Permutations as angular data: Efficient inference in factorial spaces

Sergey M. Plis, Terran Lane, Vince Daniel Calhoun

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Distributions over permutations arise in applications ranging from multi-object tracking to ranking of instances. The difficulty of dealing with these distributions is caused by the size of their domain, which is factorial in the number of considered entities (n!). It makes the direct definition of a multinomial distribution over permutation space 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) As a result of the embedding, we acquire 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 there of 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 simulations on a large number of objects hardly manageable by the state of the art inference methods, and an application to a real flight traffic control dataset.

Original languageEnglish (US)
Title of host publicationProceedings - IEEE International Conference on Data Mining, ICDM
Pages403-410
Number of pages8
DOIs
Publication statusPublished - 2010
Externally publishedYes
Event10th IEEE International Conference on Data Mining, ICDM 2010 - Sydney, NSW, Australia
Duration: Dec 14 2010Dec 17 2010

Other

Other10th IEEE International Conference on Data Mining, ICDM 2010
CountryAustralia
CitySydney, NSW
Period12/14/1012/17/10

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Plis, S. M., Lane, T., & Calhoun, V. D. (2010). Permutations as angular data: Efficient inference in factorial spaces. In Proceedings - IEEE International Conference on Data Mining, ICDM (pp. 403-410). [5693994] https://doi.org/10.1109/ICDM.2010.122