Statistical Analysis of Persistence Intensity Functions

TL;DR

This paper formalizes the persistence intensity function, a tool in topological data analysis, enabling visualization, clustering, and statistical testing of multiple persistence diagrams.

Contribution

It provides a rigorous modification and formalization of the persistence intensity function for analyzing sets of persistence diagrams.

Findings

Allows visualization of multiple diagrams

Enables clustering of topological features

Supports two-sample statistical tests

Abstract

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.