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Quantifying time series complexity by multi-scale transition network approaches

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  • Wang, Xiaoyan
  • Tang, Ming
  • Guan, Shuguang
  • Zou, Yong

Abstract

Complex network approaches for nonlinear time series analysis are still under fast developments. In this work, we propose a set of entropy measures to characterize the multi-scale transition networks which are constructed from nonlinear time series. These entropy measures compare the distances between an empirical distribution P to a uniform distribution Pe, which are achieved via the multi-scale node transition matrix from different perspectives of out-link transitions, and in-link transitions, respectively. In addition, the entropy measures show convergence to zeros for white noise while non-zero values for deterministic chaotic processes. In correlated stochastic processes, the convergence rates are influenced by the correlation length. We show that entropy measures based on transition complexity are able to capture different dynamical states, i.e., tracking routes to chaos and dynamical hysteresis. In the experimental EEG analysis, we show that epileptic brain states are successfully distinguished from healthy control by all entropy measures.

Suggested Citation

  • Wang, Xiaoyan & Tang, Ming & Guan, Shuguang & Zou, Yong, 2023. "Quantifying time series complexity by multi-scale transition network approaches," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 622(C).
    • Handle: RePEc:eee:phsmap:v:622:y:2023:i:c:s0378437123004004
    DOI: 10.1016/j.physa.2023.128845
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    References listed on IDEAS

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    1. Andriana S L O Campanharo & M Irmak Sirer & R Dean Malmgren & Fernando M Ramos & Luís A Nunes Amaral, 2011. "Duality between Time Series and Networks," PLOS ONE, Public Library of Science, vol. 6(8), pages 1-13, August.
    2. Borges, João B. & Ramos, Heitor S. & Mini, Raquel A.F. & Rosso, Osvaldo A. & Frery, Alejandro C. & Loureiro, Antonio A.F., 2019. "Learning and distinguishing time series dynamics via ordinal patterns transition graphs," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    3. Tiago A. Schieber & Laura Carpi & Albert Díaz-Guilera & Panos M. Pardalos & Cristina Masoller & Martín G. Ravetti, 2017. "Quantification of network structural dissimilarities," Nature Communications, Nature, vol. 8(1), pages 1-10, April.
    4. Rosso, Osvaldo A. & Carpi, Laura C. & Saco, Patricia M. & Gómez Ravetti, Martín & Plastino, Angelo & Larrondo, Hilda A., 2012. "Causality and the entropy–complexity plane: Robustness and missing ordinal patterns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 42-55.
    5. Wang, Xiaoyan & Han, Xiujing & Chen, Zhangyao & Bi, Qinsheng & Guan, Shuguang & Zou, Yong, 2022. "Multi-scale transition network approaches for nonlinear time series analysis," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
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