Martina Scolamiero: Extracting persistence features with hierarchical stabilisation

Abstract

It is often complicated to understand complex correlation patterns between multiple measurements on a dataset. In multi-parameter persistence we represent them through algebraic objects called persistence modules. I will present the hierarchical stabilisation framework which can be used to produce stable invariants for persistence modules. A fundamental property of such invariants is that they depend on metrics to compare persistence modules. I will then focus on one invariant, obtained via hierarchical stabilisation, called the stable rank. After explaining challenges associated to the computation of the stable rank, in the multi-parameter case, I will showcase its use for one-parameter persistence. In particular I will illustrate how the associated kernel can be used on artificial and real-world datasets and show that by varying the metric we can improve accuracy in classification tasks.

This work is in collaboration with the TDA group at KTH.