%MOG_DD Mixture of Gaussians data description%%   W = MOG_DD(A,FRACREJ,[N1 N2],CTYPE,REG,NUMITERS)%% Train a Mixture of Gaussians model on data A, using N1 clusters to% model the target class, and N2 clusters for the outlier data. The% position, size and priors of each of the clusters is optimized using% the EM algorithm. The shape of the clusters can be chosen by setting% CTYPE:% CTYPE = 'sphr':  spherical clusters (only diagonal elements with%                  equal values in the cov. matrices)%         'diag':  elliptical and aligned clusters (only diagonal%                  elements)%         'full':  arbitrary shaped clusters (full covariance matrices)%% When no outlier data is available, you can choose to use% N2=[], or N2=0. To ensure that the classifiers obtains a closed% boundary around the target class, one extra cluster is added to the% outlier clusters, that will model the uniform outlier distribution.% When you only supply N1, a fixed threshold will be used and no extra% outlier cluster is added.%% The EM algorithm was inspired by NetLab (by Bishop), but it has been% changed significantly after that.% Optionally, you can set a regularization for the covariance matrices,% by giving REG, or the maximum number of iterations by NUMITERS.%% Default: N1=5, CTYPE='full', REG=0.01, NUMITERS=25%% See also: mog_init, mog_update, mog_P, mogEMupdate, mogEMextend% Copyright: D.M.J. Tax, D.M.J.Tax@prtools.org% Faculty EWI, Delft University of Technology% P.O. Box 5031, 2600 GA Delft, The Netherlandsfunction w = mog_dd(a,fracrej,n,ctype,reg,numiters)if (nargin<6)	numiters = 25;endif (nargin<5)	reg = 0.01;endif (nargin<4)	ctype = 'full';endif (nargin<3)	n = 5;endif (nargin<2)	fracrej = 0.05;endif length(n)>1  % then we want to train using outlier data	if (n(2)<0), n(2)=0; end; % using at least 0 outlier clustersendif (nargin<1)|isempty(a)     % Define the untrained mapping.	w = mapping(mfilename,{fracrej,n,ctype,reg,numiters});	if (length(n)>1) & (n(2)>0)  % we model also the outliers		w = setname(w,sprintf('MoG (%d+%d)',n(1),n(2)));	else		% we only describe the target class		w = setname(w,sprintf('MoG (%d)',n(1)));	end	returnendif isa(fracrej,'double')           %training	% Setup some variables:	W = [];	[m,k] = size(a);	[at,ao] = target_class(a);	% Detect which type of covariance matrix we have:	switch ctype	case {'sphr' 'diag' 'full'}		W.covtype = ctype;	otherwise		error('This covariance structure is not known');	end	% First do the target class	[W.mt, W.ict, W.pt] = mog_init(at, n(1), W.covtype);	% then do the outlier class	if (length(n)>1)		if isempty(ao)			% When no outlier data is avaiable, all clusters will have			% centers on the mean of the data			[W.mo, W.ico, W.po] = mog_init(mean(at),n(2),W.covtype,cov(+at));		else			% When some outlier data is available, only the first cluster			% will be fixed to the mean of the data, the rest will be			% fitted			[W.mo, W.ico, W.po] = mog_init(ao,n(2),W.covtype,cov(+a));		end	end		% and not to forget to store:	W.threshold = 0;	W.reg = reg;	W.fracrej = fracrej;	% and store it in the mapping:	w = mapping(mfilename,'trained',W,str2mat('target','outlier'),k,2);	% also give it a suitable name	if (length(n)>1) & (n(2)>0)  % we model also the outliers		w = setname(w,sprintf('MoG (%d+%d)',n(1),n(2)));	else		% we only describe the target class		w = setname(w,sprintf('MoG (%d)',n(1)));	end		% Now start training this mapping:	w = mog_update(w,a,numiters);	w = mog_threshold(w,at,fracrej);else                               %testing	w = getdata(fracrej);  % unpack	m = size(a,1);	%compute the output, depending if the outlier class is also modelled:	out = sum(mog_P(+a,w.covtype,w.mt,w.ict,w.pt),2);	% when we have the outlier class modelled:	if isfield(w,'mo')		% Do it nicely using Bayes rule:		Po = sum(mog_P(+a,w.covtype,w.mo,w.ico,w.po),2) + 10*eps;		s = warning('off');			out = out./Po;		warning(s);	end	newout = [out repmat(w.threshold,m,1)];	% Store the density:	w = setdat(a,newout,fracrej);	w = setfeatdom(w,{[0 inf] [0 inf]});endreturn