Dyad ranking using Plackett–Luce models based on joint feature representations

摘要

Label ranking is a specific type of preference learning problem, namely the problem of learning a model that maps instances to rankings over a finite set of predefined alternatives. Like in conventional classification, these alternatives are identified by their name or label while not being characterized in terms of any properties or features that could be potentially useful for learning. In this paper, we consider a generalization of the label ranking problem that we call dyad ranking. In dyad ranking, not only the instances but also the alternatives are represented in terms of attributes. For learning in the setting of dyad ranking, we propose an extension of an existing label ranking method based on the Plackett–Luce model, a statistical model for rank data. This model is combined with a suitable feature representation of dyads. Concretely, we propose a method based on a bilinear extension, where the representation is given in terms of a Kronecker product, as well as a method based on neural networks, which allows for learning a (highly nonlinear) joint feature representation. The usefulness of the additional information provided by the feature description of alternatives is shown in several experimental studies. Finally, we propose a method for the visualization of dyad rankings, which is based on the technique of multidimensional unfolding.