%NAIVEBC Naive Bayes classifier
%
% W = NAIVEBC(A,N)
% W = A*NAIVEBC([],N)
% W = A*NAIVEBC(N)
%
% W = NAIVEBC(A,DENSMAP)
% W = A*NAIVEBC([],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.
%
% This routine assumes continuous data. It may be applied to discrete data
% in case all features have the same number of discrete values. For proper
% results the parameter N should be set to this number.
%
% 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 (<a href="http://37steps.com/prtools">PRTools Guide</a>)
% DATASETS, MAPPINGS, PARZENM, GAUSSM, UDC, QDC, PARZENC, PARZENDC, REGOPTC
% Copyright: R.P.W. Duin, r.p.w.duin@37steps.com
% 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(varargin)
mapname = 'NaiveBayes';
argin = shiftargin(varargin,{'integer','prmapping'});
argin = setdefaults(argin,[],10);
if mapping_task(argin,'definition')
w = define_mapping(argin,'untrained',mapname);
elseif mapping_task(argin,'training') % Train a mapping.
[a,arg2] = deal(argin{:});
if ismapping(arg2) && 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 = prmapping(mfilename,'trained',pars,getlablist(a),k,c);
w = setname(w,'NaiveBayes');
w = setcost(w,a);
else % construct histograms
N = arg2; % number of bins
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;
K = find(scale_a~=0);
% 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,K))); % Find out in which bin it falls.
Ia(Ia<1) = 1; Ia(Ia>N) = N; % Sanity check.
for j=1:N
p(j,K,i) = sum(Ia==j); % Count for all bins.
end
p(N+1,K,i) = sum(~isnan(+a(Ic,K))); % The missing values.
% Use Bayes estimators are used, like elsewhere in PRTools.
p(:,K,i) = (p(:,K,i)+1) / (M(i)+N); % Probabilities.
p(:,K,i) = p(:,K,i) ./ repmat(scale_a(K)/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;
pars.feats = K;
w = prmapping(mfilename,'trained',pars,getlablist(a),k,c);
w = setname(w,'Naive Bayes');
w = setcost(w,a);
end
end
else % Second argument is a mapping: testing.
[a,w] = deal(argin{1:2});
pars = getdata(w); % Unpack the mapping.
[m,k] = size(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)...
K = pars.feats; % relevant features
% Shift and scale the test set.
a(:,K) = a(:,K) - repmat(pars.offset_a(K),m,1);
a(:,K) = a(:,K) ./ repmat(pars.scale_a(K),m,1);
% Classify the test set. First find in which bins the objects fall.
Ia = ceil(pars.N*+(a(:,K)));
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,length(K),c);
for i=1:length(K)
out(:,i,:) = pars.p(Ia(:,i),K(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