%REDUCM Reduce to minimal space%%  W = REDUCM(A)%% Ortho-normal mapping to a space in which the dataset A exactly fits.% This is useful for datasets with more features than objects.  For the% objects in B = A*W holds that their dimensionality is minimum, their mean% is zero, the covariance matrix is diagonal with decreasing variances and% the inter-object distances are equal to those of A.%% For this mapping just the labeled objects in A are used, unless A is% entirely unlabeled. In that case all objects are used.%% See also MAPPINGS, DATASETS, NLFISHERM, KLM, PCA% 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: reducm.m,v 1.4 2003/10/07 10:22:16 bob Exp $function W = reducm(a)	prtrace(mfilename);		if nargin < 1 | isempty(a)		W = mapping('reducm');		W = setname(W,'Reduction mapping');		return	end	% Find the subspace R of dataset 'a' (actually data matrix 'b'):	b = +cdats(a,1);	[m,k] = size(b);	[R,s,v] = svd(b',0);	% Map the data:	b = b*R;	% Find the number of non-singular dimensions	r = rank(b);	if r == m, r = r-1; end	% Order the dimensions according to the variance:		G = cov(b);	[F V] = eig(G); 	[v,I] = sort(-diag(V)); 	I = I(1:r);	% And store the result in an affine mapping:	R = R*F(:,I);	W = affine(R,-mean(b*F(:,I)),a);return