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.2020.23
URN: urn:nbn:de:0030-drops-121818
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12181/
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Brécheteau, Claire

Robust Anisotropic Power-Functions-Based Filtrations for Clustering

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LIPIcs-SoCG-2020-23.pdf (1 MB)

Abstract

We consider robust power-distance functions that approximate the distance function to a compact set, from a noisy sample. We pay particular interest to robust power-distance functions that are anisotropic, in the sense that their sublevel sets are unions of ellipsoids, and not necessarily unions of balls. Using persistence homology on such power-distance functions provides robust clustering schemes. We investigate such clustering schemes and compare the different procedures on synthetic and real datasets. In particular, we enhance the good performance of the anisotropic method for some cases for which classical methods fail.

BibTeX - Entry

@InProceedings{brcheteau:LIPIcs:2020:12181,
  author =	{Claire Br{\'e}cheteau},
  title =	{{Robust Anisotropic Power-Functions-Based Filtrations for Clustering}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{23:1--23:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Sergio Cabello and Danny Z. Chen},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12181},
  URN =		{urn:nbn:de:0030-drops-121818},
  doi =		{10.4230/LIPIcs.SoCG.2020.23},
  annote =	{Keywords: Power functions, Filtrations, Hierarchical Clustering, Ellipsoids}
}

Keywords: Power functions, Filtrations, Hierarchical Clustering, Ellipsoids
Collection: 36th International Symposium on Computational Geometry (SoCG 2020)
Issue Date: 2020
Date of publication: 08.06.2020
Supplementary Material: At https://hal.archives-ouvertes.fr/hal-02397100, the source code is available, as an annex file.

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