Fractal dimension estimation with persistent homology: A comparative study

Jonathan Jaquette; Benjamin Schweinhart

doi:10.1016/j.cnsns.2019.105163

Fractal dimension estimation with persistent homology: A comparative study

Jonathan Jaquette, Benjamin Schweinhart

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

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.

Original language	English (US)
Article number	105163
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	84
DOIs	https://doi.org/10.1016/j.cnsns.2019.105163
State	Published - May 2020
Externally published	Yes

All Science Journal Classification (ASJC) codes

Numerical Analysis
Modeling and Simulation
Applied Mathematics

Keywords

Chaotic attractors
Fractal dimension
Persistent homology
Topological data analysis

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10.1016/j.cnsns.2019.105163

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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.",

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AU - Jaquette, Jonathan

AU - Schweinhart, Benjamin

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AB - 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.

KW - Chaotic attractors

KW - Fractal dimension

KW - Persistent homology

KW - Topological data analysis

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JO - Communications in Nonlinear Science and Numerical Simulation

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M1 - 105163

ER -

Fractal dimension estimation with persistent homology: A comparative study

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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