基于持久同调的分形维估计：一项比较研究。
FRACTAL DIMENSION ESTIMATION WITH PERSISTENT HOMOLOGY: A COMPARATIVE STUDY.
作者信息
Jaquette Jonathan, Schweinhart Benjamin
机构信息
Department of Mathematics, Brandeis University Waltham, MA 02453.
Department of Mathematics, Ohio State University Columbus, OH 43210.
出版信息
Commun Nonlinear Sci Numer Simul. 2020 May;84. doi: 10.1016/j.cnsns.2019.105163. Epub 2019 Dec 30.
Abstract
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.
摘要
我们提出，最近定义的持久同调维数是用于点样本分形维数估计的实用工具。我们实现了一种算法来估计持久同调维数，并在自相似分形、混沌吸引子和一个经验数据集的示例中，将其性能与计算关联维和盒计数维的经典方法进行比较。零维持久同调维数的性能与关联维数相当，且优于盒计数法。
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