The extension of the area under the receiver operating characteristic curve to multi-class problems

The area under the Receiver Operating Characteristic curve (AUC) has been successfully applied to binary-class tasks. However, its extension to multi-class problems has become a difficult task due to some practical issues. Up to now, its generalization work is relatively little and is not considerably ideal. In this paper, a new method is presented to estimate AUC for multi-class problems, which not only can obtain the overall AUC but also care how well each class is separated from others. Thus it is a more desirable measure to examine both the overall and detail performances of classifiers with multi-class problem. Moreover, the developed measure is independent on class distributions, which is the singular merit of the standard AUC with binary class task. As a case study, in terms of the developed measure we evaluated three different classification algorithms (NaiveBayes, KNN(5) and C4.5) on the 18 multi-class datasets.