Permutation entropy with vector embedding delays

Douglas J. Little and Deb M. Kane
Phys. Rev. E 96, 062205 – Published 12 December 2017

Abstract

Permutation entropy (PE) is a statistic used widely for the detection of structure within a time series. Embedding delay times at which the PE is reduced are characteristic timescales for which such structure exists. Here, a generalized scheme is investigated where embedding delays are represented by vectors rather than scalars, permitting PE to be calculated over a (D1)-dimensional space, where D is the embedding dimension. This scheme is applied to numerically generated noise, sine wave and logistic map series, and experimental data sets taken from a vertical-cavity surface emitting laser exhibiting temporally localized pulse structures within the round-trip time of the laser cavity. Results are visualized as PE maps as a function of embedding delay, with low PE values indicating combinations of embedding delays where correlation structure is present. It is demonstrated that vector embedding delays enable identification of structure that is ambiguous or masked, when the embedding delay is constrained to scalar form.

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  • Received 25 July 2017

DOI:https://doi.org/10.1103/PhysRevE.96.062205

©2017 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsNonlinear DynamicsAtomic, Molecular & Optical

Authors & Affiliations

Douglas J. Little* and Deb M. Kane

  • MQ Photonics Research Centre, Department of Physics and Astronomy, Macquarie University, North Ryde, NSW 2109, Australia

  • *douglas.little@mq.edu.au

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Issue

Vol. 96, Iss. 6 — December 2017

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