%KLM Karhunen-Loeve Mapping (PCA or MCA of mean covariance matrix)
%
% [W,FRAC] = KLM(A,N)
% [W,N] = KLM(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 Karhunen-Loeve mapping
% FRAC or N Fraction of variance or number of dimensions retained.
%
% DESCRIPTION
% The Karhunen-Loeve Mapping performs a principal component analysis
% (PCA) or minor component analysis (MCA) on the mean class 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*KLM([],N)*B. Default (N = inf): the features are decorrelated and
% ordered, but no feature reduction is performed.
%
% ALTERNATIVE
%
% V = KLM(A,0)
%
% Returns the cummulative fraction of the explained variance. V(N) is
% the cumulative fraction of the explained variance by using N
% eigenvectors.
%
% Use PCA for a principal component analysis on the total data
% covariance. Use FISHERM for optimizing the linear class
% separability (LDA).
%
% This function is basically a wrapper around pcaklm.m.
%
% SEE ALSO (<a href="http://37steps.com/prtools">PRTools Guide</a>)
% MAPPINGS, DATASETS, PCAKLM, PCLDC, KLLDC, PCAM, FISHERM
% Copyright: R.P.W. Duin, r.p.w.duin@37steps.com
% Faculty EWI, Delft University of Technology
% P.O. Box 5031, 2600 GA Delft, The Netherlands
% $Id: klm.m,v 1.2 2006/03/08 22:06:58 duin Exp $
function [w,truefrac] = klm (varargin)
[w,truefrac] = pcaklm(mfilename,varargin{:});
return