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 GP 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. (C) 2021 Elsevier B.V. All rights reserved.
NSTL
Elsevier