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Documents authored by Virk, Žiga

Found 2 Possible Name Variants:

Virk, Ziga

Document
DOI: 10.4230/LIPIcs.SoCG.2019.31
Topological Data Analysis in Information Space

Authors: Herbert Edelsbrunner, Žiga Virk, and Hubert Wagner

Published in: LIPIcs, Volume 129, 35th International Symposium on Computational Geometry (SoCG 2019)

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.
Cite as

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)

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@InProceedings{edelsbrunner_et_al:LIPIcs.SoCG.2019.31,
  author =	{Edelsbrunner, Herbert and Virk, \v{Z}iga and Wagner, Hubert},
  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 =	{Barequet, Gill and Wang, Yusu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2019.31},
  URN =		{urn:nbn:de:0030-drops-104357},
  doi =		{10.4230/LIPIcs.SoCG.2019.31},
  annote =	{Keywords: Computational topology, persistent homology, information theory, entropy}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2018.35
Smallest Enclosing Spheres and Chernoff Points in BregmanGeometry

Authors: Herbert Edelsbrunner, Ziga Virk, and Hubert Wagner

Published in: LIPIcs, Volume 99, 34th International Symposium on Computational Geometry (SoCG 2018)

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.
Cite as

Herbert Edelsbrunner, Ziga Virk, and Hubert Wagner. Smallest Enclosing Spheres and Chernoff Points in BregmanGeometry. In 34th International Symposium on Computational Geometry (SoCG 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 99, pp. 35:1-35:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{edelsbrunner_et_al:LIPIcs.SoCG.2018.35,
  author =	{Edelsbrunner, Herbert and Virk, Ziga and Wagner, Hubert},
  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 =	{Speckmann, Bettina and T\'{o}th, Csaba D.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2018.35},
  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}
}

Virk, Žiga

Document
DOI: 10.4230/LIPIcs.SoCG.2019.31
Topological Data Analysis in Information Space

Authors: Herbert Edelsbrunner, Žiga Virk, and Hubert Wagner

Published in: LIPIcs, Volume 129, 35th International Symposium on Computational Geometry (SoCG 2019)

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.
Cite as

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)

Copy BibTex To Clipboard

@InProceedings{edelsbrunner_et_al:LIPIcs.SoCG.2019.31,
  author =	{Edelsbrunner, Herbert and Virk, \v{Z}iga and Wagner, Hubert},
  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 =	{Barequet, Gill and Wang, Yusu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2019.31},
  URN =		{urn:nbn:de:0030-drops-104357},
  doi =		{10.4230/LIPIcs.SoCG.2019.31},
  annote =	{Keywords: Computational topology, persistent homology, information theory, entropy}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2018.35
Smallest Enclosing Spheres and Chernoff Points in BregmanGeometry

Authors: Herbert Edelsbrunner, Ziga Virk, and Hubert Wagner

Published in: LIPIcs, Volume 99, 34th International Symposium on Computational Geometry (SoCG 2018)

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.
Cite as

Herbert Edelsbrunner, Ziga Virk, and Hubert Wagner. Smallest Enclosing Spheres and Chernoff Points in BregmanGeometry. In 34th International Symposium on Computational Geometry (SoCG 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 99, pp. 35:1-35:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

Copy BibTex To Clipboard

@InProceedings{edelsbrunner_et_al:LIPIcs.SoCG.2018.35,
  author =	{Edelsbrunner, Herbert and Virk, Ziga and Wagner, Hubert},
  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 =	{Speckmann, Bettina and T\'{o}th, Csaba D.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2018.35},
  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}
}
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