AUTHOR=Agerberg Jens , Ramanujam Ryan , Scolamiero Martina , Chachólski Wojciech TITLE=Supervised Learning Using Homology Stable Rank Kernels JOURNAL=Frontiers in Applied Mathematics and Statistics VOLUME=7 YEAR=2021 URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2021.668046 DOI=10.3389/fams.2021.668046 ISSN=2297-4687 ABSTRACT=

Exciting recent developments in Topological Data Analysis have aimed at combining homology-based invariants with Machine Learning. In this article, we use hierarchical stabilization to bridge between persistence and kernel-based methods by introducing the so-called stable rank kernels. A fundamental property of the stable rank kernels is that they depend on metrics to compare persistence modules. We illustrate their use on artificial and real-world datasets and show that by varying the metric we can improve accuracy in classification tasks.