%ROC Receiver-Operator Curve% %   E = ROC(A,W,C,N)%   E = ROC(B,C,N)%% INPUT%   A  Dataset%   W  Trained classifier, or%   B  Classification result, B = A*W*CLASSC%   C  Index of desired class (default: C = 1)%   N  Number of points on the Receiver-Operator Curve (default: 100)%% OUTPUT%   E  Structure containing the error of the two classes%% DESCRIPTION% Computes N points on the receiver-operator curve of the classifier W for% class C in the labeled dataset B, which is typically the result of% B = A*W*CLASSC; or for the dataset A labelled by applying the (cell array of)% trained classifiers W.%% Note that a Receiver-Operator Curve is related to a specific class (class C)% for which the errors are plotted horizontally. The total error on all other% classes is plotted vertically. The class index C refers to its position in% the label list of the dataset (A or B). It can be found by GETCLASSI.%% The curve is computed for N thresholds of the posteriori probabilities% stored in B. The resulting error frequencies for the two classes are% stored in the structure E. E.XVALUES contains the errors in the first% class, E.ERROR contains the errors in the second class. In multi-class% problems these are the mean values in a single class, respectively the% mean values in all other classes.%% Use PLOTR(E) for plotting the result. In the plot the two types of error% are annotated as 'Error I' (error of the first kind) and 'Error II' (error% of the second kind). All error estimates are weighted according the class% prior probabilities.%% EXAMPLES%	Train set A and test set T:%	  B = T*NMC(A); E = ROC(T,50); PLOTR(E); % Plots a single curve%	  E = ROC(T,A*{NMC,UDC,QDC});  PLOTR(E); % Plots 3 curves%% REFERENCES% 1. R.O. Duda, P.E. Hart, and D.G. Stork, Pattern classification, 2nd edition, %    John Wiley and Sons, New York, 2001.% 2. A. Webb, Statistical Pattern Recognition, John Wiley & Sons, New York, %    2002.%% SEE ALSO% DATASETS, MAPPINGS, PLOTR, REJECT, TESTC, GETCLASSI% Copyright: R.P.W. Duin, duin@ph.tn.tudelft.nl% Faculty of Applied Sciences, Delft University of Technology% P.O. Box 5046, 2600 GA Delft, The Netherlands% $Id: roc.m,v 1.10 2004/12/14 20:43:25 duin Exp $function e = roc(a,w,clas,n)	prtrace(mfilename);	% Depending on the call, CLAS may the third or second argument.	% and N the third or the fourth.		if nargin < 4, n = []; end	if nargin < 3, clas= []; end	if nargin < 2, w = []; end	if nargin < 1, a= []; end		if isempty(a)		e = mapping('roc','fixed',{w,clas,n});		return;	end		name = [];	num_w = 1;	compute = 0;	if isa(w,'double') | isempty(w)		n = clas; 		clas = w;		b = a;	elseif iscell(w)		num_w = length(w); 		compute = 1;	elseif ismapping(w)		istrained(w);		b = a*w*classc;		name = getname(w);	else			error('Classifier or cell array of classifiers expected.')	end		if isempty(n),		n = 100;		prwarning(4,'number of ROC points not given, assuming 100');	end		if isempty(clas)		clas = 1;		prwarning(4,'no class given, class 1 assumed');	end	p       = getprior(a);  datname = getname(a);	lablist = getlablist(a,'string');	if clas > size(lablist,1)		error('Wrong class number')	end	clasname= lablist(clas,:);	% Set up the ROC structure.	e.error   = zeros(num_w,n+1);	e.std     = zeros(num_w,n+1);	e.xvalues = [0:n]/n;;	e.n       = 1;	e.xlabel  = 'Error I';	e.ylabel  = 'Error II';	e.plot    = 'plot';	e.names   = name;  if (~isempty(datname))		e.title = ['ROC curve for the ' datname ', class ' clasname];	end	thr = [];															% Threshold range, will be set below.	for j = 1:num_w														% If a cell array of classifiers was given, apply each one here.		if (compute)			v = w{j};			if (~istrained(v))				error('The supplied classifier mappings should be trained.')			end			b = a*v*classc;			e.names = char(e.names,getname(v));		end		[m,c] = size(b); nlab = getnlab(b); d = sort(b(:));		% Attempt to compute a good threshold range on the first classified		% dataset.		if (isempty(thr))			thr = [min(d) d(ceil(([1:n-1]/(n-1))*m*c))' 1]; 		end			e1 = []; e2 = [];		% NLAB_OUT will be one where B is larger than THR.		I = matchlablist(b.lablist,b.featlab); % Correct possible changes class orders		nlab_out = (repmat(+b(:,I(clas)),1,n+1) > repmat(thr,m,1));		% ERRS will be 1 where the numeric label is unequal to NLAB_OUT		% (i.e., where errors occur).		errs = (repmat((nlab==clas),1,n+1) ~= nlab_out);					% Split the cases where ERRS = 1 into cases for CLAS (E1) and all 		% other classes (E2).		e1 = [e1; mean(errs(find(nlab==clas),:),1)];		e2 = [e2; mean(errs(find(nlab~=clas),:),1)];				% Fill results in the ROC structure.		e.error(j,:)   = e2;		e.xvalues(j,:) = e1;	end	% First name will be the empty string [], remove it.	if (num_w > 1)		e.names(1,:) = [];	endreturn