%LOGLC Logistic Linear Classifier% %   W = LOGLC(A)% % INPUT%   A   Dataset%% OUTPUT%   W   Logistic linear classifier %% DESCRIPTION  % Computation of the linear classifier for the dataset A by maximizing the% likelihood criterion using the logistic (sigmoid) function.% % REFERENCES% A. Webb, Statistical Pattern Recognition, John Wiley & Sons, New York, 2002.%%  SEE ALSO %  MAPPINGS, DATASETS, LDC, FISHERC% 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 Netherlands% $Id: loglc.m,v 1.9 2003/11/22 23:20:39 bob Exp $function W = loglc(a)	prtrace(mfilename);	% No input data, return an untrained classifier.	if (nargin == 0) | (isempty(a))		W = mapping(mfilename); 		W = setname(W,'Logistic Classifier');		return	end	islabtype(a,'crisp');	isvaldset(a,1,2); % at least 2 object per class, 2 classes	[m,k,c] = getsize(a);	nlab = getnlab(a);	prior = getprior(a);	if (c > 2)		% Compute C classifiers: each class against all others.			W = mclassc(a,mapping(mfilename));		else		v = scalem(a,'variance');		a = a*v;		accuracy = 0.0001;		% An accuracy for the ML loop.		x = [+a,ones(m,1)];		% A standard trick to set the labels to +1 for the first class		% (NLAB=1) and to -1 for the second one (NLAB=2). Then, each 		% object vector is multiplied by its new label +/-1.		x(find(nlab==2),:) = -x(find(nlab==2),:);		alf = sum(nlab==2)/sum(nlab==1);		weights = zeros(1,k+1);		% Maximize the likelihood L to find WEIGHTS		L = -inf; Lnew = -realmax;		while (abs(Lnew - L) > accuracy)			pax = ones(m,1) ./ (1 + exp(-x*weights'));	% Estimate of P(class +1|x).			pbx = 1 - pax;                          		% Estimate of P(class -1|x).			L = Lnew; Lnew = sum(log(pax+realmin));     % Update likelihood.				p2x = sqrt(pax.*pbx); 			y = x .* p2x(:,ones(1,k+1));			weights = pbx' * x * pinv(y'*y) + weights;		end		% Define LOGLC by an affine (linear) mapping based 		% on the [K x 1] matrix R and the offset w0.		w0 = weights(k+1) + log(alf*prior(1)/prior(2));		R  = weights(1:k)';		W  = v*affine(R,w0,a,getlablist(a)); 		W  = setout_conv(W,1);	end	W = setname(W,'Logistic Classifier');	return