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Recognition of the scale-free interval for calculating the correlation dimension using machine learning from chaotic time series

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  • Zhou, Shuang
  • Wang, Xingyuan
  • Zhou, Wenjie
  • Zhang, Chuan

Abstract

Identifying the scale-free interval is an important step in calculating the correlation dimension. In this paper, we propose a method using machine learning known as density peak based clustering algorithm to recognize the scale-free interval. First, the G–P algorithm is used for computing the correlation integral index. Then, the density peak based clustering algorithm is used for classifying the second-order derivative data sets of the correlation integral curve, the zero-fluctuation data are selected to be retained, and then the gross errors are excluded from the selected data. Finally, the coefficient of determination is used to identify the scale-free interval. Some examples are provided to verify the proposed method effective. The calculated results show that our method is feasible. In addition, this research proposes a new method to identify the scale-free interval for fractional dimension calculation theory.

Suggested Citation

  • Zhou, Shuang & Wang, Xingyuan & Zhou, Wenjie & Zhang, Chuan, 2022. "Recognition of the scale-free interval for calculating the correlation dimension using machine learning from chaotic time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 588(C).
    • Handle: RePEc:eee:phsmap:v:588:y:2022:i:c:s0378437121008360
    DOI: 10.1016/j.physa.2021.126563
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    References listed on IDEAS

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    Cited by:

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    2. Zhao, Hongyu & Wang, Shengsheng & Wang, Xingyuan, 2022. "Fast image encryption algorithm based on multi-parameter fractal matrix and MPMCML system," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

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