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.2019.31
URN: urn:nbn:de:0030-drops-104357
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10435/
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Edelsbrunner, Herbert ; Virk, Ziga ; Wagner, Hubert

Topological Data Analysis in Information Space

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LIPIcs-SoCG-2019-31.pdf (1 MB)

Abstract

Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a discrete probability distribution as a point in the standard simplex of the appropriate dimension, we can understand collections of such objects in geometric and topological terms. Importantly, instead of using the standard Euclidean distance, we look into dissimilarity measures with information-theoretic justification, and we develop the theory needed for applying topological data analysis in this setting. In doing so, we emphasize constructions that enable the usage of existing computational topology software in this context.

BibTeX - Entry

@InProceedings{edelsbrunner_et_al:LIPIcs:2019:10435,
  author =	{Herbert Edelsbrunner and Ziga Virk and Hubert Wagner},
  title =	{{Topological Data Analysis in Information Space}},
  booktitle =	{35th International Symposium on Computational Geometry (SoCG 2019)},
  pages =	{31:1--31:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-104-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{129},
  editor =	{Gill Barequet and Yusu Wang},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10435},
  URN =		{urn:nbn:de:0030-drops-104357},
  doi =		{10.4230/LIPIcs.SoCG.2019.31},
  annote =	{Keywords: Computational topology, persistent homology, information theory, entropy}
}

Keywords: Computational topology, persistent homology, information theory, entropy
Collection: 35th International Symposium on Computational Geometry (SoCG 2019)
Issue Date: 2019
Date of publication: 11.06.2019

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