Beijing Institute of Mathematical Sciences and Applications

Matthew Burfitt , Jing Yan Li , Jie Wu , Jia Wei Zhou

Matias de Jong van Lier

Thursday, June 13, 2024 2:30 PM - 3:30 PM

A3-3-201

Zoom 928 682 9093 (BIMSA)

Persistent homology provides essential topological insights into datasets, representing each topological feature with an interval whose length, known as the feature's lifetime, represents its persistence. Features with short lifetimes are typically regarded as noise, while those with longer lifetimes are considered meaningful characteristics of the dataset. We introduce a novel filtering method in graph signal processing, named the Low Persistence Filter. This technique filters out low persistence classes in the persistence modules of the sublevel filtration of a signal over a graph, resulting in a topologically simplified version of the signal. Our method introduces a new structure called the Basin Hierarchy Tree. This structure encodes information about the persistence modules of the sublevel filtration and details how different intervals in the persistence diagram are correlated, which is crucial for defining the Low Persistence Filter. Finally, we showcase several applications of the Low Persistence Filter using the open-source Python implementation we developed.

This is a joint work with S. E. Graiff Zurita, and S. Kaji.