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Exploring the Entropy-Based Classification of Time Series Using Visibility Graphs from Chaotic Maps

Author

Listed:
  • J. Alberto Conejero

    (Instituto Universitario Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 Valencia, Spain)

  • Andrei Velichko

    (Institute of Physics and Technology, Petrozavodsk State University, 185910 Petrozavodsk, Russia)

  • Òscar Garibo-i-Orts

    (Instituto Universitario Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 Valencia, Spain
    GRID—Grupo de Investigación en Ciencia de Datos, Valencian International University—VIU, Carrer Pintor Sorolla 21, 46002 Valencia, Spain)

  • Yuriy Izotov

    (Institute of Physics and Technology, Petrozavodsk State University, 185910 Petrozavodsk, Russia)

  • Viet-Thanh Pham

    (Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam)

Abstract

The classification of time series using machine learning (ML) analysis and entropy-based features is an urgent task for the study of nonlinear signals in the fields of finance, biology and medicine, including EEG analysis and Brain–Computer Interfacing. As several entropy measures exist, the problem is assessing the effectiveness of entropies used as features for the ML classification of nonlinear dynamics of time series. We propose a method, called global efficiency (GEFMCC), for assessing the effectiveness of entropy features using several chaotic mappings. GEFMCC is a fitness function for optimizing the type and parameters of entropies for time series classification problems. We analyze fuzzy entropy (FuzzyEn) and neural network entropy (NNetEn) for four discrete mappings, the logistic map, the sine map, the Planck map, and the two-memristor-based map, with a base length time series of 300 elements. FuzzyEn has greater GEFMCC in the classification task compared to NNetEn. However, NNetEn classification efficiency is higher than FuzzyEn for some local areas of the time series dynamics. The results of using horizontal visibility graphs (HVG) instead of the raw time series demonstrate the GEFMCC decrease after HVG time series transformation. However, the GEFMCC increases after applying the HVG for some local areas of time series dynamics. The scientific community can use the results to explore the efficiency of the entropy-based classification of time series in “The Entropy Universe”. An implementation of the algorithms in Python is presented.

Suggested Citation

  • J. Alberto Conejero & Andrei Velichko & Òscar Garibo-i-Orts & Yuriy Izotov & Viet-Thanh Pham, 2024. "Exploring the Entropy-Based Classification of Time Series Using Visibility Graphs from Chaotic Maps," Mathematics, MDPI, vol. 12(7), pages 1-23, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:7:p:938-:d:1362118
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    References listed on IDEAS

    as
    1. Li, Sange & Shang, Pengjian, 2021. "Analysis of nonlinear time series using discrete generalized past entropy based on amplitude difference distribution of horizontal visibility graph," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    2. Ahmed Sedik & Ahmed A. Abd El-Latif & Mudasir Ahmad Wani & Fathi E. Abd El-Samie & Nariman Abdel-Salam Bauomy & Fatma G. Hashad, 2023. "Efficient Multi-Biometric Secure-Storage Scheme Based on Deep Learning and Crypto-Mapping Techniques," Mathematics, MDPI, vol. 11(3), pages 1-26, January.
    3. Ömer Akgüller & Mehmet Ali Balcı & Larissa M. Batrancea & Lucian Gaban, 2023. "Path-Based Visibility Graph Kernel and Application for the Borsa Istanbul Stock Network," Mathematics, MDPI, vol. 11(6), pages 1-25, March.
    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. Gao, Meng & Ge, Ruijun, 2024. "Mapping time series into signed networks via horizontal visibility graph," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).
    Full references (including those not matched with items on IDEAS)

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