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DTM-Based Filtrations

  • Hirokazu Anai
  • Frédéric ChazalEmail author
  • Marc Glisse
  • Yuichi Ike
  • Hiroya Inakoshi
  • Raphaël Tinarrage
  • Yuhei Umeda
Conference paper
  • 60 Downloads
Part of the Abel Symposia book series (ABEL, volume 15)

Abstract

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.

Notes

Acknowledgements

This work was partially supported by a collaborative research agreement between Inria and Fujitsu, and the Advanced Grant of the European Research Council GUDHI (Geometric Understanding in Higher Dimensions).

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Hirokazu Anai
    • 1
  • Frédéric Chazal
    • 2
    Email author
  • Marc Glisse
    • 2
  • Yuichi Ike
    • 1
  • Hiroya Inakoshi
    • 1
  • Raphaël Tinarrage
    • 2
  • Yuhei Umeda
    • 1
  1. 1.Fujitsu LaboratoriesAI LabKawasakiJapan
  2. 2.DatashapeInriaPalaiseauFrance

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