DTM-based Filtrations

Hirokazu Anai (1) , Frédéric Chazal (2) , Marc Glisse (2) , Yuichi Ike (1) , Hiroya Inakoshi (1) , Raphaël Tinarrage (2) , Yuhei Umeda (1)

1 Fujitsu Laboratories Ltd.
2 DATASHAPE - Understanding the Shape of Data

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.

Mots clés: Topological data analysis TDA; Persistent Homology

Domaines: Géométrie algorithmique [cs.CG]; Topologie algébrique [math.AT]

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