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DOI: 10.4230/LIPIcs.SoCG.2019.58

DTM-Based Filtrations

Authors: Hirokazu Anai, Frédéric Chazal, Marc Glisse, Yuichi Ike, Hiroya Inakoshi, Raphaël Tinarrage, and Yuhei Umeda

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

Abstract

Despite strong stability properties, the persistent homology of filtrations classically used in Topological Data Analysis, such as, e.g. the Čech or Vietoris-Rips filtrations, are very sensitive to the presence of outliers in the data from which they are computed. In this paper, we introduce and study a new family of filtrations, the DTM-filtrations, built on top of point clouds in the Euclidean space which are more robust to noise and outliers. The approach adopted in this work relies on the notion of distance-to-measure functions and extends some previous work on the approximation of such functions.

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Hirokazu Anai, Frédéric Chazal, Marc Glisse, Yuichi Ike, Hiroya Inakoshi, Raphaël Tinarrage, and Yuhei Umeda. DTM-Based Filtrations. In 35th International Symposium on Computational Geometry (SoCG 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 129, pp. 58:1-58:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{anai_et_al:LIPIcs.SoCG.2019.58,
  author =	{Anai, Hirokazu and Chazal, Fr\'{e}d\'{e}ric and Glisse, Marc and Ike, Yuichi and Inakoshi, Hiroya and Tinarrage, Rapha\"{e}l and Umeda, Yuhei},
  title =	{{DTM-Based Filtrations}},
  booktitle =	{35th International Symposium on Computational Geometry (SoCG 2019)},
  pages =	{58:1--58:15},
  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.2019.58},
  URN =		{urn:nbn:de:0030-drops-104623},
  doi =		{10.4230/LIPIcs.SoCG.2019.58},
  annote =	{Keywords: Topological Data Analysis, Persistent homology}
}

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DTM-Based Filtrations

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