naivebc.m

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%NAIVEBC Naive Bayes classifier
% 
% 	W = NAIVEBC(A,N)
% 	W = A*NAIVEBC([],N)
%
% 	W = NAIVEBC(A,DENSMAP)
% 	W = A*NAIVEBC([],DENSMAP)
% 
% INPUT	
%   A       Training dataset
%   N       Scalar number of bins (default: 10)
%   DENSMAP Untrained mapping for density estimation
%
% OUTPUT
%   W       Naive Bayes classifier mapping
%
% DESCRIPTION
% The Naive Bayes Classifier estimates for every class and every feature
% separately. Total class densities are constructed by assuming
% independency and consequently multiplying the separate feature densities.
%
% The default 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.
%
% If N is NaN it is optimised by REGOPTC.
%
% Alternatively an untrained mapping DENSMAP may be supplied that will be
% used to estimate the densities per class and per features separately.
% Examples are PARZENM and GAUSSM.
%
% SEE ALSO
% DATASETS, MAPPINGS, PARZENM, GAUSSM, UDC, QDC, PARZENC, PARZENDC, REGOPTC

% Copyright: R.P.W. Duin, [e-mail]
% Faculty EWI, Delft University of Technology
% P.O. Box 5031, 2600 GA Delft, The Netherlands
  
% $Id: naivebc.m,v 1.5 2007/06/15 09:58:30 duin 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;
		
		if isnan(N)             % optimize complexity parameter
			defs = {10};
			parmin_max = [2,50];
			w = regoptc(a,mfilename,{N},defs,[1],parmin_max,testc([],'soft'),0);
		
		else
	
			islabtype(a,'crisp');
			isvaldfile(a,1,2); % at least 2 object per class, 2 classes
			a = testdatasize(a);

			[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);
			
		end
		
	elseif isuntrained(arg2) % train given untrained mapping, e.g. parzen
		
		[m,k,c] = getsize(a);
		v = cell(c,k);
		for i=1:c
			b = seldat(a,i);
			for j=1:k
				v{i,j} = b(:,j)*arg2;
			end
		end
		pars.dens = v;
		pars.p0 = getprior(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); 
		
		if isfield(pars,'dens')
			
			v = pars.dens;
			[c,k] = size(v);
		
			out = zeros(size(a,1),c);
			for i=1:c
				for j=1:k
					out(:,i) = out(:,i) + +log(a(:,j)*v{i,j});
				end
			end
			
			out = exp(out);
			
		else
			
			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

		end
		
		% Weight with class priors
		out = out .* repmat(pars.p0,m,1);
		
		% Done!
		w = setdat(a,out,w);

	end

return