Robust anisotropic power-functions-based filtrations for clustering

Claire Brécheteau (1, 2)

1 ECN - École Centrale de Nantes
2 LMJL - Laboratoire de Mathématiques Jean Leray

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.

Mots clés: Power functions; Filtrations; Hierarchical Clustering; Ellipsoids; and phrases Power functions

Domaines: Géométrie algorithmique [cs.CG]

Claire Brécheteau. Robust anisotropic power-functions-based filtrations for clustering. Symposium on Computational Geometry, Jun 2020, Zurich, Switzerland. ⟨hal-02397100v2⟩