bookmaker(cm)

% results = bookmaker([contingency matrix])
% 
% contingency matrix  ->  contingency matrix/table of network classification and training targets
%                             ie. classification x target'
%                                         
% results             <-  structure of results with the following fields
%                             contingencyMatrix:  As provided as argument 1 to function
%                             recall:             Ratio of correctly claimed class to total count 
%                                                 it actually was that class
%                             precision:          Ratio correctly claimed class to total count of
%                                                 times that it was claimed to be that class
%                             weightedAverage:    Ratio of correctly claimed classes to total
%                                                 number of cases
%                             F:                  Harmonic mean
%                             Fall:               F over all classes
%                             G:                  Geometric mean
%                             Gall:               G over all classes
%                             bookmakerMatrix:    Matrix of bookmaker results per class
%                             bookmaker:          Bookmaker result for all classes
%
% The informedness of a prediction method as captured by a contingency matrix is
% defined as the probability that the prediction method will make a correct decision
% as opposed to guessing and is calculated using the bookmaker algorithm.
%
% Alternate measures of the usefulness of a prediction method are all defective
% in that they do not take into account all cells of the continency matrix,
% they do not take into account the baseline performance due to chance/guessing, or
% they are concerned with significance or information rather than correctness. 
% 
% The Recall, Precision and Rank average are calculated for comparison, along
% with the F and G measures corresponding to their harmonic and geometric means.
%
% matlab: Sean Fitzgibbon 16/03/03
% octave: David Powers 11/04/03 
%
% For technical paper see www.infoeng.flinders.edu.au/papers/20030007.doc 
% For tutorial poster see www.infoeng.flinders.edu.au/papers/20030003.ppt

function results = bookmaker(cm)

if (size(cm,1) ~= size(cm,2))
    error('Contingency matrix must be square'); 
else
    k = size(cm,1);
end

N = sum(sum(cm));
rprob = sum(cm) ./ N;
pprob = sum(cm') ./ N;

recall = diag(cm)' ./ sum(cm);
precision = diag(cm')' ./ sum(cm');
wav = sum(diag(cm)) ./ N;

% Fall is wrong - use reciprocal formula
F = (2.*precision.*recall) ./ (precision + recall);
Fall = k / sum(ones(1,k)./F);

% Gall is wrong - use kth root
G = sqrt(precision.*recall);
Gall = (prod(G)^(1/k));

mask = diag(ones(1,k));
maskc = reshape(mask,k*k,1);
ind = find(maskc==0);
maskc(ind) = -1;
mask = reshape(maskc,k,k);

prob = rprob;
prob = prob(ones(k,1),:)';
probc = reshape(prob,k*k,1);
probc(ind) = 1-probc(ind);
prob = reshape(probc,k,k);

bmcm = cm ./ prob;    
bmcm = bmcm .* mask;
bms = sum(bmcm') / N;
bm = bms * pprob';

%results.contingencyMatrix = cm;
results.N = N;
results.recall = recall;
results.precision = precision;
results.weightedAverage = wav;
results.F = F;
results.Fall = Fall;
results.G = G;
results.Gall = Gall;
%results.bookmakerMatrix = bmcm;
results.bookmakerSum = bms;
results.bookmaker = bm;