PRTools Contents PRTools User Guide
roc

ROC

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; 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. This may not be very useful, but not  much more can be done as for multi-class cases the ROC is equivalent to a  multi-dimensional surface.

Use PLOTE(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. Remove the priors in A or B (by setprior(A,[])) to  produce a vanilla ROC.

### Example(s)

Train set A and test set T:
B = T*NMC(A); E = ROC(T,50); PLOTE(E); % Plots a single curve
E = ROC(T,A*{NMC,UDC,QDC}); PLOTE(E); % Plots 3 curves

### Reference(s)

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.