Ranking Individuals by Group Comparisons

Abstract

This paper proposes new approaches to rank individuals from their group comparison results. Many real-world problems are of this type. For example, ranking players from team comparisons is important in some sports. In machine learning, a closely related application is classification using coding matrices. Group comparison results are usually in two types: binary indicator outcomes (wins/losses) or measured outcomes (scores). For each type of results, we propose new models for estimating individuals' abilities, and hence a ranking of individuals. The estimation is carried out by solving convex minimization problems, for which we develop easy and efficient solution procedures. Experiments on real bridge records and multi-class classification demonstrate the viability of the proposed models.