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.2023.20
URN: urn:nbn:de:0030-drops-178709
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/17870/
Buchet, Mickaël ;
B. Dornelas, Bianca ;
Kerber, Michael
Sparse Higher Order Čech Filtrations
Abstract
For a finite set of balls of radius r, the k-fold cover is the space covered by at least k balls. Fixing the ball centers and varying the radius, we obtain a nested sequence of spaces that is called the k-fold filtration of the centers. For k = 1, the construction is the union-of-balls filtration that is popular in topological data analysis. For larger k, it yields a cleaner shape reconstruction in the presence of outliers. We contribute a sparsification algorithm to approximate the topology of the k-fold filtration. Our method is a combination and adaptation of several techniques from the well-studied case k = 1, resulting in a sparsification of linear size that can be computed in expected near-linear time with respect to the number of input points.
BibTeX - Entry
@InProceedings{buchet_et_al:LIPIcs.SoCG.2023.20,
author = {Buchet, Micka\"{e}l and B. Dornelas, Bianca and Kerber, Michael},
title = {{Sparse Higher Order \v{C}ech Filtrations}},
booktitle = {39th International Symposium on Computational Geometry (SoCG 2023)},
pages = {20:1--20:17},
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/2023/17870},
URN = {urn:nbn:de:0030-drops-178709},
doi = {10.4230/LIPIcs.SoCG.2023.20},
annote = {Keywords: Sparsification, k-fold cover, Higher order \v{C}ech complexes}
}
Keywords: |
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Sparsification, k-fold cover, Higher order Čech complexes |
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 |