DTM-Based Filtrations

Authors Hirokazu Anai, Frédéric Chazal, Marc Glisse, Yuichi Ike, Hiroya Inakoshi, Raphaël Tinarrage, Yuhei Umeda

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Author Details

Hirokazu Anai
  • Fujitsu Laboratories, AI Lab, Kawasaki, Japan
Frédéric Chazal
  • Datashape, Inria Paris-Saclay, France
Marc Glisse
  • Datashape, Inria Paris-Saclay, France
Yuichi Ike
  • Fujitsu Laboratories, AI Lab, Kawasaki, Japan
Hiroya Inakoshi
  • Fujitsu Laboratories, AI Lab, Kawasaki, Japan
Raphaël Tinarrage
  • Datashape, Inria Paris-Saclay, France
Yuhei Umeda
  • Fujitsu Laboratories, AI Lab, Kawasaki, Japan

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Hirokazu Anai, Frédéric Chazal, Marc Glisse, Yuichi Ike, Hiroya Inakoshi, Raphaël Tinarrage, and Yuhei Umeda. DTM-Based Filtrations. In 35th International Symposium on Computational Geometry (SoCG 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 129, pp. 58:1-58:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


Despite strong stability properties, the persistent homology of filtrations classically used in Topological Data Analysis, such as, e.g. the Čech 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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Topological Data Analysis
  • Persistent homology


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