subsm.m

模式识别工具包

%SUBSM Find subspace map
%
%	[W,alf] = subsm(A,n)
%
% A n-dimensional subspace map for the dataset A is found using PCA,
% such that it contains the origin. All object in A are normalized
% first on unit length. The explained variance is returned in alf.
%
%	[W,n] = subsm(A,alf)
%
% In this case a subspace explaining at least a fraction alf of the 
% variance is determined. In n the subspace dimensionality is returned.
%
% Note that the resulting eigenvectors can be made explicite by a
% back projection of the axes into the original space by
% e = +(eye(n)*W')
%
% See datasets, mappings, subsc, fisherm, 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,alf] = subsm(a,n);
b = normm(+a,2);
b = [b;-b];
v = reducm(b);
[e,alf] = klm(b*v,min(n,size(v,2)));
w = v*e;