Learning how to rank from heavily perturbed statistics - digraph clustering approach

Ranking is one of the most fundamental problems in machine learning with applications in many branches of computer science such as: information retrieval systems, recommendation systems, machine translation and computational biology. Ranking objects based on possibly conflicting preferences is a central problem in voting research and social choice theory. In this paper we present a new simple combinatorial ranking algorithm adapted to the preference-based setting. We apply this new algorithm to the well-known scenario where the edges of the preference tournament are determined by the majority-voting model. It outperforms existing methods when it cannot be assumed that there exists global ranking of good enough quality and applies combinatorial techniques that havent been used in the ranking context before. Performed experiments show the superiority of the new algorithm over existing methods, also over these that were designed to handle heavily perturbed statistics. By combining our techniques with those presented in \cite{mohri}, we obtain a purely combinatorial algorithm that answers correctly most of the queries in the heterogeneous scenario, where the preference tournament is only locally of good quality but is not necessarily pseudotransitive. As a byproduct of our methods, we obtain the algorithm solving clustering problem for the directed planted partition model. To the best of our knowledge, it is the first purely combinatorial algorithm tackling this problem.