About the relationship between ROC curves and Cohen's kappa

Receiver operating characteristic (ROC) curves are very powerful tools for measuring classifiers’ accuracy in binary-class problems. However, their usefulness in real-world multi-class problems has not been demonstrated yet. In these frequently occurring multi-class cases, simple accuracy meters that do compensate for random successes, such as the kappa statistic, are needed.ROC curves are two-dimensional graphs. Kappa is a scalar. Each comes from an entirely different discipline. This research investigates whether they do have anything in common. A mathematical formulation that links ROC spaces with the kappa statistic is derived here for the first time. The understanding of how these two accuracy meters relate to each other can assist in a better understanding of their respective pros and cons.