# On the Bootstrap for Persistence Diagrams and Landscapes

arXiv: https://arxiv.org/abs/1311.0376 · HTML: https://mlsanity.com/paper/1311.0376/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Nov 2013.

## Built on by (most cited first, 7 of 7)

- [On the effectiveness of persistent homology](https://mlsanity.com/paper/2206.10551/) (2022)
- [TopP&R: Robust Support Estimation Approach for Evaluating Fidelity and Diversity in Generative Models](https://mlsanity.com/paper/2306.08013/) (2023)
- [Euler Characteristic Curves and Profiles: a stable shape invariant for big data problems](https://mlsanity.com/paper/2212.01666/) (2022)
- [Diffeomorphic interpolation for efficient persistence-based topological optimization](https://mlsanity.com/paper/2405.18820/) (2024)
- [Emotion recognition in talking-face videos using persistent entropy and neural networks](https://mlsanity.com/paper/2110.13571/) (2021)
- [Topology of Out-of-Distribution Examples in Deep Neural Networks](https://mlsanity.com/paper/2501.12522/) (2025)
- [Lattice Paths for Persistent Diagrams](https://mlsanity.com/paper/2105.00351/) (2021)

## Abstract (arXiv)

Persistent homology probes topological properties from point clouds and functions. By looking at multiple scales simultaneously, one can record the births and deaths of topological features as the scale varies. In this paper we use a statistical technique, the empirical bootstrap, to separate topological signal from topological noise. In particular, we derive confidence sets for persistence diagrams and confidence bands for persistence landscapes.