DTM-based Filtrations
Computational Geometry
2024-01-03 v3 Algebraic Topology
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.
Keywords
Cite
@article{arxiv.1811.04757,
title = {DTM-based Filtrations},
author = {Hirokazu Anai and Frédéric Chazal and Marc Glisse and Yuichi Ike and Hiroya Inakoshi and Raphaël Tinarrage and Yuhei Umeda},
journal= {arXiv preprint arXiv:1811.04757},
year = {2024}
}
Comments
Abel Symposia, Springer, In press, Topological Data Analysis