Published June 18, 2019
| Version v1
Conference paper
DTM-based Filtrations
Contributors
Others:
- Fujitsu Laboratories Ltd.
- Understanding the Shape of Data (DATASHAPE) ; Inria Sophia Antipolis - Méditerranée (CRISAM) ; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Inria Saclay - Ile de France ; Institut National de Recherche en Informatique et en Automatique (Inria)
- European Project: 339025,EC:FP7:ERC,ERC-2013-ADG,GUDHI(2014)
Description
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.
Abstract
This version is an extended abstract. The complete version of the paper, including proofs and additional comments, can be found at https://arxiv.org/abs/1811.04757Abstract
International audienceAdditional details
Identifiers
- URL
- https://hal.archives-ouvertes.fr/hal-02093445
- URN
- urn:oai:HAL:hal-02093445v1
Origin repository
- Origin repository
- UNICA