@inproceedings{6252ec21bc0b44228b2b09ac7b8a40ff,
title = "Sparse Higher Order {\v C}ech 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.",
keywords = "Higher order {\v C}ech complexes, k-fold cover, Sparsification",
author = "Micka{\"e}l Buchet and Dornelas, {Bianca B.} and Michael Kerber",
note = "Publisher Copyright: {\textcopyright} Micka{\"e}l Buchet, Bianca B. Dornelas, and Michael Kerber; licensed under Creative Commons License CC-BY 4.0.; 39th International Symposium on Computational Geometry : SoCG 2023, SoCG 2023 ; Conference date: 12-06-2023 Through 15-06-2023",
year = "2023",
month = jun,
day = "1",
doi = "10.4230/LIPIcs.SoCG.2023.20",
language = "English",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl - Leibniz-Zentrum f{\"u}r Informatik",
editor = "Chambers, {Erin W.} and Joachim Gudmundsson",
booktitle = "39th International Symposium on Computational Geometry, SoCG 2023",
address = "Germany",
}