% NAIVEBCC Naive Bayes Combining Classifier
%
% W = A*(WU*NAIVEBCC)
% W = WT*NAIVEBCC(B*WT)
% D = C*W
%
% INPUT
% A Dataset used for training base classifiers as well as combiner
% B Dataset used for training combiner of trained base classifiers
% C Dataset used for testing (executing) the combiner
% WU Set of untrained base classifiers, see STACKED
% WT Set of trained base classifiers, see STACKED
%
% OUTPUT
% W Trained Naive Bayes Combining Classifier
% D Dataset with prob. products (over base classifiers) per class
%
% DESCRIPTION
% During training the combiner computes the probabilities
% P(class | classifier outcomes) based on the crisp class assignements
% made by the base classifiers for the training set. During execution the
% product of these probabilities are computed, again following the crisp
% class assignments of the base classifiers. These products are returned
% as columns in D. Use CLASSC to normalise the outcomes. Use TESTD or
% LABELD to inspect performances and assigned labels.
%
% NAIVEBCC differs from the classifier NAIVEBC by the fact that the
% latter uses continuous inputs (no crisp labeling) and does not make a
% distinction between classifiers. Like almost any other classifier
% however, NAIVEBC may be used as a trained combiner as well.
%
% REFERENCE
% 1. Kuncheva, LI. Combining pattern classifiers, 2004, pp.126-128.
%
% SEE ALSO (<a href="http://37steps.com/prtools">PRTools Guide</a>)
% DATASETS, MAPPINGS, STACKED, NAIVEBC, CLASSC, TESTD, LABELD
% Copyright: Chunxia Zhang, 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
function V = naivebcc(A,W)
name = 'Naive Bayes combiner';
if nargin < 1 | isempty(A)
% If there are no inputs, return an untrained mapping.
V = prmapping(mfilename);
V = setname(V,name);
elseif nargin == 1
% call like V = NBC(A): train a NB classifier on the outcomes of the
% base classifiers. So A has c x k columns:
% c outcomes (classes) x k classifiers
islabtype(A,'crisp'); % allow crisp labels only
isvaldfile(A,1,2); % at least one object per class, 2 classes
A = testdatasize(A,'features'); % test whether they fit
A = setprior(A,getprior(A,0)); % avoid many warnings
[m,k,c] = getsize(A); % size of training set (m objects; k features; c classes)
L = k/c; % compute the number of classifiers
G = zeros(L*c,c); % confusion matrix for each base classifier
for i = 1:L
data = +A(:,(i-1)*c+1:i*c);
[max_val,max_ind] = max(data,[],2);
CM = zeros(c,c); % the (k,s)th entry indicates the number of elements
% whose true labels are omega_k and are assigned to omega_s
for k = 1:c
for s = 1:c
CM(k,s) = sum(A.nlab == k & max_ind == s);
end
end
G((i-1)*c+1:i*c,:) = CM'; % transpose the confusion matrix to facilitate
% the further computation
end
vector = classsizes(A);
% Find all class probs for all classifiers P(class | classifiers)
% P = (vector/m)*prod((G+1/c)./repmat(vector+1,size(G,1),1));
P = (G+1/c)./repmat(vector+1,size(G,1),1); % P(x|class)
P = P.*repmat(getprior(A),size(P,1),1); % P(x|class) P(class)
q = sum(P,2); % P(x)
P = P./repmat(q,1,c); % P(class|x)
V = prmapping(mfilename,'trained',P,getlablist(A),L*c,c);
V = setname(V,name);
elseif nargin == 2 & ismapping(W) % execution
% call like V = A*W, in which W is a trained NBC
isdataset(A);
[m,k] = size(A);
P = getdata(W); % Prob matrix found by training
c = size(P,2); % Number of classes
L = size(P,1)/c; % number of classifiers
% We assume that the k features of A (columns) are the results of
% L classifiers producing c outcomes. We will construct a matrix
% M with for every classifier a 1 for its maximum class (most
% confident) class.
M = zeros(m,k);
for i = 1:L
NM = zeros(m,c);
S = (i-1)*c+1:i*c;
[maxv,maxi] = max(+A(:,S),[],2);
NM(sub2ind([m,c],[1:m]',maxi)) = ones(m,1);
M(:,S) = NM;
end
% Now the confidences of the combiner will be estimated according
% to the product over the classifiers of P(classifier|class)
% estimated during training
d = zeros(m,c);
R = reshape(find(M'==1)-[1:c:m*c*L]',L,m)'+repmat([1:c:c*L],m,1);
for j=1:c
q = P(:,j)';
d(:,j) = prod(q(R),2);
end
%d = d*normm; % normalise confidences, leave to user
V = setdat(A,d,W); % store in dataset
end
return