VLFeat - Documentation - Matlab API - PLOTOP

[TP,TN] = VL_ROC(Y, SCORE) computes the ROC curve for the specified data. Y are the ground thruth labels (+1 or -1) and SCORE is the discriminant score assigned to them by a classifier (higher scores correspond to positive labels).

[TP,TN] are the true positive and true negative rates for incereasing values of the decision threshold.

[TP,TN,INFO] = VL_ROC(...) returns the following additional information:

INFO.EER Equal error rate.
INFO.AUC Area under the VL_ROC (AUC).
INFO.UR Uniform prior best op point rate.
INFO.UT Uniform prior best op point threhsold.
INFO.NR Natural prior best op point rate.
INFO.NT Natural prior best op point threshold.

VL_ROC(...) plots the VL_ROC diagram in the current axis.

About the ROC curve

Consider a classifier that predicts as positive all lables Y whose SCORE is not smaller than a threshold R. The ROC curve represents the performance of such classifier as the threshold R is varied. Let:

  #P   = num of positive samples
  #N   = num of negative samples
  #TP = num of samples that are correctly classified as positive
  #TN = num of samples that are correctly classified as negative
  #FP = num of samples that are incorrectly classified as positive
  #FN = num of samples that are incorrectly classified as negative

Consider also the rates:

            TP = #TP / #P,      FN = #FN / #P,
            TN = #TN / #N,      FP = #FP / #N.

Notice that:

             P = #TP + #FN ,    N = #TN + #FP,
             1 = TP + FN,       1 = TN + FP.

The ROC curve is the parametric curve (TP, TN) obtained as the classifier threshold R is varied.

The ROC curve is contained in the square with vertices (0,0) The (average) ROC curve of a random classifier is a line which connects (1,0) and (0,1).

The ROC curve is independent of the prior probability of the labels Y (i.e. of #P/(#P+#N) and #N/(#P+#N)).

An OPERATING POINT is a point on the ROC curve, corresponding to a certain threshold R. Each operating point corresponds to minimizing the empirical 01 error of the classifier for given prior probabilty of the labels Y. VL_ROC() computes the following operating points:

 Natural operating point
 Uniform operating point

 Options:

 Plot
   'TrueNegative' plots the true positives vs. the true negatives.
   'FalseNegative' plots the true positives vs. the false
   negatives.

See also VL_HELP().

VLFeat.org