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Entropy measures for biological signal analyses

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Abstract

Entropies are among the most popular and promising complexity measures for biological signal analyses. Various types of entropy measures exist, including Shannon entropy, Kolmogorov entropy, approximate entropy (ApEn), sample entropy (SampEn), multiscale entropy (MSE), and so on. A fundamental question is which entropy should be chosen for a specific biological application. To solve this issue, we focus on scaling laws of different entropy measures and introduce an ensemble forecasting framework to find the connections among them. One critical component of the ensemble forecasting framework is the scale-dependent Lyapunov exponent (SDLE), whose scaling behavior is found to be the richest among all the entropy measures. In fact, SDLE contains all the essential information of other entropy measures, and can act as a unifying multiscale complexity measure. Furthermore, SDLE has a unique scale separation property to aptly deal with nonstationarity and characterize high-dimensional and intermittent chaos. Therefore, SDLE can often be the first choice for exploratory studies in biology. The effectiveness of SDLE and the ensemble forecasting framework is illustrated by considering epileptic seizure detection from EEG.

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Authors and Affiliations

  1. PMB Intelligence LLC, PO Box 2077, West Lafayette, IN, 47996, USA

    Jianbo Gao

  2. Mechanical and Materials Engineering, Wright State University, Dayton, OH, 45435, USA

    Jianbo Gao

  3. Affymetrix, Inc., 3380 Central Expressway, Santa Clara, CA, 95051, USA

    Jing Hu

  4. Department of Earth & Atmospheric Sciences, Purdue University, West Lafayette, IN, 47907, USA

    Wen-wen Tung

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  1. Jianbo Gao
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  2. Jing Hu
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Correspondence to Jianbo Gao.

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Gao, J., Hu, J. & Tung, Ww. Entropy measures for biological signal analyses. Nonlinear Dyn 68, 431–444 (2012). https://doi.org/10.1007/s11071-011-0281-2

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  • DOI: https://doi.org/10.1007/s11071-011-0281-2

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