%GAUSSM Mixture of Gaussians density estimate%%  W = GAUSSM(A,K)%  W = A*GAUSSM([],K);%% INPUT%   A	  Dataset%   K   Number of Gaussians to use (default: 1)%% OUTPUT%   W   Mixture of Gaussians density estimate%% DESCRIPTION% Estimation of a PDF for the dataset A by a Mixture of Gaussians% procedure. Use is made of EMCLUST(A,QDC,K). Unlabeled objects are% neglected, unless A is entirely unlabeled or double. Then all objects% are used. If A is a multi-class crisp labeled dataset the densities are% estimated class by class and then weighted and combined according their% prior probabilities. In all cases, just single density estimator W is% computed.%% Note that it is necessary to set the label type of A to soft labels% (A = LABTYPE(A,'soft') in order to use the traditional EM algorithm% based on posterior probabilities instead of using crisp labels.% See also EMCLUST.% % The mapping W may be applied to a new dataset B using DENSITY = B*W.%% SEE ALSO% DATASETS, MAPPINGS, QDC, MOGC, EMCLUST, PLOTM, TESTC% 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: gaussm.m,v 1.12 2006/03/07 16:17:44 duin Exp $function w = gaussm(a,n)	prtrace(mfilename)  if (nargin < 2)		prwarning (2,'number of Gaussians not specified, assuming 1.');		n = 1; 	end	% No arguments specified: return an empty mapping.	if (nargin < 1) | (isempty(a))		w = mapping(mfilename,n);		w = setname(w,'Mixture of Gaussians');		return	end		if (~isdataset(a) | (getsize(a,3) ~= 1 & islabtype(a,'crisp')))		w = mclassm(a,mapping(mfilename,n),'weight');		return	end	lablist = getlablist(a);	[m,k] = getsize(a);		if n == 1		p = getprior(a);		[U,G] = meancov(a);		res.mean = +U;		res.cov  = G;		res.prior= 1;	else		[e,v] = emclust(a,qdc,n);			ncomp0 = size(v.data.mean,1);			iter = 0;		while (ncomp0 ~= n & iter < 5)   % repeat until exactly n components are found	 		[e,v1] = emclust(a,qdc,n);				 			ncomp1 = size(v1.data.mean,1);			if ncomp1 > ncomp0				v = v1;				ncomp0 = ncomp1;			end			iter = iter + 1;  		end  	res.mean = v.data.mean;  	res.cov  = v.data.cov;  	res.prior= v.data.prior;		res.nlab = ones(n,1); % defines that all Gaussian components have to be		                      % combined into a single class.	end	w = mapping('normal_map','trained',res,lablist,k,1);	w = setname(w,'Mixture of Gaussians');return