%LMNM Levenberg-Marquardt neural net diabolo mapping% % 	[W,R] = lmnm(A,n,iter,fid)% % A linear n-dimensional mapping is found for the labeled dataset A% using a diabolo network with a single hidden layer of n linear% neurons and a classification output layer of sigmoidal neurons.% Training is stopped after iter epochs (default infinity) or if its% number is twice that of the best classification result. Progress% is reported in fid (default: not), The entire training sequence is% returned in R. Default n = 2. %% See also datasets, mappings, nlklm, fisherm, klm% 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, R] = lmnm(a,n,itermax,fid)if nargin < 2, n = 2; endif nargin < 3, itermax = []; endif nargin < 4, fid = 0; endif nargin == 0 | isempty(a)	W = mapping('lmnm',{n,itermax,fid});	returnend[nlab,lablist,m,k,cout] = dataset(a);if cout < 2	error('Dataset should contain at least 2 classes')endif isempty(itermax), itermax = inf; end				% pre-whiteningww = klms(a);a = a*ww;[m,k] = size(a);				% set targetsif cout > 1	TAR = eye(cout); 	%TAR(find(TAR==0)) = 0.1*ones(sum(sum(TAR==0)),1); 	%TAR = reshape(TAR,cout,cout);else	TAR = [0 1];endT = TAR(nlab,:);nl = length(n)+1;nn = [k,n(:)',cout];				% PCA initialisationw = klm(+a,n(1));v = +(a*w*fisherc);u = zeros(n(1)+1,cout);for j = 1:cout	u(:,j) = +v{j};endw = +w;w = [w(:)',u(:)'];				% randomize lightlyr = rand(1,length(w))*0.05 + ones(1,length(w));w = w.*r;				% set standard training parametersdisp_freq = inf;max_epoch = min(1,itermax); % this is our iteration unityerr_goal = 0.02;min_grad = 1e-6;init_mu = 0.001;mu_inc = 10;mu_dec = 0.1;mu_max = 1e10;TP = [disp_freq, max_epoch, err_goal, min_grad, init_mu, ...    mu_inc, mu_dec, mu_max];	 			% initialize loop and runemin = 1;nmin = 1;iter = 0;actf = ['purelin';'logsig '];R = [];while (iter <= 2*nmin | iter < 50) & iter < itermax	[w,TE,TR] = ttlm(w,actf,n,a',T',TP,0);	iter = iter + TE;	W = mapping('affine',reshape(w(1:k*n(1)+n(1)),k+1,n(1)),[],k,n(1),1);	W = W*(a*W*ldc);	ea = testd(a,W);		RR = [iter ea];	R = [R; RR];%	fprintf('.');	if ea < emin				% if better, store		emin = ea;		v = w;		nmin = iter;%		fprintf('\n%3.3f',e);	end	fprintf(fid,'epochs:%5i  ea: %3.3f  min_error: %3.3f\n', RR,emin);	if TE == 0, break; endendv1 = reshape(v(1:k*n(1)+n(1)),k+1,n(1));W = ww*mapping('affine',v1,[],k,n(1),1);