Area under the ROC Curve

Synonyms

AUC

Definition

The area under a receiver operating characteristic (ROC) curve, abbreviated as AUC, is a single scalar value that measures the overall performance of a binary classifier (Hanley and McNeil 1982). The AUC value is within the range [0.5–1.0], where the minimum value represents the performance of a random classifier and the maximum value would correspond to a perfect classifier (e.g., with a classification error rate equivalent to zero).

The AUC is a robust overall measure to evaluate the performance of score classifiers because its calculation relies on the complete ROC curve and thus involves all possible classification thresholds. The AUC is typically calculated by adding successive trapezoid areas below the ROC curve. Figure 1 shows the ROC curves for two score classifiers A and B. In this example, classifier A has a larger AUC value than classifier B.

Area under the ROC Curve, Fig. 1

The AUC is used as an overall measure to compare classifiers