TY - GEN

T1 - Permutations as angular data

T2 - 10th IEEE International Conference on Data Mining, ICDM 2010

AU - Plis, Sergey M.

AU - Lane, Terran

AU - Calhoun, Vince D.

PY - 2010/12/1

Y1 - 2010/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=79951752604&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79951752604&partnerID=8YFLogxK

U2 - 10.1109/ICDM.2010.122

DO - 10.1109/ICDM.2010.122

M3 - Conference contribution

AN - SCOPUS:79951752604

SN - 9780769542560

T3 - Proceedings - IEEE International Conference on Data Mining, ICDM

SP - 403

EP - 410

BT - Proceedings - 10th IEEE International Conference on Data Mining, ICDM 2010

Y2 - 14 December 2010 through 17 December 2010

ER -