License:
Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2023.45
URN: urn:nbn:de:0030-drops-178953
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/17895/
Kerber, Michael ;
Söls, Matthias
The Localized Union-Of-Balls Bifiltration
Abstract
We propose an extension of the classical union-of-balls filtration of persistent homology: fixing a point q, we focus our attention to a ball centered at q whose radius is controlled by a second scale parameter. We discuss an absolute variant, where the union is just restricted to the q-ball, and a relative variant where the homology of the q-ball relative to its boundary is considered. Interestingly, these natural constructions lead to bifiltered simplicial complexes which are not k-critical for any finite k. Nevertheless, we demonstrate that these bifiltrations can be computed exactly and efficiently, and we provide a prototypical implementation using the CGAL library. We also argue that some of the recent algorithmic advances for 2-parameter persistence (which usually assume k-criticality for some finite k) carry over to the ∞-critical case.
BibTeX - Entry
@InProceedings{kerber_et_al:LIPIcs.SoCG.2023.45,
author = {Kerber, Michael and S\"{o}ls, Matthias},
title = {{The Localized Union-Of-Balls Bifiltration}},
booktitle = {39th International Symposium on Computational Geometry (SoCG 2023)},
pages = {45:1--45:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-273-0},
ISSN = {1868-8969},
year = {2023},
volume = {258},
editor = {Chambers, Erin W. and Gudmundsson, Joachim},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2023/17895},
URN = {urn:nbn:de:0030-drops-178953},
doi = {10.4230/LIPIcs.SoCG.2023.45},
annote = {Keywords: Topological Data Analysis, Multi-Parameter Persistence, Persistent Local Homology}
}
Keywords: |
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Topological Data Analysis, Multi-Parameter Persistence, Persistent Local Homology |
Collection: |
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39th International Symposium on Computational Geometry (SoCG 2023) |
Issue Date: |
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2023 |
Date of publication: |
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09.06.2023 |
Supplementary Material: |
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A prototypical implementation can be found here: https://bitbucket.org/mkerber/demo_absolute_2d/src/master/. |