IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v187y2024ics0960077924009366.html
   My bibliography  Save this article

Belief Tsallis-Deng Structure Entropy and its uniform framework for analyzing multivariate time-series complexity based on evidence theory

Author

Listed:
  • Xie, Jieren
  • Xu, Guanghua
  • Chen, Xiaobi
  • Zhang, Xun
  • Chen, Ruiquan
  • Yang, Zengyao
  • Fang, Churui
  • Tian, Peiyuan
  • Wu, Qingqiang
  • Zhang, Sicong

Abstract

In the framework of evidence theory, this paper proposes a new measure of uncertainty and introduces an entirely new unified framework for analyzing the complexity of multivariate time series. The theoretical foundation of this paper is random sets, viewing multivariate sequences as a new type of set variable, and using the belief theory framework to describe their behavior. Set variables are a natural extension of point variables, thus providing stronger universality in the analysis of multivariate time series. We tested our proposed new analytical framework on the logistic map and used the Tsallis-Deng Structure Entropy introduced in this paper to analyze the generated multivariate time series. Compared to the traditional Deng entropy, Tsallis-Deng Structure Entropy can adjust the sensitivity to time series complexity by tuning its structural parameter p. As the parameters of the logistic map change, the changes in Tsallis-Deng Structure Entropy show a high correlation with the Lyapunov exponent. In addition, we applied the proposed framework to analyze a multivariate epileptic EEG dataset. The results showed that using the novel evidence theory-based analysis framework for the 23-channel multivariate time series, the average classification accuracies of Deng entropy, Tsallis-Deng entropy, and Tsallis-Deng structural entropy for 24 epilepsy patients were 79 %, 74 %, and 82 %, respectively. In contrast, the average recognition accuracy using the traditional probabilistic framework based on multivariate embedding theory was 64 %. The evidence theory-based framework generally outperformed the multivariate embedding theory, with Tsallis-Deng structural entropy achieving the best performance. These results indicate that the proposed evidence theory-based framework not only avoids the dimensionality curse of the multivariate embedding theory but also better quantifies the complexity of multivariate time series from the same system and distinguishes different types of multivariate time series.

Suggested Citation

  • Xie, Jieren & Xu, Guanghua & Chen, Xiaobi & Zhang, Xun & Chen, Ruiquan & Yang, Zengyao & Fang, Churui & Tian, Peiyuan & Wu, Qingqiang & Zhang, Sicong, 2024. "Belief Tsallis-Deng Structure Entropy and its uniform framework for analyzing multivariate time-series complexity based on evidence theory," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
    • Handle: RePEc:eee:chsofr:v:187:y:2024:i:c:s0960077924009366
    DOI: 10.1016/j.chaos.2024.115384
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077924009366
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2024.115384?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Contreras-Reyes, Javier E. & Kharazmi, Omid, 2023. "Belief Fisher–Shannon information plane: Properties, extensions, and applications to time series analysis," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    2. Inoue, Kei & Tani, Kazuki, 2023. "Quantification of chaos in a time series generated from a traffic flow model using the extended entropic chaos degree," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhao, Tong & Li, Zhen & Deng, Yong, 2024. "Linearity in Deng entropy," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    2. Zhan, Tianxiang & Zhou, Jiefeng & Li, Zhen & Deng, Yong, 2024. "Generalized information entropy and generalized information dimension," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    3. Rostaghi, Mostafa & Rostaghi, Reza & Humeau-Heurtier, Anne & Azami, Hamed, 2024. "Refined composite multivariate multiscale fuzzy dispersion entropy: Theoretical analysis and applications," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    4. Contreras-Reyes, Javier E. & Jeldes-Delgado, Fabiola & Carrasco, Raúl, 2024. "Jensen-Detrended Cross-Correlation function for non-stationary time series with application to Latin American stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 654(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:187:y:2024:i:c:s0960077924009366. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.