Statistical ranking and combinatorial Hodge theory

@article{Jiang2011StatisticalRA,
  title={Statistical ranking and combinatorial Hodge theory},
  author={Xiaoye Jiang and Lek-Heng Lim and Y. Yao and Yinyu Ye},
  journal={Mathematical Programming},
  year={2011},
  volume={127},
  pages={203-244}
}
We propose a technique that we call HodgeRank for ranking data that may be incomplete and imbalanced, characteristics common in modern datasets coming from e-commerce and internet applications. We are primarily interested in cardinal data based on scores or ratings though our methods also give specific insights on ordinal data. From raw ranking data, we construct pairwise rankings, represented as edge flows on an appropriate graph. Our statistical ranking method exploits the graph Helmholtzian… 
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