Statistical Analysis of Persistence Intensity Functions
By Yen-Chi Chen, Daren Wang, Alessandro Rinaldo, Larry A. Wasserman. 2015
54 citations recorded by the source corpus.
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.
View Paper: https://www.semanticscholar.org/paper/51cfc5a2ed0b84f9325494a37a1667597d90ae9f
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Citations in the corpus
- Persistence Images: A Stable Vector Representation of Persistent Homology (2015, methodology): “Our surfaces are studied from the statistical point of view by Chen et al. (2015), who cite a preprint version of our work; their applications in Section 4 use the L 1 norm between these surfaces, which can be justified as a reasonable notion of distance due to our Theorem 3 that proves the L 1…”