South African - Japanese Discrete Homotopy Meeting 2025  - Satellite Event

12th of September 2025  - 10.00/10.40  

Department of Mathematics and Applied Mathematics - University of the Western Cape - Bellville - South Africa

Speaker:   Martin Mijangos (Universidad Nacional Autónoma de México, México City, México)

Title:          Divergence measures over the set of persistence diagrams

Abstract: Persistent homology is a powerful tool from algebraic topology that enables the computation of topological features while keeping track of them along different scales. It has been widely applied to data analysis, including point cloud data, complex networks, images, etc. The result of the persistent homology is summarized in barcodes or persistence diagrams. Then, in order to extract statistical information from these barcodes, sometimes one computes statistical indicators over the length of its bars. An issue with this approach is that infinite bars must be deleted or cut to finite ones; however, so far there is no systematic way to perform such procedure. With the aim of accomplishing this by minimizing certain functions, and motivated by ideas of information geometry, we have proposed divergence measures over the set of persistence diagrams that generalize the standard Wasserstein and bottleneck distances. In this talk I will introduce the persistent homology, the persistence diagrams and the Wasserstein distance. I will also present a divergence measure defined over the set of persistence diagrams.