# Topological data analysis for random sets and its application in detecting outliers and goodness of fit testing

arXiv: https://arxiv.org/abs/2404.04702 · HTML: https://mlsanity.com/paper/2404.04702/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Apr 2024.

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

- [Persistence Spheres: Bi-continuous Representations of Persistence Diagrams](https://mlsanity.com/paper/2509.16999/) (2025)

## Abstract (arXiv)

In this paper we present the methodology for detecting outliers and testing the goodness-of-fit of random sets using topological data analysis. We construct the filtration from level sets of the signed distance function and consider various summary functions of the persistence diagram derived from the obtained persistence homology. The outliers are detected using functional depths for the summary functions. Global envelope tests using the summary statistics as test statistics were used to construct the goodness-of-fit test. The procedures were justified by a simulation study using germ-grain random set models.