%LDC Linear Bayes Normal Classifier (BayesNormal_1)%%   W = LDC(A,R,S)% % INPUT%   A    Dataset%   R,S  Regularization parameters, 0 <= R,S <= 1%        (optional; default: no regularization, i.e. R,S = 0)% % OUTPUT%   W    Linear Bayes Normal classifier %% DESCRIPTION  % Computation of the linear classifier between the classes of the dataset A% by assuming normal densities with equal covariance matrices. The joint% covariance matrix is the weighted (by a priori probabilities) average of% the class covariance matrices. R and S (0 <= R,S <= 1) are regularization% parameters used for finding the covariance matrix G by:%%      G = (1-R-S)*G + R*diag(diag(G)) + S*mean(diag(G))*eye(size(G,1))%% The use of soft labels is supported. The classification A*W is computed% by NORMAL_MAP.%% Note that A*(KLMS([],N)*NMC) performs a very similar operation by first% pre-whitening the data in an N-dimensional space, followed by the% nearest mean classifier. The regularization controlled by N is different% from the above in LDC as it entirely removes small variance directions.%% To some extend LDC is also similar ot FISHERC%% EXAMPLES% See PREX_PLOTC.%% REFERENCES% 1. R.O. Duda, P.E. Hart, and D.G. Stork, Pattern classification, 2nd edition, % John Wiley and Sons, New York, 2001.% 2. A. Webb, Statistical Pattern Recognition, John Wiley & Sons, New York, 2002.% 3. C. Liu and H. Wechsler, Robust Coding Schemes for Indexing and Retrieval% from Large Face Databases, IEEE Transactions on Image Processing, vol. 9, % no. 1, 2000, 132-136.%%  SEE ALSO%  MAPPINGS, DATASETS, NMC, NMSC, LDC, UDC, QUADRC, NORMAL_MAP, FISHERC% Copyright: R.P.W. Duin, r.p.w.duin@prtools.org% Faculty EWI, Delft University of Technology% P.O. Box 5031, 2600 GA Delft, The Netherlands% $Id: ldc.m,v 1.17 2004/12/06 07:42:48 duin Exp $function W = ldc(a,r,s)	prtrace(mfilename);	if (nargin < 3)		prwarning(4,'Regularisation parameter S not given, assuming 0.');		s = 0; 	end	if (nargin < 2)		prwarning(4,'Regularisation parameter R not given, assuming 0.');		r = 0;	end	% No input arguments: return an untrained mapping.	if (nargin < 1) | (isempty(a))		W = mapping(mfilename,{r,s});		W = setname(W,'Bayes-Normal-1');		return	end	islabtype(a,'crisp','soft');	isvaldset(a,2,2); % at least 2 object per class, 2 classes	[m,k,c] = getsize(a);	if (c==0)		error('Cannot train the classifier, because unlabeled data is supplied');	end	% Calculate mean vectors, priors and the covariance matrix G.	[U,G] = meancov(a);	w.mean  = +U;	w.prior = getprior(a);	G = reshape(sum(reshape(G,k*k,c)*w.prior',2),k,k);	% Regularize 	if (s > 0) | (r > 0)		G = (1-r-s)*G + r * diag(diag(G)) + s*mean(diag(G))*eye(size(G,1));	end	w.cov = G;	W = mapping('normal_map','trained',w,getlab(U),k,c);	W = setname(W,'Bayes-Normal-1');	W = setcost(W,a);		return