Hypothesis Testing for Vectorized Persistence Diagrams

• Activity Number: 471 - Advances in High-Dimensional Inference and Multiple Testing
• Type: Contributed
• Date/Time: Wednesday, July 31, 2019 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Chul Moon* and Sangjin Kim
• Companies: Southern Methodist University and The University of Texas at El Paso
• Keywords: Persistent Homology; Topological Data Analysis; Hypothesis Testing

Abstract

Topological data analysis (TDA) is an approach that focuses on analyzing the shape of data. In TDA, topological characteristics of data are summarized as persistence diagrams. Because persistence diagrams are not vectors, most of the statistical methods cannot be directly applied to persistence diagrams. Various approaches have suggested methods to represent persistence diagrams as vectors in a Euclidean space while preserving the summarized topological information. In this talk, we present a two-stage null hypothesis significant test procedure for vectorized persistence diagrams to make an inference on the shape of data. Also, we demonstrate its application on simulated point clouds and three-dimensional rock image data. Our results show that the proposed hypothesis tests can identify differences of data sampled from different-shaped spaces.