Label ranking by learning pairwise preferences

Preference learning is a challenging problem that involves the prediction of complex structures, such as weak or partial order relations, rather than single values. In the recent literature, the problem appears in many different guises, which we will first put into a coherent framework. This work then focuses on a particular learning scenario called label ranking, where the problem is to learn a mapping from instances to rankings over a finite number of labels. Our approach for learning such a ranking function, ranking by pairwise comparison (RPC), first induces a binary preference relation from suitable training data using a natural extension of pairwise classification. A ranking is then derived from the learned relation relation by means of a ranking procedure, whereby different ranking functions can be used for minimizing different loss functions. In particular, we show that weighted voting minimizes the Spearman rank correlation. Finally, we compare RPC to constraint classification, an alternative approach to label ranking, and show empirically and theoretically that RPC is computationally more efficient.