Rank Aggregation via Nuclear Norm Minimization

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Rank Aggregation via Nuclear Norm Minimization
The process of rank aggregation is intimately intertwined with the structure of skew-symmetric matrices. We apply recent advances in the theory and algorithms of matrix completion to skew-symmetric matrices. This combination of ideas produces a new method for ranking a set of items. The essence of our idea is that a rank aggregation describes a partially filled skew-symmetric matrix. We extend an algorithm for matrix completion to handle skew-symmetric data and use that to extract ranks for each item. Our algorithm applies to both pairwise comparison and rating data. Because it is based on matrix completion, it is robust to both noise and incomplete data. We show a formal recovery result for the noiseless case and present a detailed study of the algorithm on synthetic data and Netflix ratings. Categories and Subject Descriptors H.3.5 [Information Storage and Retrieval]: On-line in
David F. Gleich, Lek-Heng Lim
Added 19 Aug 2011
Updated 19 Aug 2011
Type Journal
Year 2011
Where CORR
Authors David F. Gleich, Lek-Heng Lim
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