Directional statistics on permutations

Sergey M. Plis, Stephen McCracken, Terran Lane, Vince D. Calhoun

Research output: Contribution to journalConference articlepeer-review


Distributions over permutations arise in applications ranging from multi-object tracking to ranking. The difficulty in dealing with these distributions is caused by the size of their domain, which is factorial in the number of entities (n!). The direct definition of a multinomial distribution over the permutation space is impractical for all but a very small n. In this work we propose an embedding of all n! permutations for a given n in a surface of a hypersphere defined in ℝ(n-1) 2.As a result, we acquire the ability to define continuous distributions over a hypersphere with all the benefits of directional statistics. We provide polynomial time projections between the continuous hypersphere representation and the n!-element permutation space. The framework provides a way to use continuous directional probability densities and the methods developed thereof for establishing densities over permutations. As a demonstration of the benefits of the framework we derive an inference procedure for a state-space model over permutations. We demonstrate the approach with applications and comparisons to existing models.

Original languageEnglish (US)
Pages (from-to)600-608
Number of pages9
JournalJournal of Machine Learning Research
StatePublished - Dec 1 2011
Externally publishedYes
Event14th International Conference on Artificial Intelligence and Statistics, AISTATS 2011 - Fort Lauderdale, FL, United States
Duration: Apr 11 2011Apr 13 2011

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Statistics and Probability
  • Artificial Intelligence

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