# Optimal rates of convergence for persistence diagrams in Topological Data Analysis

arXiv: https://arxiv.org/abs/1305.6239 · HTML: https://mlsanity.com/paper/1305.6239/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 May 2013.

## Built on by (most cited first, 1 of 1)

- [How high is `high'? Rethinking the roles of dimensionality in topological data analysis and manifold learning](https://mlsanity.com/paper/2505.16879/) (2025)

## Abstract (arXiv)

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.