function [e, thr] = dd_roc(a,w)%DD_ROC Receiver Operating Characteristic curve %%        E = DD_ROC(A,W)%        E = DD_ROC(A*W)%        E = A*W*DD_ROC%% Find for a (data description) method W the Receiver Operating% Characteristic curve over dataset A.  The results are returned in a% structure E, containing two fields. E.err contains the classification% errors, E.thr contains the trhesholds for the different operating% points.%% The first column of E.err gives the fraction of target objects% rejected (false negative fraction, FN), the second column the fraction% of outlier objects accepted (the false positive fraction, FP). %% NOTE: people typically use this ROC definition: false positive FP% (outlier accepted) on the x-axis, and true positive TP (target% accepted) on the y-axis. You can retrieve that by using:%   NEWE = [E(:,2) 1-E(:,1)]% I choose to define E consistent, i.e. both numbers indicate% 'errors'. In the routines PLOTROC and DD_AUC the variable E is% automatically converted to get the 'standard' plots and AUC values.%% See also: plotroc, dd_auc, dd_error, simpleroc, dd_eer.%%@article{Metz1978,%	author = {Metz, C.E.},%	title = {Basic principles of {ROC} analysis},%	journal = {Seminars in Nuclear Medicine},%	year = {1978},%	volume = {VIII},%	number = {4},%	month = {October}%}% Copyright: D.M.J. Tax, D.M.J.Tax@prtools.org% Faculty EWI, Delft University of Technology% P.O. Box 5031, 2600 GA Delft, The Netherlands% Use the same setup as testc% When no input arguments are given, return an empty mappingif nargin==0		e = mapping(mfilename,'fixed');elseif nargin == 1	% Now we should have a mapped dataset, so the real work is done!	% for evaluation, we need both target and outlier objects:	if ~isocset(a)		error('I need an OC dataset for computing the ROC curve.');	end	[It,Io] = find_target(a);	if isempty(It)		error('Dataset A does not contain target objects');	end	if isempty(Io)		error('Dataset A does not contain outlier objects');	end	% get the labels of A:	truelab = zeros(size(a,1),1);	truelab(It) = 1;	% check if we have sane results:	if ~all(isfinite(+a))		warning('dd_tools:NonfiniteOutputs',...			'Some strange (non-finite) classifier outputs: can you check your classifier?');		% only keep the outputs which have finite values:		I = all(isfinite(+a),2);		a = a(I,:);	end	% store the operating poiont for later:	% First check if we are dealing with a mapping, or a classifier:	fl = getfeatlab(a);	if size(fl,1)<2 % it is a mapping, so no OP available		e.op = [];	else % it is a classifier, we can just apply dd_error		e.op = a*dd_error;	end	% first find out where the output for the target objects are stored:	if ~isempty(fl)		tcolumn = strmatch('target ',fl);		if isempty(tcolumn)			warning('I cannot find the target feature, using feature 1.');			tcolumn = 1;		end	else  % there are no feature labels defined... suspicious...		tcolumn = 1;		warning('No feature labels defined, using feature 1.');	end	% and now extract the required column 'resemblance to target set':	a = +a(:,tcolumn);	% now the real computation is done:	[err, thr] = simpleroc(a,truelab);	e.err = err;	% Find the errors and the thresholds between the points on the curve:	derr = diff(err)/2;	e.thrcoords = [err(1,:); err(1:(end-1),:)+derr; err(end,:)];	dthr = diff(thr)/2;	if ~isempty(dthr) % in some cases there is just 1 threshold value		               % defined :-( (sigh)		e.thresholds = [thr(1); thr(1:(end-1))+dthr; thr(end)];	else		e.thresholds = [thr(1); thr(end)];	endelse	% Separate mapping and dataset are given, so we have to map the data	% first:	ismapping(w);	istrained(w);	e = feval(mfilename,a*w);endreturn