%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, duin@ph.tn.tudelft.nl% Faculty of Applied Physics, Delft University of Technology% P.O. Box 5046, 2600 GA Delft, The Netherlandsfunction [W,q] = maf(a,alf)if nargin < 2 | isempty(alf), alf = inf; endif nargin < 1 | isempty(a)   W = mapping('klm',alf); returnend[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 = [];endif 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;	returnelseif 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);endif ~isempty(u)	R = double(u)*F(:,I);	k = korg;else	R = [F(:,I); -mean(a*F(:,I))];endW = 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;	endend