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Journal Articles Abel Symposia Year : 2020

DTM-based Filtrations

Abstract

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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Dates and versions

hal-01919562 , version 1 (12-11-2018)
hal-01919562 , version 2 (22-03-2019)
hal-01919562 , version 3 (22-05-2020)

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Hirokazu Anai, Frédéric Chazal, Marc Glisse, Yuichi Ike, Hiroya Inakoshi, et al.. DTM-based Filtrations. Abel Symposia, 2020, Topological Data Analysis, 15, pp.33-66. ⟨10.1007/978-3-030-43408-3_2⟩. ⟨hal-01919562v3⟩

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