  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.
