# Statistical Parameter Selection for Clustering Persistence Diagrams

arXiv: https://arxiv.org/abs/1910.08398 · HTML: https://mlsanity.com/paper/1910.08398/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Oct 2019.

## Built on by (most cited first, 2 of 2)

- [Discrete Morse Sandwich: Fast Computation of Persistence Diagrams for Scalar Data -- An Algorithm and A Benchmark](https://mlsanity.com/paper/2206.13932/) (2022)
- [Visualizing Topological Importance: A Class-Driven Approach](https://mlsanity.com/paper/2309.13185/) (2023)

## Abstract (arXiv)

In urgent decision making applications, ensemble simulations are an important way to determine different outcome scenarios based on currently available data. In this paper, we will analyze the output of ensemble simulations by considering so-called persistence diagrams, which are reduced representations of the original data, motivated by the extraction of topological features. Based on a recently published progressive algorithm for the clustering of persistence diagrams, we determine the optimal number of clusters, and therefore the number of significantly different outcome scenarios, by the minimization of established statistical score functions. Furthermore, we present a proof-of-concept prototype implementation of the statistical selection of the number of clusters and provide the results of an experimental study, where this implementation has been applied to real-world ensemble data sets.