Optimal rates of convergence for persistence diagrams in Topological Data Analysis
Statistics Theory
2013-05-28 v1 Computational Geometry
Machine Learning
Geometric Topology
Statistics Theory
Abstract
Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field. In this paper, we study topological persistence in general metric spaces, with a statistical approach. We show that the use of persistent homology can be naturally considered in general statistical frameworks and persistence diagrams can be used as statistics with interesting convergence properties. Some numerical experiments are performed in various contexts to illustrate our results.
Keywords
Cite
@article{arxiv.1305.6239,
title = {Optimal rates of convergence for persistence diagrams in Topological Data Analysis},
author = {Frédéric Chazal and Marc Glisse and Catherine Labruère and Bertrand Michel},
journal= {arXiv preprint arXiv:1305.6239},
year = {2013}
}