Literature DB >> 32256012

FRACTAL DIMENSION ESTIMATION WITH PERSISTENT HOMOLOGY: A COMPARATIVE STUDY.

Jonathan Jaquette1, Benjamin Schweinhart2.   

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.

Entities:  

Keywords:  Persistent homology; chaotic attractors; fractal dimension; topological data analysis

Year:  2019        PMID： 32256012      PMCID： PMC7117095          DOI： 10.1016/j.cnsns.2019.105163

Source DB:  PubMed          Journal:  Commun Nonlinear Sci Numer Simul        ISSN： 1007-5704            Impact factor:   4.260


  12 in total

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Journal:  Phys Rev Lett       Date:  2001-01-01       Impact factor: 9.161

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Journal:  Phys Rev A       Date:  1990-03-15       Impact factor: 3.140

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Authors:  Kelin Xia; Guo-Wei Wei
Journal:  Int J Numer Method Biomed Eng       Date:  2014-06-24       Impact factor: 2.747

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Authors:  M C Mackey; L Glass
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9.  Persistent homology of complex networks for dynamic state detection.

Authors:  Audun Myers; Elizabeth Munch; Firas A Khasawneh
Journal:  Phys Rev E       Date:  2019-08       Impact factor: 2.529

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Journal:  Cancer Res       Date:  2000-07-15       Impact factor: 12.701
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  1 in total

1.  An exploration of fractal-based prognostic model and comparative analysis for second wave of COVID-19 diffusion.

Authors:  D Easwaramoorthy; A Gowrisankar; A Manimaran; S Nandhini; Lamberto Rondoni; Santo Banerjee
Journal:  Nonlinear Dyn       Date:  2021-09-08       Impact factor: 5.022
  1 in total

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