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DOI: 10.4230/LIPIcs.SoCG.2018.35
URN: urn:nbn:de:0030-drops-87487
URL: http://drops.dagstuhl.de/opus/volltexte/2018/8748/
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Edelsbrunner, Herbert ; Virk, Ziga ; Wagner, Hubert

Smallest Enclosing Spheres and Chernoff Points in BregmanGeometry

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Abstract

Smallest enclosing spheres of finite point sets are central to methods in topological data analysis. Focusing on Bregman divergences to measure dissimilarity, we prove bounds on the location of the center of a smallest enclosing sphere. These bounds depend on the range of radii for which Bregman balls are convex.

BibTeX - Entry

@InProceedings{edelsbrunner_et_al:LIPIcs:2018:8748,
  author =	{Herbert Edelsbrunner and Ziga Virk and Hubert Wagner},
  title =	{{Smallest Enclosing Spheres and Chernoff Points in BregmanGeometry}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{35:1--35:13},
  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/2018/8748},
  URN =		{urn:nbn:de:0030-drops-87487},
  doi =		{10.4230/LIPIcs.SoCG.2018.35},
  annote =	{Keywords: Bregman divergence, smallest enclosing spheres, Chernoff points, convexity, barycenter polytopes}
}

Keywords: Bregman divergence, smallest enclosing spheres, Chernoff points, convexity, barycenter polytopes
Seminar: 34th International Symposium on Computational Geometry (SoCG 2018)
Issue Date: 2018
Date of publication: 24.05.2018


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