IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v391y2012i24p6601-6610.html
   My bibliography  Save this article

On the relation between correlation dimension, approximate entropy and sample entropy parameters, and a fast algorithm for their calculation

Author

Listed:
  • Zurek, Sebastian
  • Guzik, Przemyslaw
  • Pawlak, Sebastian
  • Kosmider, Marcin
  • Piskorski, Jaroslaw

Abstract

We explore the relation between correlation dimension, approximate entropy and sample entropy parameters, which are commonly used in nonlinear systems analysis. Using theoretical considerations we identify the points which are shared by all these complexity algorithms and show explicitly that the above parameters are intimately connected and mutually interdependent. A new geometrical interpretation of sample entropy and correlation dimension is provided and the consequences for the interpretation of sample entropy, its relative consistency and some of the algorithms for parameter selection for this quantity are discussed. To get an exact algorithmic relation between the three parameters we construct a very fast algorithm for simultaneous calculations of the above, which uses the full time series as the source of templates, rather than the usual 10%. This algorithm can be used in medical applications of complexity theory, as it can calculate all three parameters for a realistic recording of 104 points within minutes with the use of an average notebook computer.

Suggested Citation

  • Zurek, Sebastian & Guzik, Przemyslaw & Pawlak, Sebastian & Kosmider, Marcin & Piskorski, Jaroslaw, 2012. "On the relation between correlation dimension, approximate entropy and sample entropy parameters, and a fast algorithm for their calculation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6601-6610.
  • Handle: RePEc:eee:phsmap:v:391:y:2012:i:24:p:6601-6610
    DOI: 10.1016/j.physa.2012.07.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437112006656
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

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

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. repec:eee:energy:v:129:y:2017:i:c:p:185-200 is not listed on IDEAS
    2. Restrepo, Juan F. & Schlotthauer, Gastón & Torres, María E., 2014. "Maximum approximate entropy and r threshold: A new approach for regularity changes detection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 409(C), pages 97-109.

    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:eee:phsmap:v:391:y:2012:i:24:p:6601-6610. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.