%CMAPM Compute some special maps% % INPUT%  Various%% OUTPUT%  W  Mapping%% DESCRIPTION% CMAPM computes some special data-independent maps for scaling, selecting or % rotating K-dimensional feature spaces.% %  W = CMAPM(K,N)            Selects the features listed in the vector N%  W = CMAPM(K,P)            Polynomial feature map. P should be an N*K matrix%                            in which each row defines the exponents for the%                            original features in a polynomial term. Note: for%                            N = 1 and/or K = 1, feature selection is applied!%  W = CMAPM(K,'EXP')        Exponential, negative exponential and logarithmic %  W = CMAPM(K,'NEXP')       mappings.%  W = CMAPM(K,'LOG')%  W = CMAPM(K,'RANDROT')    Defines a random K-dimensional rotation.%  W = CMAPM(F,'ROT')        The N*K matrix F defines N linear combinations %                            to be computed by X*F'.%  W = CMAPM(X,'SHIFT')      Defines a shift of the origin by X.%  W = CMAPM(S,'SCALE')      Divides the features by the components of the %                            vector S.%  W = CMAPM({X,S},'SCALE')  Shift by X and scale by S.% % EXAMPLES % For the polynomial feature map, CMAPM(K,P), P defines exponents for each% feature. So P = [1 0; 0 1; 1 1; 2 0; 0 2; 3 0; 0 3] defines 7 features,% the original 2 (e.g. x and y), a mixture (xy) and all powers of the second% (x^2,y^2) and third (x^3,y^3) order. Another example is P = diag([0.5 0.5% 0.5]), defining 3 features to be the square roots of the original ones.%% SEE ALSO% MAPPINGS, SCALEM, FEATSELM, KLM% 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: cmapm.m,v 1.6 2004/06/04 13:23:33 duin Exp $function w = cmapm(arg1,arg2,par1,par2,par3)	prtrace(mfilename);	if (nargin < 2)		error('insufficient arguments');	end	if (~isa(arg1,'dataset'))								% First form: ARG1 is a matrix, construct a mapping.		data = arg1;		if (isstr(arg2))											type = arg2;			switch (type)				case {'exp','nexp','log'}			% Function mappings.					w = mapping(mfilename,'fixed',{type},[],data,data);					w = setname(w,type);				case 'randrot'								% Random rotation matrix.					[F,V] = eig(covm(randn(100*data,data)));					w = affine(F,zeros(1,data));					w = setname(w,'Random Rotation');				case 'rot'			  						% Rotation by given matrix.					[n,k] = size(data);					w = affine(data',zeros(1,n));					w = setname(w,'Rotation');				case 'shift'									% Shift by given vector.					k = length(data);					w = affine(eye(k),-data);					w = setname(w,'Shift');				case 'scale'									% Shift, scale & (optionally) clip.					if (iscell(data))							% Extract and check parameters.						shift = data{1}; scale = data{2}; 												if (length(data) == 3), clip = data{3}; else, clip = 0; end						k = length(scale);						if (~isempty(scale)) & (length(shift) ~= k)							error('shift and scale should have same dimension')						end					else						% Only a scale is specified; set shift and clip to 0.						scale = data; k = length(scale);						shift = zeros(1,k); clip = 0;					end					% Create mapping					if (clip)						w = mapping(mfilename,'fixed',{'normalize',shift,ones(1,k)./scale,clip},[],k,k);						w = setname(w,'Scaling');					else						w = affine(1./scale,-shift./scale);					end				otherwise					error(['unknown option ' arg2])			end		else			% ARG2 is not a string: feature selection or polynomial mapping.			if (min(size(arg2)) == 1)				% ARG2 is a vector: feature selection, DATA is input feature size				prwarning(4,'second input argument is a vector: performing feature selection');				if (min(arg2) < 1) | (max(arg2) > data)					error('Selected features out of range')				end				w = mapping(mfilename,'fixed',{'featsel',arg2},[],data,length(arg2));				w = setname(w,'Feature Selection');			else				% ARG2 is a matrix: polynomial mapping.				prwarning(4,'second input argument is a matrix: performing polynomial mapping');				[n,k] = size(arg2);				if (data ~= k)					error('matrix has wrong size')				else					w = mapping(mfilename,'fixed',{'polynomial',arg2},[],k,n);					w = setname(w,'Polynomial');				end			end		end		else 		% Second form: ARG1 is a dataset, execute some fixed mappings		a = +arg1; [m,k] = size(a);					% Extract dataset.		featlist = getfeatlab(arg1);		type = arg2;		switch (type)			case 'exp'				b = exp(a);			case 'nexp'				b = exp(-a);			case 'log'				b = log(a);			case 'normalize'				b = a - repmat(par1,m,1);				% Subtract mean (par1).				% Multiply by scale; use different ways of looping for small and P = diag([0.5 0.5% 0.5])				% large feature sizes				if (m > k), for j = 1:k, b(:,j) = b(:,j)*par2(j); end				else,       for i = 1:m, b(i,:) = b(i,:).*par2;   end         end				% Clip, if necessary (par3 ~= 0, see SCALEM).				if (exist('par3')) & (par3)					J = find(b < 0); b(J) = zeros(size(J));		% Set values < 0 to 0...					J = find(b > 1); b(J) = ones(size(J));		% ...and values > 1 to 1.				end			case 'featsel'				b = a(:,par1);									% Select feature indices (par1).				featlist = featlist(par1,:);			case 'polynomial'					[n,k] = size(par1);							% Create polynomial features.				b = zeros(m,n); 				for i = 1:n		    	b(:,i) = prod((a .^ (repmat(par1(i,:),m,1))),2);				end				featlist = [1:n]';			otherwise				error('unknown mapping')		end		w = setdata(arg1,b,featlist);	end	return