function [y, dfce] = bayescls( X, model )
% BAYESCLS Bayesian classifier with reject option.
%
% Synopsis:
% [y, dfce] = bayescls(X,model)
%
% Description:
% This function implements the classifier minimizing the Bayesian risk
% with 0/1-loss function. It corresponds to the minimization of
% probability of misclassification. The input vectors X are classified
% into classes with the highest a posterior probabilities computed from
% given model.
%
% The model contains parameters of conditional class probabilities
% in model.Pclass [cell 1 x num_classes] and a priory probabilities
% in model.Prior [1 x num_classes].
%
% The function
% p = feval(model.Pclass{i}.fun, X, model.pclass{i})
% is called to evaluate the i-the class conditional probability of X.
%
% It returns class labels y [1 x num_data] for each input vector
% and matrix dfce [num_class x num_data] of unnormalized a posterior
% probabilities
% dfce(y,i) = Conditional_probability(X(:,i)|y)*Prior(y).
%
% If the field model.eps exists then the Bayesian classifier
% with the reject option is used. The eps is penalty for the
% decision "don't know" which is indicated by label y = 0.
%
% Input:
% X [dim x num_data] Vectors to be classified.
%
% model [struct] Describes probabilistic model:
% .Pclass [cell 1 x num_classes] Class conditional probabilities.
% .Prior [1 x num_classes] A priory probabilities.
%
% .eps [1x1] (optional) Penalty of decision "don't know".
%
% Output:
% y [1 x num_data] Labels (1 to num_classes); 0 for "don't know".
% dfce [num_classes x num_data] Unnormalized a posterior
% probabilities (see above).
%
% Example:
% trn = load('riply_trn');
% tst = load('riply_tst');
% inx1 = find(trn.y==1);
% inx2 = find(trn.y==2);
% model.Pclass{1} = mlcgmm(trn.X(:,inx1));
% model.Pclass{2} = mlcgmm(trn.X(:,inx2));
% model.Prior = [length(inx1) length(inx2)]/(length(inx1)+length(inx2));
% ypred = bayescls(tst.X,model);
% cerror(ypred,tst.y)
%
% See also
% BAYESDF, BAYESERR.
%
% About: Statistical Pattern Recognition Toolbox
% (C) 1999-2003, Written by Vojtech Franc and Vaclav Hlavac
% <a href="http://www.cvut.cz">Czech Technical University Prague</a>
% <a href="http://www.feld.cvut.cz">Faculty of Electrical Engineering</a>
% <a href="http://cmp.felk.cvut.cz">Center for Machine Perception</a>
% Modifications:
% 09-jun-2004, VF
% 01-may-2004, VF
% 11-mar-2004, VF, "don't" know decision added.
% 19-sep-2003, VF
[dim,num_data]=size(X);
num_classes = length( model.Pclass );
dfce=zeros(num_classes,num_data);
for i=1:num_classes,
dfce(i,:) = model.Prior(i)*feval(model.Pclass{i}.fun,X,model.Pclass{i});
end
[tmp,y] = max(dfce);
if isfield(model, 'eps'),
perror = 1-tmp./sum(dfce,1);
inx = find( perror > model.eps);
y(inx) = 0;
end
return;