# Spectral Ranking using Seriation

arXiv: https://arxiv.org/abs/1406.5370 · HTML: https://mlsanity.com/paper/1406.5370/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jun 2014.

## Built on by (most cited first, 9 of 9)

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- [Representer Theorems for Metric and Preference Learning: Geometric Insights and Algorithms](https://mlsanity.com/paper/2304.03720/) (2023)
- [Cold-Start Active Preference Learning in Socio-Economic Domains](https://mlsanity.com/paper/2508.05090/) (2025)
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- [Scorio.jl: A Julia package for ranking stochastic responses](https://mlsanity.com/paper/2603.14103/) (2026)
- [Temporal Context Reinstatement Drives Episodic-Like Order Memory in Long-Context Language Models](https://mlsanity.com/paper/2607.22575/) (2026)

## Abstract (arXiv)

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.