DTM-based Filtrations

Hirokazu Anai 1 Frédéric Chazal 2 Marc Glisse 2 Yuichi Ike 1 Hiroya Inakoshi 1 Raphaël Tinarrage 2 Yuhei Umeda 1
2 DATASHAPE - Understanding the Shape of Data
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
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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Submitted on : Friday, March 22, 2019 - 10:51:20 AM
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  • HAL Id : hal-01919562, version 2
  • ARXIV : 1811.04757

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Hirokazu Anai, Frédéric Chazal, Marc Glisse, Yuichi Ike, Hiroya Inakoshi, et al.. DTM-based Filtrations. Abel Symposia, Springer, In press, Topological Data Analysis. ⟨hal-01919562v2⟩

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