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Refined scale-dependent permutation entropy to analyze systems complexity

Author

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  • Wu, Shuen-De
  • Wu, Chiu-Wen
  • Humeau-Heurtier, Anne

Abstract

Multiscale entropy (MSE) has become a prevailing method to quantify the complexity of systems. Unfortunately, MSE has a temporal complexity in O(N2), which is unrealistic for long time series. Moreover, MSE relies on the sample entropy computation which is length-dependent and which leads to large variance and possible undefined entropy values for short time series. Here, we propose and introduce a new multiscale complexity measure, the refined scale-dependent permutation entropy (RSDPE). Through the processing of different kinds of synthetic data and real signals, we show that RSDPE has a behavior close to the one of MSE. Furthermore, RSDPE has a temporal complexity in O(N). Finally, RSDPE has the advantage of being much less length-dependent than MSE. From all this, we conclude that RSDPE over-performs MSE in terms of computational cost and computational accuracy.

Suggested Citation

  • Wu, Shuen-De & Wu, Chiu-Wen & Humeau-Heurtier, Anne, 2016. "Refined scale-dependent permutation entropy to analyze systems complexity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 454-461.
    • Handle: RePEc:eee:phsmap:v:450:y:2016:i:c:p:454-461
    DOI: 10.1016/j.physa.2016.01.044
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    References listed on IDEAS

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    1. Costa, M. & Peng, C.-K. & L. Goldberger, Ary & Hausdorff, Jeffrey M., 2003. "Multiscale entropy analysis of human gait dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 330(1), pages 53-60.
    2. Wu, Shuen-De & Wu, Chiu-Wen & Lee, Kung-Yen & Lin, Shiou-Gwo, 2013. "Modified multiscale entropy for short-term time series analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(23), pages 5865-5873.
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    2. Jingming Su & Xuguang Han & Yan Hong, 2023. "Short Term Power Load Forecasting Based on PSVMD-CGA Model," Sustainability, MDPI, vol. 15(4), pages 1-23, February.

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