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Time series clustering of dynamical systems via deterministic learning

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Abstract

A recent deterministic learning theory has achieved locally-accurate identification of unknown system dynamics. This article presents a novel application of deterministic learning theory to unsupervised learning for the first time. Specifically, a new time series clustering strategy with a dynamics-based similarity measure is proposed. Firstly, the dynamics knowledge learned from the time series is represented and stored in the form of constant weights through deterministic learning theory. Secondly, dynamical estimators constructed with the learned dynamics knowledge are used to generate recognition errors, forming a similarity measure matrix to characterize the dynamics-based similarity between time series. Finally, the clustering of time series data with different dynamical behaviors is achieved based on the K-medoids prototype according to the dynamics-based similarity measure matrix. To verify the effectiveness of the proposed method, a dynamical pattern dataset based on benchmark dynamical systems (e.g., Lorenz, Chen, and Lü systems) is also constructed. The experimental results on a synthetic dataset and two real datasets demonstrate that the proposed method is superior to other well-known clustering algorithms in the clustering task for dynamical systems.

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Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Notes

  1. The recurrent trajectory is a broad category of trajectories derived from nonlinear dynamical systems, including periodic, quasi-periodic, almost-periodic, and chaotic trajectories. A formal definition of this concept can be found in references [33] and [38].

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (61890922, 62203263) and the Natural Science Foundation of Shandong Province (ZR2020ZD40, ZR2022QF062).

Funding

This article is funded by National Natural Science Foundation of China, 61890922, Cong Wang, 62203263, Weiming Wu, Major Basic Program of Shandong Provincial Natural Science Foundation, ZR2020ZD40, Cong Wang, Natural Science Foundation of Shandong Province, ZR2022QF062, Weiming Wu.

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Authors and Affiliations

  1. Center for Intelligent Medical Engineering, School of Control Science and Engineering, Shandong University, Jinan, 250061, China

    Chen Sun, Weiming Wu, Zirui Zhang, Zhirui Li, Bing Ji & Cong Wang

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  1. Chen Sun
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  3. Zirui Zhang
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Correspondence to Weiming Wu or Cong Wang.

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Sun, C., Wu, W., Zhang, Z. et al. Time series clustering of dynamical systems via deterministic learning. Int. J. Mach. Learn. & Cyber. 15, 2761–2779 (2024). https://doi.org/10.1007/s13042-023-02062-7

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