Fractal dimension estimation with persistent homology: A comparative study

被引：12
|
作者：
Jaquette, Jonathan [1 ]
Schweinhart, Benjamin [2 ]
机构：
[1] Brandeis Univ, Dept Math, Waltham, MA 02453 USA
[2] Ohio State Univ, Dept Math, Columbus, OH 43210 USA
来源：
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2020年 / 84卷 / 84期
基金：
美国国家科学基金会; 美国国家卫生研究院;
关键词：
Persistent homology; Fractal dimension; Chaotic attractors; Topological data analysis; MINIMAL SPANNING-TREES; STRANGE; ATTRACTORS; ALGORITHM; TOPOLOGY;
D O I：
10.1016/j.cnsns.2019.105163
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We propose that the recently defined persistent homology dimensions are a practical tool for fractal dimension estimation of point samples. We implement an algorithm to estimate the persistent homology dimension, and compare its performance to classical methods to compute the correlation and box-counting dimensions in examples of self-similar fractals, chaotic attractors, and an empirical dataset. The performance of the 0-dimensional persistent homology dimension is comparable to that of the correlation dimension, and better than box-counting. (C) 2020 Elsevier B.V. All rights reserved.
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页数：19
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