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.2018.31
URN: urn:nbn:de:0030-drops-87443
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8744/
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Dey, Tamal K. ; Wang, Jiayuan ; Wang, Yusu

Graph Reconstruction by Discrete Morse Theory

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LIPIcs-SoCG-2018-31.pdf (1 MB)

Abstract

Recovering hidden graph-like structures from potentially noisy data is a fundamental task in modern data analysis. Recently, a persistence-guided discrete Morse-based framework to extract a geometric graph from low-dimensional data has become popular. However, to date, there is very limited theoretical understanding of this framework in terms of graph reconstruction. This paper makes a first step towards closing this gap. Specifically, first, leveraging existing theoretical understanding of persistence-guided discrete Morse cancellation, we provide a simplified version of the existing discrete Morse-based graph reconstruction algorithm. We then introduce a simple and natural noise model and show that the aforementioned framework can correctly reconstruct a graph under this noise model, in the sense that it has the same loop structure as the hidden ground-truth graph, and is also geometrically close. We also provide some experimental results for our simplified graph-reconstruction algorithm.

BibTeX - Entry

@InProceedings{dey_et_al:LIPIcs:2018:8744,
  author =	{Tamal K. Dey and Jiayuan Wang and Yusu Wang},
  title =	{{Graph Reconstruction by Discrete Morse Theory}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{31:1--31:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-066-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{99},
  editor =	{Bettina Speckmann and Csaba D. T{\'o}th},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8744},
  URN =		{urn:nbn:de:0030-drops-87443},
  doi =		{10.4230/LIPIcs.SoCG.2018.31},
  annote =	{Keywords: graph reconstruction, discrete Morse theory, persistence}
}

Keywords: graph reconstruction, discrete Morse theory, persistence
Collection: 34th International Symposium on Computational Geometry (SoCG 2018)
Issue Date: 2018
Date of publication: 08.06.2018

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