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Improved Permutation Entropy for Measuring Complexity of Time Series under Noisy Condition

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  • Zhe Chen
  • Yaan Li
  • Hongtao Liang
  • Jing Yu

Abstract

Measuring complexity of observed time series plays an important role for understanding the characteristics of the system under study. Permutation entropy (PE) is a powerful tool for complexity analysis, but it has some limitations. For example, the amplitude information is discarded; the equalities (i.e., equal values in the analysed signal) are not properly dealt with; and the performance under noisy condition remains to be improved. In this paper, the improved permutation entropy (IPE) is proposed. The presented method combines some advantages of previous modifications of PE. Its effectiveness is validated through both synthetic and experimental analyses. Compared with PE, IPE is capable of detecting spiky features and correctly differentiating heart rate variability (HRV) signals. Moreover, it performs better under noisy condition. Ship classification experiment results demonstrate that IPE achieves 28.66% higher recognition rate than PE at 0dB. Hence, IPE could be used as an alternative of PE for analysing time series under noisy condition.

Suggested Citation

  • Zhe Chen & Yaan Li & Hongtao Liang & Jing Yu, 2019. "Improved Permutation Entropy for Measuring Complexity of Time Series under Noisy Condition," Complexity, Hindawi, vol. 2019, pages 1-12, March.
    • Handle: RePEc:hin:complx:1403829
    DOI: 10.1155/2019/1403829
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    References listed on IDEAS

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    2. Luca Faes & Alberto Porta & Michal Javorka & Giandomenico Nollo, 2017. "Efficient Computation of Multiscale Entropy over Short Biomedical Time Series Based on Linear State-Space Models," Complexity, Hindawi, vol. 2017, pages 1-13, December.
    3. Xinzhong Zhu & Huiying Xu & Jianmin Zhao & Jie Tian, 2017. "Automated Epileptic Seizure Detection in Scalp EEG Based on Spatial-Temporal Complexity," Complexity, Hindawi, vol. 2017, pages 1-8, December.
    4. Zunino, Luciano & Zanin, Massimiliano & Tabak, Benjamin M. & Pérez, Darío G. & Rosso, Osvaldo A., 2009. "Forbidden patterns, permutation entropy and stock market inefficiency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(14), pages 2854-2864.
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