Spectral Ranking using Seriation
Fajwel Fogel, Alexandre d'Aspremont, Milan Vojnovic

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…
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Taxonomy
TopicsData Management and Algorithms · Neural Networks and Applications · Multi-Criteria Decision Making
