Rank Aggregation via Nuclear Norm Minimization

TL;DR

This paper introduces a novel rank aggregation method leveraging skew-symmetric matrix completion, providing a robust approach to ranking items from pairwise comparisons and ratings, even with noisy or incomplete data.

Contribution

It extends matrix completion algorithms to skew-symmetric matrices for the first time, enabling effective rank aggregation from various data types.

Findings

The method accurately recovers true rankings in noiseless synthetic data.

It demonstrates robustness to noise and incomplete data in experiments.

The approach successfully ranks items using real-world Netflix ratings.

Abstract

The process of rank aggregation is intimately intertwined with the structure of skew-symmetric matrices. We apply recent advances in the theory and algorithms of matrix completion to skew-symmetric matrices. This combination of ideas produces a new method for ranking a set of items. The essence of our idea is that a rank aggregation describes a partially filled skew-symmetric matrix. We extend an algorithm for matrix completion to handle skew-symmetric data and use that to extract ranks for each item. Our algorithm applies to both pairwise comparison and rating data. Because it is based on matrix completion, it is robust to both noise and incomplete data. We show a formal recovery result for the noiseless case and present a detailed study of the algorithm on synthetic data and Netflix ratings.