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Mixing Bandt-Pompe and Lempel-Ziv approaches: another way to analyze the complexity of continuous-state sequences

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  • S. Zozor
  • D. Mateos
  • P. Lamberti

Abstract

In this paper, we propose to mix the approach underlying Bandt-Pompe permutation entropy with Lempel-Ziv complexity, to design what we call Lempel-Ziv permutation complexity. The principle consists of two steps: (i) transformation of a continuous-state series that is intrinsically multivariate or arises from embedding into a sequence of permutation vectors, where the components are the positions of the components of the initial vector when re-arranged; (ii) performing the Lempel-Ziv complexity for this series of ‘symbols’, as part of a discrete finite-size alphabet. On the one hand, the permutation entropy of Bandt-Pompe aims at the study of the entropy of such a sequence; i.e., the entropy of patterns in a sequence (e.g., local increases or decreases). On the other hand, the Lempel-Ziv complexity of a discrete-state sequence aims at the study of the temporal organization of the symbols (i.e., the rate of compressibility of the sequence). Thus, the Lempel-Ziv permutation complexity aims to take advantage of both of these methods. The potential from such a combined approach – of a permutation procedure and a complexity analysis – is evaluated through the illustration of some simulated data and some real data. In both cases, we compare the individual approaches and the combined approach. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • 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.
    • Handle: RePEc:spr:eurphb:v:87:y:2014:i:5:p:1-12:10.1140/epjb/e2014-41018-5
    DOI: 10.1140/epjb/e2014-41018-5
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    Cited by:

    1. Mateos, Diego M. & Gómez-Ramírez, Jaime & Rosso, Osvaldo A., 2021. "Using time causal quantifiers to characterize sleep stages," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    2. Šapina, Matej & Karmakar, Chandan Kumar & Kramarić, Karolina & Kośmider, Marcin & Garcin, Matthieu & Brdarić, Dario & Milas, Krešimir & Yearwood, John, 2021. "Lempel-Ziv complexity of the pNNx statistics – an application to neonatal stress," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    3. 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).
    4. Pinar Deniz Tosun & Derk-Jan Dijk & Raphaelle Winsky-Sommerer & Daniel Abasolo, 2019. "Effects of Ageing and Sex on Complexity in the Human Sleep EEG: A Comparison of Three Symbolic Dynamic Analysis Methods," Complexity, Hindawi, vol. 2019, pages 1-12, January.

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    Keywords

    Statistical and Nonlinear Physics;

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