A Riemannian Framework for Statistical Analysis of Topological Persistence Diagrams

Topological data analysis is becoming a popular way to study high dimensional feature spaces without any contextual clues or assumptions. This paper concerns itself with one popular topological feature, which is the number of d–dimensional holes in the dataset, also known as the Betti–d number. The persistence of the Betti numbers over various scales is encoded into a persistence diagram (PD), which indicates the birth and death times of these...