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Robust Anisotropic Power-Functions-Based Filtrations for Clustering

Authors: Claire Brécheteau

Published in: LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020)

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.

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Claire Brécheteau. Robust Anisotropic Power-Functions-Based Filtrations for Clustering. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 23:1-23:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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  author =	{Br\'{e}cheteau, Claire},
  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 =	{Cabello, Sergio and Chen, Danny Z.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.23},
  URN =		{urn:nbn:de:0030-drops-121818},
  doi =		{10.4230/LIPIcs.SoCG.2020.23},
  annote =	{Keywords: Power functions, Filtrations, Hierarchical Clustering, Ellipsoids}
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