ordered, but no % feature reduction is performed.%% ALTERNATIVE%%   V = PCA(A,0)% % Returns the cumulative fraction of the explained variance. V(N) is the % cumulative fraction of the explained variance by using N eigenvectors.%% Use KLM for a principal component analysis on the mean class covariance.% Use FISHERM for optimizing the linear class separability (LDA).% % SEE ALSO% MAPPINGS, DATASETS, PCLDC, KLLDC, KLM, FISHERM% Copyright: R.P.W. Duin, duin@ph.tn.tudelft.nl% Faculty of Applied Sciences, Delft University of Technology% P.O. Box 5046, 2600 GA Delft, The Netherlands% $Id: pca.m,v 1.6 2003/10/07 11:56:15 bob Exp $function [w,truefrac] = pca (varargin)	prtrace(mfilename);	[w,truefrac] = pcaklm(mfilename,varargin{:});	return