function [tp, fp] = rocch(t, y)
%
% ROCCH - generate a receiver operating characteristic convex hull
%
% [TP,FP] = ROCCH(T,Y) gives the true-positive rate (TP) and false positive
% rate (FP), corresponding to the convex hull of the receiver operating
% characteristic, where Y is a column vector giving the score assigned to
% each pattern and T indicates the true class (a value above zero
% represents the positive class and anything else represents the negative
% class). To plot the ROC convex hull,
%
% PLOT(FP,TP);
% XLABEL('FALSE POSITIVE RATE');
% YLABEL('TRUE POSITIVE RATE');
% TITLE('RECEIVER OPERATING CHARACTERISTIC CONVEX HULL (ROCCH)');
%
% See [1,2] for further information.
%
% [1] Fawcett, T., "ROC graphs : Notes and practical
% considerations for researchers", Technical report, HP
% Laboratories, MS 1143, 1501 Page Mill Road, Palo Alto
% CA 94304, USA, April 2004.
%
% [2] Provost, F. and Fawcett, T., "Robust classification for
% imprecise environments", Machine Learning, vol. 42,
% no. 3, pp. 203-231, 2001.
%
% See also : ROCCH, AUROC
%
% File : rocch.m
%
% Date : Wednesday 10th November 2004
%
% Author : Dr Gavin C. Cawley
%
% Description : Generate the convex hull of an ROC curve for a two-class
% classifier (see [1] and [2] for details).
%
% References : [1] Fawcett, T., "ROC graphs : Notes and practical
% considerations for researchers", Technical report, HP
% Laboratories, MS 1143, 1501 Page Mill Road, Palo Alto
% CA 94304, USA, April 2004.
%
% [2] Provost, F. and Fawcett, T., "Robust classification for
% imprecise environments", Machine Learning, vol. 42,
% no. 3, pp. 203-231, 2001.
%
% History : 10/11/2004 - v1.00
%
% To do : Add an option to specify the maximum number of points to
% consider to minimise memory usage.
%
% Copyright : (c) G. C. Cawley, November 2004.
%
% This program is free software; you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation; either version 2 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program; if not, write to the Free Software
% Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
%
% generate the ROC curve
[tp,fp] = roc(t,y);
tp = [tp ; 0];
fp = [fp ; 1];
% we are really interested in the convex hull
idx = unique(convhull(fp, tp));
fp = fp(idx(1:end-1));
tp = tp(idx(1:end-1));
% bye bye...