Hypothesis testing for shapes using vectorized persistence diagrams

Abstract Topological data analysis involves the statistical characterization of shape data. Persistent homology is a primary tool topological analysis, which can be used to analyze features and perform inference. In this paper, we present two-stage hypothesis test for vectorized persistence diagrams. The first stage filters vector elements in diagrams enhance power test. second consists multiple tests, with false positives controlled by discovery rates. We demonstrate flexibility our method applying it variety simulated real-world types. Our results show that proposed enables accurate informative inferences on compared existing testing methods persistent homology.