# Statistical Analysis of Persistence Intensity Functions

arXiv: https://arxiv.org/abs/1510.02502 · HTML: https://mlsanity.com/paper/1510.02502/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Oct 2015.

## Built on by (most cited first, 8 of 8)

- [TDA-Net: Fusion of Persistent Homology and Deep Learning Features for COVID-19 Detection in Chest X-Ray Images](https://mlsanity.com/paper/2101.08398/) (2021)
- [Persistent Homology and Graphs Representation Learning](https://mlsanity.com/paper/2102.12926/) (2021)
- [Topology Applied to Machine Learning: From Global to Local](https://mlsanity.com/paper/2103.05796/) (2021)
- [A computationally efficient framework for vector representation of persistence diagrams](https://mlsanity.com/paper/2109.08239/) (2021)
- [A Domain-Oblivious Approach for Learning Concise Representations of Filtered Topological Spaces for Clustering](https://mlsanity.com/paper/2105.12208/) (2021)
- [Vector Summaries of Persistence Diagrams for Permutation-based Hypothesis Testing](https://mlsanity.com/paper/2306.06257/) (2023)
- [Persistence-based topological optimization: a survey](https://mlsanity.com/paper/2603.24613/) (2026)
- [Where Do Two Populations of Persistence Diagrams Differ? Calibrated Local Inference at a Fixed Budget](https://mlsanity.com/paper/2610.08292/) (2026)

## Abstract (arXiv)

Persistence diagrams are two-dimensional plots that summarize the topological features of functions and are an important part of topological data analysis. A problem that has received much attention is how deal with sets of persistence diagrams. How do we summarize them, average them or cluster them? One approach -- the persistence intensity function -- was introduced informally by Edelsbrunner, Ivanov, and Karasev (2012). Here we provide a modification and formalization of this approach. Using the persistence intensity function, we can visualize multiple diagrams, perform clustering and conduct two-sample tests.