%KERNELM Kernel mapping, kernel PCA% %   W = KERNELM(A,TYPE,P,N)%% INPUT%   A     Dataset%   TYPE  Type of the kernel (optional; default: 'distance')%   P     Kernel parameter (optional; default: 1)%   N     Output dimensionality (optional; default: dimensionality of A)%% OUTPUT%   W     Mapping: Kernel PCA%% DESCRIPTION% Computes the kernel mapping W for the representation objects in A. The % kernel is defined by TYPE, using the function PROXM. Look in PROXM for % details and the meaning of P. The kernel mapping is almost identical % to PROXM with some minor differences to increase accuracy.%% If N is given, the mapping is afterwords reduced to N dimensions by the % principle component analysis (kernel-PCA).%% New objects B can be mapped by B*W.% % SEE ALSO% DATASETS, MAPPINGS, PROXM, PCA.% Copyright: R.P.W. Duin, duin@ph.tn.tudelft.nl% Faculty of Applied Physics, Delft University of Technology% P.O. Box 5046, 2600 GA Delft, The Netherlands% $Id: kernelm.m,v 1.8 2004/11/18 12:44:22 davidt Exp $function w = kernelm(a,type,p,n);	prtrace(mfilename);	if (nargin < 4) 		n = []; 		prwarning(4,'Output dimensionality not specified, the data dimensionality assumed.')	end	if (nargin < 3)		prwarning(3,'P is not specified, assumed 1.')		p = 1; 	end	if (nargin < 2)		prwarning(3,'Kernel TYPE is not specified, assumed ''DISTANCE''.')		type = 'd'; 	end	if (nargin < 1) | (isempty(a))  		% Definition: an untrained mapping.		w = mapping(mfilename,{type,p,n});		if (isempty(n))			w = setname(w,'Kernel mapping');		else			w = setname(w,'Kernel PCA');		end		elseif ~isa(type,'mapping') 			% Training: W will be the trained mapping.		[m,k] = size(a);		some  = char('polynomial','p','sigmoid','s');		if (any(strcmp(cellstr(some),type)))			u  = mean(a,1);					aa = a - ones(m,1)*u; 	% Shift A such that the mean is at the origin.		else			u  = [];			aa = a;		end		w = mapping('kernelm','trained',{u,aa,type,p},getlab(a),k,m);		w = setname(w,'Kernel Mapping');		if ~isempty(n)			w = w*pca(a*w,n);			w = setname(w,'Kernel PCA');			end	else 		% Execution of the mapping, W will be a dataset.		v = +type;		if (isempty(v{1}))			d = a*proxm(v{2},v{3},v{4});		else			m = size(a,1);			d = (a-ones(m,1)*v{1})*proxm(v{2},v{3},v{4});		end%		d = [d ones(m,1)] * v{3};		w = setdat(a,d,type);	endreturn;