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Robust Anisotropic Power-Functions-Based Filtrations for Clustering

Author Claire Brécheteau

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Claire Brécheteau
  • Laboratoire de Mathématiques Jean Leray & École Centrale de Nantes, France

Acknowledgements

I am extremely grateful to Samuel Tapie, for his suggestion to use tangency of ellipsoids at their first intersection point, to derive the expression of their intersection radius.

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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) https://doi.org/10.4230/LIPIcs.SoCG.2020.23

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Unsupervised learning and clustering
Keywords
  • Power functions
  • Filtrations
  • Hierarchical Clustering
  • Ellipsoids

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