License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2020.18
URN: urn:nbn:de:0030-drops-121762
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12176/
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Blaser, Nello ; Brun, Morten

Relative Persistent Homology

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LIPIcs-SoCG-2020-18.pdf (0.4 MB)

Abstract

The alpha complex efficiently computes persistent homology of a point cloud X in Euclidean space when the dimension d is low. Given a subset A of X, relative persistent homology can be computed as the persistent homology of the relative Čech complex Č(X, A). But this is not computationally feasible for larger point clouds X. The aim of this note is to present a method for efficient computation of relative persistent homology in low dimensional Euclidean space. We introduce the relative Delaunay-Čech complex DelČ(X, A) whose homology is the relative persistent homology. It is constructed from the Delaunay complex of an embedding of X in (d+1)-dimensional Euclidean space.

BibTeX - Entry

@InProceedings{blaser_et_al:LIPIcs:2020:12176,
  author =	{Nello Blaser and Morten Brun},
  title =	{{Relative Persistent Homology}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{18:1--18:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Sergio Cabello and Danny Z. Chen},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12176},
  URN =		{urn:nbn:de:0030-drops-121762},
  doi =		{10.4230/LIPIcs.SoCG.2020.18},
  annote =	{Keywords: topological data analysis, relative homology, Delaunay-Čech complex, alpha complex}
}

Keywords: topological data analysis, relative homology, Delaunay-Čech complex, alpha complex
Collection: 36th International Symposium on Computational Geometry (SoCG 2020)
Issue Date: 2020
Date of publication: 08.06.2020

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