reducm.m

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%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 interobject distances are equal to
% those of A.
%
% See also datasets, mappings, nlfisherm, klm

% Copyright: R.P.W. Duin, [e-mail]
% Faculty of Applied Physics, Delft University of Technology
% P.O. Box 5046, 2600 GA Delft, The Netherlands

function W = reducm(a)
if nargin < 1 | isempty(a)
   W = mapping('reducm'); return
end
if isa(a,'dataset')
	imheight = getimheight(a);
	a = +a;
else
	imheight = 0;
end
[m,k] = size(a);
[R,s,v] = svd(a',0);
a = a*R;
r = rank(a);
if r == m, r = r-1; end
a = a/max(abs(a(:))); % occasionally necessary to prevent inf's in cov
G = cov(a);
[F V] = eig(G); 
[v,I] = sort(-diag(V)); 
I = I(1:r);
R = R*F(:,I);
W = mapping('affine',[R;-mean(a*F(:,I))],[],k,r,1,imheight);