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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.2020.53
URN: urn:nbn:de:0030-drops-122116
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12211/
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Kerber, Michael ; Nigmetov, Arnur

Efficient Approximation of the Matching Distance for 2-Parameter Persistence

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LIPIcs-SoCG-2020-53.pdf (0.5 MB)

Abstract

In topological data analysis, the matching distance is a computationally tractable metric on multi-filtered simplicial complexes. We design efficient algorithms for approximating the matching distance of two bi-filtered complexes to any desired precision ε>0. Our approach is based on a quad-tree refinement strategy introduced by Biasotti et al., but we recast their approach entirely in geometric terms. This point of view leads to several novel observations resulting in a practically faster algorithm. We demonstrate this speed-up by experimental comparison and provide our code in a public repository which provides the first efficient publicly available implementation of the matching distance.

BibTeX - Entry

@InProceedings{kerber_et_al:LIPIcs:2020:12211,
  author =	{Michael Kerber and Arnur Nigmetov},
  title =	{{Efficient Approximation of the Matching Distance for 2-Parameter Persistence}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{53:1--53:16},
  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/2020/12211},
  URN =		{urn:nbn:de:0030-drops-122116},
  doi =		{10.4230/LIPIcs.SoCG.2020.53},
  annote =	{Keywords: multi-parameter persistence, matching distance, approximation algorithm}
}

Keywords: multi-parameter persistence, matching distance, approximation algorithm
Collection: 36th International Symposium on Computational Geometry (SoCG 2020)
Issue Date: 2020
Date of publication: 08.06.2020
Supplementary Material: Our code is available as part of the Hera library https://bitbucket.org/grey_narn/hera/src/master/matching/ and provides an efficient implementation for computing the matching distance for bi-filtrations.

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