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Time series classification of dynamical systems using deterministic learning

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Abstract

This paper studies the classification of large-scale time series data constructed by nonlinear dynamical systems via deterministic learning. Firstly, a large-scale time series dataset including five classes of dynamical patterns is constructed based on the benchmark Lorenz system. Secondly, the performance of the dynamical pattern recognition method based on deterministic learning is evaluated for the time series classification task in the large-scale time series dataset. Last but not least, based on the concept of representative selection and the recent research on the deterministic learning theory, a novel dynamical pattern recognition-based time series classification framework is modified, including: (1) the selection of a representative training subset with the largest Lyapunov exponent as an example; (2) inherent dynamics modeling via deterministic learning in the representative subset; (3) dynamics comparing between representative training patterns and a given test pattern through generating recognition errors; (4) and label assigning based on the minimal recognition error principle. The significance of this paper is that it improves the application of existing dynamical pattern recognition methods to large-scale datasets by incorporating representative selection strategies. The proposed method can achieve comparable classification accuracy on a small representative subset of chaotic trajectories, as compared to the original large-scale training set. Numerical simulations are provided to demonstrate the effectiveness of the proposed method. The simulation results show that the proposed method outperforms even the baseline deep learning methods on the representative subset in the dynamical system classification tasks.

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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. Large scale in this study refers to a dataset with a size of ten thousand.

  2. \(K\) was pre-labeled in the training set \(\mathcal{P}\), and in the simulation of this study \(K=5\).

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Funding

This study was funded by National Natural Science Foundation of China, 61890922, Cong Wang, 62203263, Weiming Wu, Natural Science Foundation of Shandong Province,ZR2020ZD4, Cong Wang, 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 & Cong Wang

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

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Sun, C., Wu, W. & Wang, C. Time series classification of dynamical systems using deterministic learning. Nonlinear Dyn 111, 21837–21859 (2023). https://doi.org/10.1007/s11071-023-08977-8

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