Supervised Learning Using Homology Stable Rank Kernels

Supervised Learning Using Homology Stable Rank Kernels

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...

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Bibliographic Details
Main Authors: Jens Agerberg, Ryan Ramanujam, Martina Scolamiero, Wojciech Chachólski
Format: Article
Language:English
Published: Frontiers Media S.A. 2021-07-01
Series:Frontiers in Applied Mathematics and Statistics
Subjects:
topological data analysis
kernel methods
metrics
hierarchical stabilisation
persistent homology
Online Access:https://www.frontiersin.org/articles/10.3389/fams.2021.668046/full
Description
Summary: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.
ISSN:2297-4687

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