We describe a seriation algorithm for ranking a set of $n$ 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 even when some pairwise comparisons are corrupted or missing, and that seriation based spectral ranking is more robust to noise than other scoring methods. 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.

本文提出了一种用于排序一系列物品的序列算法，将基于成对比较构建相似性矩阵后使用序列方法进行排序。在排名恢复和噪声处理方面，它比传统评分方法更具鲁棒性，并且还可以解决半监督排名问题。使用该算法进行排名的表现竞争性更好。

利用序列法进行频谱排名