# Bottleneck Profiles and Discrete Prokhorov Metrics for Persistence Diagrams

arXiv: https://arxiv.org/abs/2106.02538 · HTML: https://mlsanity.com/paper/2106.02538/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jun 2021.

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

- [Topological Social Choice: Designing a Noise-Robust Polar Distance for Persistence Diagrams](https://mlsanity.com/paper/2507.14340/) (2025)

## Abstract (arXiv)

In topological data analysis (TDA), persistence diagrams have been a succesful tool. To compare them, Wasserstein and Bottleneck distances are commonly used. We address the shortcomings of these metrics and show a way to investigate them in a systematic way by introducing bottleneck profiles. This leads to a notion of discrete Prokhorov metrics for persistence diagrams as a generalization of the Bottleneck distance. They satisfy a stability result and bounds with respect to Wasserstein metrics. We provide algorithms to compute the newly introduced quantities and end with an discussion about experiments.