IDEAS home Printed from https://ideas.repec.org/a/spr/eurphb/v92y2019i4d10.1140_epjb_e2019-90422-6.html
   My bibliography  Save this article

Partially ordered permutation entropies

Author

Listed:
  • Taichi Haruna

    (School of Arts and Sciences, Tokyo Woman’s Christian University)

Abstract

In the past decade, it has been shown through both theoretical and practical studies of permutation entropies that complexity of time series can be captured by order relations between numerical values. In this paper, we investigate a generalisation of permutation entropies in terms of the order structure for further understanding of their nature. To calculate conventional permutation entropies of time series, one needs to assume a total order on the alphabet. We generalise this to an arbitrary partial order; that is, the alphabet is assumed to be a partially ordered set, and we introduce partially ordered permutation entropies. The relationship between entropies and their partial-order analogues for discrete-time finite-alphabet stationary stochastic processes is theoretically studied. We will show that the entropy rate and its partial-order analogues are equal without restriction, whereas equalities between excess entropy and partial-order analogues depend on asymmetry of the order structure of the alphabet. As all finite totally ordered sets are asymmetric, our results explain one reason why conventional permutation entropies are so effective. Graphical abstract

Suggested Citation

  • Taichi Haruna, 2019. "Partially ordered permutation entropies," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 92(4), pages 1-8, April.
    • Handle: RePEc:spr:eurphb:v:92:y:2019:i:4:d:10.1140_epjb_e2019-90422-6
    DOI: 10.1140/epjb/e2019-90422-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1140/epjb/e2019-90422-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1140/epjb/e2019-90422-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    More about this item

    Keywords

    Statistical and Nonlinear Physics;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:eurphb:v:92:y:2019:i:4:d:10.1140_epjb_e2019-90422-6. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.