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arXiv · 1811.04757

DTM-based Filtrations

Hirokazu Anai·Frédéric Chazal·Marc Glisse·Yuichi Ike·Hiroya Inakoshi·Raphaël Tinarrage·Yuhei Umeda
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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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Hirokazu Anai, Frédéric Chazal, Marc Glisse, Yuichi Ike, Hiroya Inakoshi, Raphaël Tinarrage, Yuhei Umeda. 2018-11-12. DTM-based Filtrations. https://doi.org/10.1007/978-3-030-43408-3

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