%STACKED Combining classifiers in the same feature space%%	  WC = STACKED(W1,W2,W3,  ....) or WC = [W1,W2,W3, ...]%	  WC = STACKED({W1,W2,W3, ...}) or WC = [{W1,W2,W3, ...}]%	  WC = STACKED(WC,W1,W2,  ....) or WC = [WC,W2,W3, ...]%% INPUT%	  W1,W2,W3  Set of classifiers%% OUTPUT%	  WC        Combined classifier%% DESCRIPTION% The base classifiers (or mappings) W1, W2, W3, ... defined in the same% feature space are combined in WC. This is a classifier defined for the% same number of features as each of the base classifiers 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. 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, 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.%% It is also possible to combine a set of untrained classifiers, e.g. WC =% [LDC NMC KNNC([],1)]*CLASSC, in which CLASSC takes care that all outputs% will be transformed to appropriate posterior probabilities. Training of% all base classifiers is done by WC = A*WC. Again, this may be combined% with training of a combiner by WTC = A*(WC*FISHERC).%% EXAMPLES% PREX_COMBINING% SEE ALSO% MAPPINGS, DATASETS, MAXC, MINC, SUMC,% MEDIANC, PRODC, FISHERC, PARALLEL% 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: stacked.m,v 1.2 2006/03/08 22:06:58 duin Exp $function w = stacked(varargin)	prtrace(mfilename);	% No arguments given: just return map information.	if (nargin == 0) 		w = mapping(mfilename,'combiner');		return	end	% Single argument: should be a mapping or cell array of mappings.  if (nargin == 1)  	v = varargin{1};		% If V is a single mapping, process it directly.		if (~iscell(v))	  	if (~isa(v,'mapping')) 	 			error('Mapping expected.') 		 	end	  	w = mapping('stacked',getmapping_type(v),{v},getlabels(v));  		w = set(w,'size',getsize(v));	  else			% If V is a cell array of mappings, call this function recursively.  		if (size(v,1) ~= 1)	  		error('Row of cells containing mappings expected') 		 	end 	 		w = feval(mfilename,v{:});  	end  	return  end	% Multiple arguments, all of which are mappings: combine them.  if (~((nargin == 2) & (isa(varargin{1},'dataset')))) 		% Get the first mapping.  	v1 = varargin{1};  	if (isempty(v1))  		start = 3; v1 = varargin{2};   	else  		start = 2;  	end  	ismapping(v1);														% Assert V1 is a mapping.  	k = prod(getsize_in(v1)); labels = getlabels(v1); type = getmapping_type(v1);		% If V1 is already a stacked mapping, unpack it to re-stack.  	if (~strcmp(getmapping_file(v1),mfilename))  		v = {v1};  	else  		v = getdata(v1);  	end  			% Now stack the second to the last mapping onto the first.  	for j = start:nargin  		v2 = varargin{j};  		if (~strcmp(type,getmapping_type(v2)))  			error('All mappings should be of the same type.')  		end  		if (getsize(v2,1) ~= k)  			error('Mappings should have equal numbers of inputs.')  		end  		v = [v {v2}];  		labels = [labels;getlabels(v2)];  	end  	w = mapping('stacked',type,v,labels,k);  else  	% The first argument is a dataset: apply the stacked mapping.  	a = varargin{1};  	v = varargin{2};  	if (~isa(v,'mapping'))  		error('Mapping expected as second argument.')  	end		% Calculate W, the output of the stacked mapping on A.  	w = [];  	for j = 1:length(v.data)  		b = a*v{j};			% If, for a mapping to 1D (e.g. a 2-class discriminant)			% more than 1 output is returned, truncate.  		if (size(v{j},2) == 1)  			b = b(:,1);  		end  		w = [w b];								% Concatenate the outputs.  	end  endreturn