Session S27 - Categories and Topology

Friday, July 16, 12:30 ~ 13:00 UTC-3

The Interleaving Distance for Graphical Signatures

Elizabeth Munch

Michigan State University, United States   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Reeb graphs and other related graphical signatures have extensive use in applications, but only recently has there been intense interest in finding metrics for these objects. The idea is that graphical signatures such as Reeb graphs, merge trees, and contour trees encode data in both a space and a real valued function, and we want to build metrics that are sensitive to this information. In this talk, we will focus on a particular metric for comparing Reeb graphs known as the interleaving distance which is a categorical reformulation of the eponymous metric from persistence modules arising in Topological Data Analysis, and show how it can be used as input to statistical and machine learning problems.

Joint work with Anastasios Stefanou (Ohio State University), Erin Chambers (St Louis University) and Tim Ophelders (TU Eindhoven).

View abstract PDF