Spectral Ranking using Seriation
This addresses ranking problems in domains like recommendation systems or sports, but it is incremental as it builds on existing seriation and spectral methods.
The paper tackles the problem of ranking items from pairwise comparisons by introducing a spectral seriation algorithm that constructs a similarity matrix and reorders it to derive rankings. It shows exact recovery under ideal conditions, robustness to noise and missing data, and achieves competitive or superior performance in experiments on synthetic and real datasets.
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.