Supervised Learning Using Homology Stable Rank Kernels - Agerberg, Jens; Ramanujam, Ryan; Scolamiero, Martina; Chachólski, Wojciech (Frontiers in Applied Mathematics and Statistics, 2021)
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.