%KNNM K-Nearest Neighbour based density estimate%%   W = KNNM(A,KNN)%%   D = B*W% % INPUT% 	A     Dataset%   KNN   Number of nearest neighbours	%% OUTPUT%   W     Density estimate %% DESCRIPTION  % A density estimator is constructed based on the k-Nearest Neighbour rule% using the labeled objects in A. All objects, however, are used if the% entire dataset is unlabeled or if A is not a dataset, but a double. % In all cases, just single density estimator W is computed.% Class priors in A are neglected.% % The mapping W may be applied to a new dataset B using DENSITY = B*W.%% SEE ALSO% DATASETS, MAPPINGS, KNNC, QDC, PARZENM, GAUSSM% $Id: knnm.m,v 1.4 2008/03/06 05:05:23 duin Exp $function w = knnm(a,arg2)	prtrace(mfilename);	if (nargin < 2)		prwarning(2,'number of neighbours to use not specified, assuming 1');		arg2 = 1; 	end  mapname = 'KNN Density Estimation';	if (nargin < 1) | (isempty(a)) 		% No arguments given: return empty mapping.		w = mapping(mfilename,arg2);		w = setname(w,mapname);	elseif (~isa(arg2,'mapping'))			% Train a mapping.		knn = arg2;				labname = getname(a);		if (~isdataset(a) & ~isdatafile(a)) | getsize(a,3) ~= 1			w = mclassm(a,mapping(mfilename,knn),'weight');			w = setlabels(w,labname);			w = setname(w,mapname);		return				return		end		islabtype(a,'crisp');		isvaldfile(a,1);		a = testdatasize(a,'objects');		a = remclass(a);		[m,k] = size(a);		w = mapping(mfilename,'trained',{a,knn},labname,k,1);		w = setname(w,mapname);	else															% Execute a trained mapping V.		v = arg2;		b   = v.data{1};								% B is the original training data.		knn = v.data{2};		iscomdset(a,b,0);		[m,k] = size(b); 		u = scalem(b,'variance');		a = a*u;		b = b*u;		d = sqrt(distm(+a,+b));					% Calculate squared distances		[s,J] = sort(d,2);							%   and find nearest neighbours.		ss = s(:,knn);									% Find furthest neighbour		ss(find(ss==0)) = realmin.^(1/k);	% Avoid zero distances		f = knn./(m*nsphere(k)*(ss.^k)); 	% Normalize by the volume of sphere																		%   defined by the furthest neighbour.		f = f*prod(u.data.rot);         % Correct for scaling																		w = setdat(a,f,v);							% proper normalisation has still to be done.	endreturnfunction v = nsphere(k)	% Volume k-dimensional sphere	v = (2*(pi^(k/2))) / (k*gamma(k/2));	return