%PARALLEL Combining classifiers in different feature spaces%%    WC = PARALLEL(W1,W2,W3,  ....) or WC = [W1;W2;W3; ...]%    WC = PARALLEL({W1;W2;W3; ...}) or WC = [{W1;W2;W3; ...}]%    WC = PARALLEL(WC,W1,W2,  ....) or WC = [WC;W2;W3; ...]%    WC = PARALELL(C);%    WC = PARALLEL(WC,N);%% INPUT%   W1,W2,...  Base classifiers to be combined.%   WC         Parallel combined classifier%   C          Cell array of classifiers%   N          Integer array%% OUTPUT%    WC        Combined classifier.%% DESCRIPTION% The base classifiers (or mappings) W1, W2, W3, ... defined in different% feature spaces are combined in WC. This is a classifier defined for the % total number of features and with the combined set of outputs. So, for three % two-class classifiers defined for the classes 'c1' and 'c2', a dataset A is % mapped by D = A*WC on the outputs 'c1','c2','c1','c2','c1','c2' which are % the feature labels of D. Note that classification by LABELD(D) finds for % each vector in D the feature label of the column with the maximum value.% This is equivalent to using the maximum combiner MAXC.%% Other fixed combining rules like PRODC, SUMC, and MAJORC can be applied % by D = A*WC*PRODC etc. A trained combiner like FISHERC has to be supplied% with the appropriate training set by AC = A*WC; VC = AC*FISHERC. So the% expression VC = A*WC*FISHERC yields a classifier and not a dataset as with % fixed combining rules. This classifier operates in the intermediate feature % space, the output space of the set of base classifiers. A new dataset B has % to be mapped to this intermediate space first by BC = B*WC before it can be % classified by D = BC*VC. As this is equivalent to D = B*WC*VC, the total % trained combiner is WTC = WC*VC = WC*A*WC*FISHERC. To simplify this procedure% PRTools executes the training of a combined classifier by % WTC = A*(WC*FISHERC) as WTC = WC*A*WC*FISHERC.%% In order to allow for training an untrained parallel combined classifier by% A*WC the subsets of the features of A that apply for the individual base% classifiers of WC should be known to WC. This is facilitated by the% call WC = PARALLEL(WC,N), in which N is an array of integers, such that% sum(N) equals the feature size of A.%% SEE ALSO% MAPPINGS, DATASETS, MAXC, MINC, SUMC, MEDIANC, PRODC, FISHERC, STACKED%% EXAMPLES% See PREX_COMBINING.% Copyright: R.P.W. Duin, duin@ph.tn.tudelft.nl% Faculty of Applied Sciences, Delft University of Technology% P.O. Box 5046, 2600 GA Delft, The Netherlands% $Id: parallel.m,v 1.7 2004/02/20 12:50:29 bob Exp $function out = parallel (varargin)	prtrace(mfilename);	% If there are no arguments, just return an empty map.	if (nargin == 0) 		out = mapping(mfilename,'combiner');		return	end	% If there is one argument, assume it is a mapping or cell array of these.	if (nargin == 1)		v = varargin{1};		if (~iscell(v))			ismapping(v);         % Assert that V is a single mapping.			out = mapping('parallel',getmapping_type(v),{v},getlabels(v));			out = set(out,'size',getsize(v));		else			% If V is a cell array of mappings, unpack it and call this function			% for each cell.			out = feval(mfilename,v{:});		end		return	end	if ( nargin == 2 & ( isparallel(varargin{1}) | iscell(varargin{1}) ) ...			& ~ismapping(varargin{2}) )		% special case, store dataset sizes		if iscell(varargin{1})			w = parallel(varargin{1});		else			w = varargin{1};		end		n = varargin{2};		if length(w.data) ~= length(n)			error('Wrong number of classsizes')		end		w.data = [w.data {n}];		out = w;			% If there are multiple arguments and the first is not a dataset,	% combine the supplied mappings.	elseif ((nargin > 2) | ~isa(varargin{1},'dataset')) 		v1 = varargin{1};   	if (isempty(v1))  		start = 3; v1 = varargin{2};   	else  		start = 2;  	end		ismapping(v1);     % Assert that V1 is a mapping.		k      = getsize_in(v1);             % Extract V1's characteristics.		labels = getlabels(v1);		type   = getmapping_type(v1);		if (~strcmp(getmapping_file(v1),mfilename))			% If V1 is not already a parallel combiner, make it into a cell array			% of mappings.			v = {v1};		else					% V1 is already a parallel combiner: get the mapping data.			v = getdata(v1);		end				% Now concatenate all base classifiers as cells in V.		for j = start:nargin			v2 = varargin{j}; 			if (~strcmp(type,getmapping_type(v2)))				error('mappings should be of equal type')			end			v      = [v {v2}]; 			k      = k + getsize_in(v2);			labels = [labels; getlabels(v2)];		end		% Construct the combined classifier.		out = mapping('parallel',type,v,labels,k);			else 		% Execution: dataset * parallel_mapping.		a = varargin{1}; 		v = varargin{2}; ismapping(v);    % Assert that V is a mapping.		out = []; n = 0;		if isuntrained(v)			if ismapping(v.data{end})				error(['Training of parallel combined untrained classifier not possible.' ...						newline 'Feature sizes should be stored in the classifier first.'])			end			s = v.data{end};			if sum(s) ~= size(a,2)				error('Feature size of dataset does not match with classifier')			end			v.data = v.data(1:end-1);			for j=1:length(v.data)				N  = [n+1:n+s(j)];       % to features indexed by N.				n = n + s(j);				w  = a(:,N)*v{j};				out = [out; w];			end		else			for j = 1:length(v.data)				sz = size(v{j},1);     % Classifier V{J} is applied				N  = [n+1:n+sz];       % to features indexed by N.				b  = a(:,N)*v{j}; 				if (size(v{j},2) == 1) % Restore 2D outputs for k->1 classifiers.					b = b(:,1);				end				n = n + sz;				out = [out b];         % Concatenate mapped data.			end		end	end	return