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Topological Data Analysis in Information Space

Authors Herbert Edelsbrunner, Žiga Virk, Hubert Wagner

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Author Details

Herbert Edelsbrunner
  • IST Austria (Institute of Science and Technology Austria) , Am Campus 1, 3400 Klosterneuburg, Austria
Žiga Virk
  • Faculty of Computer and Information Science, University of Ljubljana , Vecna pot 113, 1000 Ljubljana, Slovenia
Hubert Wagner
  • IST Austria (Institute of Science and Technology Austria) , Am Campus 1, 3400 Klosterneuburg, Austria

Funding

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).

Cite AsGet BibTex

Herbert Edelsbrunner, Žiga Virk, and Hubert Wagner. Topological Data Analysis in Information Space. In 35th International Symposium on Computational Geometry (SoCG 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 129, pp. 31:1-31:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.SoCG.2019.31

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Computational topology
  • persistent homology
  • information theory
  • entropy

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