Fractal dimension estimation with persistent homology: A comparative study

Jonathan Jaquette, Benjamin Schweinhart

Research output: Contribution to journalArticlepeer-review

11 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 languageEnglish (US)
Article number105163
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume84
DOIs
StatePublished - May 2020
Externally publishedYes

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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