DTM-based Filtrations
Résumé
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.
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A comme version hal-02093445 Objet présenté à une conférence Hirokazu Anai, Frédéric Chazal, Marc Glisse, Yuichi Ike, Hiroya Inakoshi, et al.. DTM-based Filtrations. SoCG 2019 - 35th International Symposium on Computational Geometry, Jun 2019, Portland, United States. pp.58:1--58:15, ⟨10.4230/LIPIcs.SoCG.2019.58⟩. ⟨hal-02093445⟩