Department of Mathematics, University of Hawaii at Manoa
"Random Persistence Diagram Generation"
Dec 1, 2021 Schedule:
- 2:30 to 3:30 PM Eastern Time (US and Canada)
Meeting # 93068773299
Abstract:
Topological data analysis (TDA) studies the shape patterns of data. Persistent homology (PH) is a widely used method in TDA that summarizes homological features of data at multiple scales and stores them in persistence diagrams (PDs). However, a sufficiently large amount of PDs that allow performing statistical analysis is typically unavailable or requires inordinate computational resources.In this talk, I will presenta novel sampling method for random persistence diagram generation (RPDG)that augments topological summaries of the data,thus facilitating statistical inference with a limited amount of data.RPDG is underpinned by(i) a model based on pairwise interacting point processes for inference of PDs, and (ii) by a reversible jump Markov chain Monte Carlo algorithm for generating samples of PDs. This framework is applicable to a wide variety of datasets. I will present an applicationto amaterials scienceproblem.