%CHERNOFFM Optimal discrimination mapping using Chernoff criterion%%       W = cernoffm(A,n)%% Finds a mapping of the labeled dataset A to a n-dimensional% linear subspace such that it maximizes the the between scatter% over the within scatter (also called Chernoff mapping).%% See also datasets, mappings, nlfisherm, klm, fisherm% 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 = chernoffm(a,n)if nargin == 1,  n = []; endif nargin == 0 | isempty(a)	W = mapping('chernoffm',n);	returnend[nlab,lablist,m,k,c,p,featlist,imheight] = dataset(a);if c > 2	error('Implementation for two classes only')enda = a*scalem(a); % set mean to origina = a/max(abs(a(:))); % occasionally necessary to prevent inf's in covif m <= k        u = reducm(a);        a = a*u;        korg = k;        [m,k] = size(a);else        u = [];end[U,G] = meancov(a,1);p1 = p(1);p2 = 1-p1;m1 = +U(1,:);m2 = +U(2,:);M = (m1-m2)'*(m1-m2);S1 = G(:,:,1);S2 = G(:,:,2);S = p1*S1+(1-p2)*S2;Ss = sqrtmat(S);Si = inv(S);Sis = invsqrtmat(S);Sb = Si*M;Sc = Si*(Sb - Ss*(p1*logmat(Sis*S1*Sis)+p2*logmat(Sis*S2*Sis))*Ss/(p1*p2));[F V] = eig(Sc);[v,I] = sort(-diag(V));q = sum(v(1:n))/sum(v);I = I(1:n);if ~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);returnfunction a = logmat(a)[f v] = eig(a);v = diag(log(diag(v)));a = f*v*f';function a = sqrtmat(a)[f v] = eig(a);v = diag(sqrt(diag(v)));a = f*v*f';function a = invsqrtmat(a)[f v] = eig(a);v = diag(1./sqrt(diag(v)));a = f*v*f';