klm.m

模式识别工具箱,本人毕业论文时用到的,希望对大家有用!

%KLM Karhunen-Loeve Mapping (PCA of mean covariance matrix)
% 
% 	[W,alf] = klm(A,n)
% 	[W,n] = klm(A,alf)
%
% The Karhunen-Loeve Mapping performs a principal component analysis
% (PCA) on the mean class convariance matrix (weighted by the class
% posterior probabilities). It finds a rotation of the dataset A to
% a n-dimensional linear subspace such that at least a fraction alf
% of the total variance is preserved.
% If n is given (n>=1), alf is maximized. If alf is given (alf<1) 
% n is minimized. If n < 0 an abs(n)-dimensional subspace is found
% that minimizes the preserved variance. If alf<0 (abs(alf<1)) the
% maximum n is found for which the preserved variance <= abs(alf).
% New objects B can be mapped by B*W, W*B or by A*klm([],n)*B.
% Default: the features are decorrelated and ordered, but no
% feature reduction is made.
%
% 	v = klm(A,0)
% 
% Returns the cummulative fraction of the explained variance. v(n) 
% is the cummulative 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).
% 
% See also mappings, datasets, kljlc, klclc, pca, fisherm

% 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,q] = klm(a,alf)
if nargin < 2 | isempty(alf), alf = inf; end
if nargin < 1 | isempty(a)
   W = mapping('klm',alf); return
end

[nlab,lablist,m,k,c,p,fl,imheight] = dataset(a);
a = a*scalem(a); % set mean to origin
if m <= k
	u = reducm(a);
	a = a*u;
	korg = k;
	[m,k] = size(a);
else
	u = [];
end
[U,GG] = meancov(a); G = zeros(k,k);
for i = 1:c
	G = G + p(i)*GG(:,:,i);
end
[F V] = eig(G);
[v,I] = sort(-diag(V));
if alf == inf
	n = k;
	q = k;
elseif alf >= 1
	n = alf;
	if n > k
		error('Illegal dimensionality requested');
	end
	q = sum(v(1:n))/sum(v);
	I = I(1:n);
elseif alf > 0
	vv = v'*triu(ones(k,k)) / sum(v) - alf;
	J = find(vv > 0);
	n = J(1); q = n;
	I = I(1:n);
elseif alf == 0
	W = ones(1,k);
	w = v'*triu(ones(k,k)) / sum(v);
	W(1:length(w)) = w;
	return
elseif alf > -1
	alf = abs(alf);
	v = flipud(v); I = flipud(I);
	vv = v'*triu(ones(k,k)) / sum(v) - alf;
	J = find(vv > 0);
	n = J(1)-1; q = n;
	I = I(1:n);
else
	n = abs(alf);
	v = flipud(v); I = flipud(I);
	if n > k
		error('Illegal dimensionality requested');
	end
	q = sum(v(1:n));
	sv = sum(v);
	if sv ~= 0, q = q/sv; end
	I = I(1:n);
end
if ~isempty(u)
	R = double(u)*F(:,I);
	k = korg;
else
	R = [F(:,I); -mean(a*F(:,I))];
end
W = mapping('affine',R,[],k,n,1,imheight);
return

%IMCOV Image covariance
%
%	c = imcov(a)

function c = imcov(a)
[m,n,k] = size(a);
g = mean(reshape(a,m*n,k));
J = bord(reshape(1:m*n,m,n),NaN);
cc = zeros(k,k);
for i=1:k
	a1 = a(:,:,i) - g(i);
	for j=i:k
		a2 = a(:,:,j) - g(j);
		cc = mean(mean(a1.*a2(J(1:m,2:n+1)) + a1.*a2(J(3:m+2,2:n+1))));
		cc = cc + mean(mean(a1.*a2(J(2:m+1,1:n)) + a1.*a2(J(2:m+1,3:n+2))));
		cc = cc/4;
		c(i,j) = cc; c(j,i) = cc;
	end
end