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.ESA.2018.67
URN: urn:nbn:de:0030-drops-95302
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9530/
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Boissonnat, Jean-Daniel ; Pritam, Siddharth ; Pareek, Divyansh

Strong Collapse for Persistence

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LIPIcs-ESA-2018-67.pdf (0.5 MB)

Abstract

We introduce a fast and memory efficient approach to compute the persistent homology (PH) of a sequence of simplicial complexes. The basic idea is to simplify the complexes of the input sequence by using strong collapses, as introduced by J. Barmak and E. Miniam [DCG (2012)], and to compute the PH of an induced sequence of reduced simplicial complexes that has the same PH as the initial one. Our approach has several salient features that distinguishes it from previous work. It is not limited to filtrations (i.e. sequences of nested simplicial subcomplexes) but works for other types of sequences like towers and zigzags. To strong collapse a simplicial complex, we only need to store the maximal simplices of the complex, not the full set of all its simplices, which saves a lot of space and time. Moreover, the complexes in the sequence can be strong collapsed independently and in parallel. As a result and as demonstrated by numerous experiments on publicly available data sets, our approach is extremely fast and memory efficient in practice.

BibTeX - Entry

@InProceedings{boissonnat_et_al:LIPIcs:2018:9530,
  author =	{Jean-Daniel Boissonnat and Siddharth Pritam and Divyansh Pareek},
  title =	{{Strong Collapse for Persistence}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{67:1--67:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Yossi Azar and Hannah Bast and Grzegorz Herman},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9530},
  URN =		{urn:nbn:de:0030-drops-95302},
  doi =		{10.4230/LIPIcs.ESA.2018.67},
  annote =	{Keywords: Computational Topology, Topological Data Analysis, Strong Collapse, Persistent homology}
}

Keywords: Computational Topology, Topological Data Analysis, Strong Collapse, Persistent homology
Collection: 26th Annual European Symposium on Algorithms (ESA 2018)
Issue Date: 2018
Date of publication: 14.08.2018

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