Statistical Analysis of Persistence Intensity Functions
Yen‐Chi Chen, Daren Wang, Alessandro Rinaldo, Larry Wasserman · arXiv (Cornell University) · 2015
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.