Statistical Analysis of Persistence Intensity Functions
This work addresses a known bottleneck in topological data analysis for researchers, but it is incremental as it builds on an existing informal method.
The paper tackles the problem of analyzing sets of persistence diagrams in topological data analysis by modifying and formalizing the persistence intensity function approach, enabling visualization, clustering, and two-sample tests.
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.