klclc.m

模式识别工具包

%KLCLC Linear classifier using KL expansion of common covariance 
% matrix
% 
% 	W = klclc(A,n)
% 
% Finds the linear discriminant function W for the dataset A 
% computing the ldc on a projection of the data on the first n  
% eigenvectors of the mean covariance matrix of the classes. 
% (Karhunen Loeve expansion).
% 
% 	W = klclc(A,alf)
% 
% In this case the number of eigenvalues is chosen such that at 
% least a part alf of the total variance is explained.
% Default alf = 0.9.
% 
% See also mappings, datasets, kljlc, klm, 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 = klclc(a,n)
if nargin == 0, W = mapping('klclc'); return; end
if isempty(a), W = mapping('klclc',n); return; end
[nlab,lablist,m,k,c,p,fl,imheight] = dataset(a);

if nargin == 2
	if n >= m, n = m-1; end
	if n > k
		W = ldc(a);
		return
	end
end

 				% decorrelate data
G = zeros(k,k);
u = zeros(1,k);
for j = 1:c
	if sum(nlab==j) < 2 
		error('Classes should have more than one vector')
	end
	J = find(nlab==j);
	G = G + p(j)*covm(a(J,:));
	u = u + p(j)*mean(a(J,:),1);
end

[F V] = eig(G);
[v I] = sort(-diag(V));
R = F(:,I);
b = (a-ones(m,1)*u) * R;
v = -v';

alf = 0;			% find alf
if nargin < 2
	alf = 0.9;
elseif n < 1
	alf = n;
	if alf <= 0
		error('alf should be > 0')
	end
end
				% find dimensionality n
if alf > 0
	vv = v*triu(ones(k,k)) / sum(v) - alf;
	I = find(vv > 0);
	n = I(1);
end
				% compute w in subspace
            
[w,labl,type] = mapping(ldc(b(:,1:n)));
if c == 2 & strcmp(type,'affine')
   w = [R(:,1:n)*w(1:n);w(n+1)-u*R(:,1:n)*w(1:n)];
   W = mapping('affine',w,lablist,k,1,1,imheight);
   W = cnormc(W,a);
else
	U = w{1}*R(:,1:n)'+ones(c,1)*u;
	G = w{2};
	if n < k	% make G non-singular
		G = [[G,zeros(n,k-n)];[zeros(k-n,n),eye(k-n)]];
	end
	G = R * G * R';
	W = mapping('normal_map',{U,G,w{3}},lablist,k,c,1);
end
return