%TESTAUC Multiclass error area under the ROC
%
% E = TESTAUC(A*W)
% E = TESTAUC(A,W)
% E = A*TESTAUC(W)
% E = A*W*TESTAUC
%
% INPUT
% A Dataset to be classified
% W Classifier
%
% OUTPUT
% E Error, Area under the ROC
%
% DESCRIPTION
% The area under the ROC is computed for the datset A w.r.t. the
% classifer W. The estimator is based on a rank analysis of the classifier
% outcomes. Ties are broken by a two-way sorting and averaging.
%
% The multiclass situation is solved by averaging over all outcomes of
% the one-against-rest ROCs.
%
% Note that E is an error and not a performance measure like the AUC often
% used in literature.
%
% SEE ALSO (<a href="http://37steps.com/prtools">PRTools Guide</a>)
% DATASETS, MAPPINGS, TESTC, PRROC
% 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
function e = testauc(varargin)
argin = shiftargin(varargin,'prmapping');
argin = setdefaults(argin,[],[]);
if mapping_task(argin,'definition')
e = define_mapping(argin,'fixed');
else % Evaluate.
[a,w] = deal(argin{:});
if (isempty(w))
% Classification matrix already computed
d = a;
else
% Compute classification matrix now
d = a*w;
end
[m,k,c] = getsize(d);
s = classsizes(d);
if k == 1 % classifier with a single class outcome, make two for consistency
d = [d 1-d];
k = 2;
end
class_names = getfeatlab(d); % class names
e = zeros(1,c);
for j=1:c % run over all classes
% forward sorting
[ds,J1] = sort(-d(:,j)); [j1,K1] = sort(J1);
% backward sorting to solve ties
[ds,J2] = sort(flipud(-d(:,j))); [j2,K2] = sort(J2); K2 = flipud(K2);
% get all object indices for this class
K = findlabels(d,class_names(j,:));
% retrieve number of wrong pairs
e(j) = (sum(K1(K)) + sum(K2(K))-(s(j)*(s(j)+1)))/2;
% error contribution
e(j) = e(j) / ((m-s(j))*s(j));
end
% average over all classes
e = mean(e);
end