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Measuring time series based on multiscale dispersion Lempel–Ziv complexity and dispersion entropy plane

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  • Mao, Xuegeng
  • Shang, Pengjian
  • Xu, Meng
  • Peng, Chung-Kang

Abstract

In this paper, we propose dispersion Lempel–Ziv complexity and combine it with dispersion entropy to construct complexity-entropy plane. This measure aims to identify time series with different properties. These two quantities take advantage of nonlinear symbolic representation and quantify the complexity of series. In addition, they are relatively stable for different parameters and robust against white noise with different levels. The complexity-entropy plane is able to identify nonlinear chaotic maps and distinguish them from stochastic process. Also, the multiscale features of signals are detected, suggesting the underlying dynamics. This technique is effective to track the dynamical changes of heart rate time series and to characterize different pathologic states. It can also prove that aging and disease correspond to the loss of complexity.

Suggested Citation

  • Mao, Xuegeng & Shang, Pengjian & Xu, Meng & Peng, Chung-Kang, 2020. "Measuring time series based on multiscale dispersion Lempel–Ziv complexity and dispersion entropy plane," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    • Handle: RePEc:eee:chsofr:v:137:y:2020:i:c:s096007792030268x
    DOI: 10.1016/j.chaos.2020.109868
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    References listed on IDEAS

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    1. S. Zozor & D. Mateos & P. Lamberti, 2014. "Mixing Bandt-Pompe and Lempel-Ziv approaches: another way to analyze the complexity of continuous-state sequences," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 87(5), pages 1-12, May.
    2. Liu, Zhengli & Shang, Pengjian, 2018. "Generalized information entropy analysis of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 1170-1185.
    3. Osvaldo Rosso & Felipe Olivares & Luciano Zunino & Luciana Micco & André Aquino & Angelo Plastino & Hilda Larrondo, 2013. "Characterization of chaotic maps using the permutation Bandt-Pompe probability distribution," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 86(4), pages 1-13, April.
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    Cited by:

    1. Wan, Li & Ling, Guang & Guan, Zhi-Hong & Fan, Qingju & Tong, Yu-Han, 2022. "Fractional multiscale phase permutation entropy for quantifying the complexity of nonlinear time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    2. Li, Yuxing & Wu, Junxian & Yi, Yingmin & Gu, Yunpeng, 2023. "Unequal-step multiscale integrated mapping dispersion Lempel-Ziv complexity: A novel complexity metric for signal analysis," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    3. Li, Yuxing & Geng, Bo & Jiao, Shangbin, 2022. "Dispersion entropy-based Lempel-Ziv complexity: A new metric for signal analysis," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    4. Li, Sange & Shang, Pengjian, 2022. "A new complexity measure: Modified discrete generalized past entropy based on grain exponent," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    5. Gu, Danlei & Lin, Aijing & Lin, Guancen, 2022. "Sleep and cardiac signal processing using improved multivariate partial compensated transfer entropy based on non-uniform embedding," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    6. Zhao, Zhigao & Chen, Fei & He, Xianghui & Lan, Pengfei & Chen, Diyi & Yin, Xiuxing & Yang, Jiandong, 2024. "A universal hydraulic-mechanical diagnostic framework based on feature extraction of abnormal on-field measurements: Application in micro pumped storage system," Applied Energy, Elsevier, vol. 357(C).

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