The AUK : a simple alternative to the AUC

The area under the receiver operating characteristic (ROC) curve, also known as the AUC-index, is commonly used for ranking the performance of data mining models. The AUC has various merits, such as ease of interpretation. However, since it is class indifferent, its usefulness while dealing with highly skewed data sets is questionable. In this paper, we propose a simple alternative scalar measure to the AUC-index, the area under the Kappa curve (AUK). The proposed AUK-index compensates for the class indifference of the AUC by being sensitive to the class distribution. Therefore, it is particularly suitable for measuring classifiers' performance on skewed data sets. After introducing the AUK we explore its mathematical relationship with the AUC and show that there is a non-linear relation between them.