Spectral Ranking using Seriation

TL;DR

This paper introduces a spectral seriation algorithm for ranking items based on pairwise comparisons, demonstrating its robustness, accuracy, and applicability to semi-supervised ranking tasks through theoretical analysis and experiments.

Contribution

It presents a novel spectral seriation method for ranking, showing its effectiveness and robustness compared to classical methods, including semi-supervised ranking capabilities.

Findings

Exact recovery with complete comparisons

Robustness to noise and missing data

Superior performance in experiments

Abstract

We describe a seriation algorithm for ranking a set of items given pairwise comparisons between these items. Intuitively, the algorithm assigns similar rankings to items that compare similarly with all others. It does so by constructing a similarity matrix from pairwise comparisons, using seriation methods to reorder this matrix and construct a ranking. We first show that this spectral seriation algorithm recovers the true ranking when all pairwise comparisons are observed and consistent with a total order. We then show that ranking reconstruction is still exact when some pairwise comparisons are corrupted or missing, and that seriation based spectral ranking is more robust to noise than classical scoring methods. Finally, we bound the ranking error when only a random subset of the comparions are observed. An additional benefit of the seriation formulation is that it allows us to solve semi-supervised ranking problems. Experiments on both synthetic and real datasets demonstrate that seriation based spectral ranking achieves competitive and in some cases superior performance compared to classical ranking methods.