%NAIVEBC Naive Bayes classifier% % 	W = NAIVEBC(A,K)% % INPUT	%   A   Training dataset%   N   Scalar number of bins (default: 10)%% OUTPUT%   W   Naive Bayes classifier mapping%% DESCRIPTION% Stores the naive Bayes classifier. This version divides each axis into N% bins, counts the number of training examples for each of the classes in% each of the bins, and classifies the object to the class that gives% maximum posterior probability. Missing values will be put into a separate% bin.%% A future version may handle discrete features properly, this one treats% them as continuous variables.%% SEE ALSO% DATASETS, MAPPINGS, UDC, QDC, PARZENC, PARZENDC% Copyright: D.M.J. Tax, 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: naivebc.m,v 1.18 2004/02/28 21:28:54 bob Exp $function w = naivebc(a,arg2)	if (nargin < 2)		prwarning (2,'number of bins not specified, assuming 10.');		arg2 = 10; 	end	% No arguments given: return untrained mapping.	if (nargin < 1) | (isempty(a))		w = mapping(mfilename,{arg2});		w = setname(w,'Naive Bayes');		return	end	if (~ismapping(arg2))     % Second argument is not a mapping: training.		N = arg2;			islabtype(a,'crisp');		isvaldset(a,1,2); % at least 2 object per class, 2 classes		[m,k,c] = getsize(a); M = classsizes(a);		% Train the mapping. First, find the scale and offset of the data 		% and normalise (this is very non-robust, but ok...)		offset_a = min(a); maxa = max(a); scale_a = maxa - offset_a;				if(any(scale_a==0))			prwarning (2,'one of the features has the same value for all data; scale change to realmin');			scale_a(scale_a==0) = realmin;				end		a = a - repmat(offset_a,m,1);		a = a ./ repmat(scale_a,m,1);		% P will contain the probability per bin per class, P0 the probability		% per class. The highest and lowest bounds will not be used; the lowest		% bound will be used to store the missing values.		p  = zeros(N+1,k,c);		% Count the number of objects for each of the classes.		for i = 1:c			Ic = findnlab(a,i);											% Extract one class.			Ia = ceil(N*+(a(Ic,:)));								% Find out in which bin it falls.			Ia(Ia<1) = 1; Ia(Ia>N) = N;							% Sanity check.			for j=1:N				p(j,:,i) = sum(Ia==j);								% Count for all bins.			end			p(N+1,:,i) = sum(~isnan(+a(Ic,:))); 	% The missing values.						% Use Bayes estimators are used, like elsewhere in PRTools.						p(:,:,i) = (p(:,:,i)+1) / (M(i)+N); 						% Probabilities.			p(:,:,i) = p(:,:,i) ./ repmat(scale_a/N,N+1,1); 	% Densities.		end		% Save all useful data.		pars.p0 = getprior(a); pars.p = p; pars.N = N;		pars.offset_a = offset_a; pars.scale_a = scale_a;		w = mapping(mfilename,'trained',pars,getlablist(a),k,c);		w = setname(w,'Naive Bayes');		w = setcost(w,a);	else                      % Second argument is a mapping: testing.		w = arg2;		pars = getdata(w);		 	% Unpack the mapping.		[m,k] = getsize(a); 		c = length(pars.p0);       % Could also use size(w.labels,1)...		% Shift and scale the test set.		a = a - repmat(pars.offset_a,m,1);		a = a ./ repmat(pars.scale_a,m,1);		% Classify the test set. First find in which bins the objects fall.		Ia = ceil(pars.N*+(a));		Ia(Ia<1) = 1; Ia(Ia>pars.N) = pars.N;			% Sanity check.		% Find the class probability for each object for each feature		out = zeros(m,k,c);		for i=1:k			out(:,i,:) = pars.p(Ia(:,i),i,:);		end		% Multiply the per-feature probs.		out = squeeze(prod(out,2));				if m == 1			out = out';		end		% Weight with class priors		out = out .* repmat(pars.p0,m,1);				% Done!		w = setdat(a,out,w);	endreturn