Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Optimal rates of convergence for persistence diagrams in Topological Data Analysis

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.
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-00827162
Contributor : Frédéric Chazal <>
Submitted on : Tuesday, May 28, 2013 - 9:47:23 PM
Last modification on : Friday, September 20, 2019 - 4:56:35 PM

Links full text

Identifiers

  • HAL Id : hal-00827162, version 1
  • ARXIV : 1305.6239

Citation

Frédéric Chazal, Marc Glisse, Catherine Labruère, Bertrand Michel. Optimal rates of convergence for persistence diagrams in Topological Data Analysis. 2013. ⟨hal-00827162⟩

Share

Metrics

Record views

621