Grouped rank centrality: Ranking and grouping from pairwise comparisons simultaneously

Interpretation of ranking can be simplified by grouping when the number of ranking items is large. This paper is concerned with the problem of ranking and grouping from pairwise comparisons simultaneously so that items with similar abilities are clustered into the same group. To achieve this, a penalised spectral ranking method, named as grouped rank centrality, is designed. In the method, the fused lasso estimator is used in conjunction with a spectral-based method, rank centrality. We reconstruct and simplify the original problem to a concise structure which has the same form with the linear adaptive lasso problem. The ability score estimation is finally obtained by applying the refitting strategy based on the group structure identified by the grouped rank centrality. Theoretical results are provided to present the grouping consistent property and asymptotic normality of the estimator under the Bradley-Terry assumption. The simulation study and real examples including National Basketball Association (NBA) data and journal meta-rankings are provided to demonstrate the validity of our theory and the practical significance of the proposed approach.