License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2019.58
URN: urn:nbn:de:0030-drops-104623
URL: https://drops.dagstuhl.de/opus/volltexte/2019/10462/
Go to the corresponding LIPIcs Volume Portal


Anai, Hirokazu ; Chazal, Frédéric ; Glisse, Marc ; Ike, Yuichi ; Inakoshi, Hiroya ; Tinarrage, Raphaël ; Umeda, Yuhei

DTM-Based Filtrations

pdf-format:
LIPIcs-SoCG-2019-58.pdf (1 MB)


Abstract

Despite strong stability properties, the persistent homology of filtrations classically used in Topological Data Analysis, such as, e.g. the Cech 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.

BibTeX - Entry

@InProceedings{anai_et_al:LIPIcs:2019:10462,
  author =	{Hirokazu Anai and Fr{\'e}d{\'e}ric Chazal and Marc Glisse and Yuichi Ike and Hiroya Inakoshi and Rapha{\"e}l Tinarrage and Yuhei Umeda},
  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 =	{Gill Barequet and Yusu Wang},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10462},
  URN =		{urn:nbn:de:0030-drops-104623},
  doi =		{10.4230/LIPIcs.SoCG.2019.58},
  annote =	{Keywords: Topological Data Analysis, Persistent homology}
}

Keywords: Topological Data Analysis, Persistent homology
Collection: 35th International Symposium on Computational Geometry (SoCG 2019)
Issue Date: 2019
Date of publication: 11.06.2019


DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI