---
_id: '9630'
abstract:
- lang: eng
  text: 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.
acknowledgement: This research is partially supported by the Office of Naval Research,
  through grant no. N62909-18-1-2038, and the DFG Collaborative Research Center TRR
  109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of
  the Austrian Science Fund (FWF).
article_processing_charge: Yes
article_type: original
author:
- first_name: Herbert
  full_name: Edelsbrunner, Herbert
  id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
  last_name: Edelsbrunner
  orcid: 0000-0002-9823-6833
- first_name: Ziga
  full_name: Virk, Ziga
  id: 2E36B656-F248-11E8-B48F-1D18A9856A87
  last_name: Virk
- first_name: Hubert
  full_name: Wagner, Hubert
  id: 379CA8B8-F248-11E8-B48F-1D18A9856A87
  last_name: Wagner
citation:
  ama: Edelsbrunner H, Virk Z, Wagner H. Topological data analysis in information
    space. <i>Journal of Computational Geometry</i>. 2020;11(2):162-182. doi:<a href="https://doi.org/10.20382/jocg.v11i2a7">10.20382/jocg.v11i2a7</a>
  apa: Edelsbrunner, H., Virk, Z., &#38; Wagner, H. (2020). Topological data analysis
    in information space. <i>Journal of Computational Geometry</i>. Carleton University.
    <a href="https://doi.org/10.20382/jocg.v11i2a7">https://doi.org/10.20382/jocg.v11i2a7</a>
  chicago: Edelsbrunner, Herbert, Ziga Virk, and Hubert Wagner. “Topological Data
    Analysis in Information Space.” <i>Journal of Computational Geometry</i>. Carleton
    University, 2020. <a href="https://doi.org/10.20382/jocg.v11i2a7">https://doi.org/10.20382/jocg.v11i2a7</a>.
  ieee: H. Edelsbrunner, Z. Virk, and H. Wagner, “Topological data analysis in information
    space,” <i>Journal of Computational Geometry</i>, vol. 11, no. 2. Carleton University,
    pp. 162–182, 2020.
  ista: Edelsbrunner H, Virk Z, Wagner H. 2020. Topological data analysis in information
    space. Journal of Computational Geometry. 11(2), 162–182.
  mla: Edelsbrunner, Herbert, et al. “Topological Data Analysis in Information Space.”
    <i>Journal of Computational Geometry</i>, vol. 11, no. 2, Carleton University,
    2020, pp. 162–82, doi:<a href="https://doi.org/10.20382/jocg.v11i2a7">10.20382/jocg.v11i2a7</a>.
  short: H. Edelsbrunner, Z. Virk, H. Wagner, Journal of Computational Geometry 11
    (2020) 162–182.
date_created: 2021-07-04T22:01:26Z
date_published: 2020-12-14T00:00:00Z
date_updated: 2021-08-11T12:26:34Z
day: '14'
ddc:
- '510'
- '000'
department:
- _id: HeEd
doi: 10.20382/jocg.v11i2a7
file:
- access_level: open_access
  checksum: f02d0b2b3838e7891a6c417fc34ffdcd
  content_type: application/pdf
  creator: asandaue
  date_created: 2021-08-11T11:55:11Z
  date_updated: 2021-08-11T11:55:11Z
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  file_name: 2020_JournalOfComputationalGeometry_Edelsbrunner.pdf
  file_size: 1449234
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file_date_updated: 2021-08-11T11:55:11Z
has_accepted_license: '1'
intvolume: '        11'
issue: '2'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 162-182
project:
- _id: 0aa4bc98-070f-11eb-9043-e6fff9c6a316
  grant_number: I4887
  name: Discretization in Geometry and Dynamics
publication: Journal of Computational Geometry
publication_identifier:
  eissn:
  - 1920180X
publication_status: published
publisher: Carleton University
quality_controlled: '1'
scopus_import: '1'
status: public
title: Topological data analysis in information space
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/3.0/legalcode
  name: Creative Commons Attribution 3.0 Unported (CC BY 3.0)
  short: CC BY (3.0)
type: journal_article
user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf
volume: 11
year: '2020'
...