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

Shuang Zhou, Xingyuan Wang, Wenjie Zhou and Chuan Zhang

Physica A: Statistical Mechanics and its Applications, 2022, vol. 588, issue C

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.

Keywords: Scale-free interval; Correlation dimension; Fractal dimension; Chaotic time series (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:588:y:2022:i:c:s0378437121008360

DOI: 10.1016/j.physa.2021.126563

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