maf.m

模式识别工具包

%MAF Maximum autocorrelation mapping (ICA)
% 
% 	[W,alf] = maf(A,n)
% 	[W,n] = maf(A,alf)
%
% This is a special purpose version of pca for images stored as features
% in the dataset. The covariance matrix is slightly modified such that
% the covariances are computed for the one-pixel shifted images.
% As a result the autocorrelation is maximized for the principal components..
% In this way an independent component type of result is obtained (ICA).
% 
% 	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.
%
% See also mappings, datasets, pca

% 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] = maf(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);
if m <= k
	u = reducm(a);
	a = a*u;
	korg = k;
	[m,k] = size(a);
else
	u = [];
end
if isa(a,'dataset') & isfeatim(a) & c == 1
	G = imcov(data2im(a));
else
	error('Images in dataset expected')
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