Multi-class AUC metrics and weighted alternatives

The area under the receiver operating characteristic curve (AUC) is a useful and widely used measure to evaluate the performance of binary and multi-class classification models. However, it does not take into account the exact numerical output of the models, but rather looks at how the output ranks the cases. AUC metrics that incorporate the exact numerical output have been developed for binary classification. In this paper, we try to extend such weighted metrics to the multi-class case. Several metrics are suggested. Using real world data, we investigate intercorrelations between these metrics and demonstrate their use.