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

Author

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  • 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
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    Cited by:

    1. Ye, Xuemin & Ding, Xueliang & Zhang, Jiankun & Li, Chunxi, 2017. "Numerical simulation of pressure pulsation and transient flow field in an axial flow fan," Energy, Elsevier, vol. 129(C), pages 185-200.
    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.
    3. Brechtl, Jamieson & Xie, Xie & Liaw, Peter K. & Zinkle, Steven J., 2018. "Complexity modeling and analysis of chaos and other fluctuating phenomena," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 166-175.
    4. Vaidheeswaran, Avinash & Rowan, Steven, 2021. "Chaos and recurrence analyses of pressure signals from bubbling fluidized beds," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    5. Tamara Skoric & Olivera Sarenac & Branislav Milovanovic & Nina Japundzic-Zigon & Dragana Bajic, 2017. "On Consistency of Cross-Approximate Entropy in Cardiovascular and Artificial Environments," Complexity, Hindawi, vol. 2017, pages 1-15, September.

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