Multiparameter Persistence

Abstract: This talk is the first in a series of two talks (the second one will be in the Dioscuri TDA seminar), outlining a new vectorization method for multiparameter persistence modules with an arbitrary number of parameters. Multiparameter persistence extends the foundational ideas of persistent homology. Importantly, it can capture topological information of a point clouds with several functions. This talk introduces the definition and motivation behind multiparameter persistence. We will compare the structure and interpretability of multiparameter persistence modules with their one-parameter counterparts, highlighting the challenges that arise when working with multiple parameters. To address these issues, we will explore several approaches that extract meaningful topological information without requiring full classification of the modules. In particular, we will take a closer look at the Generalized Rank Invariant Landscape (GRIL), a recent vectorization method that provides a computable and interpretable invariant.

machine learning

Audience: general audience

Basic Notions and Applied Topology Seminar