Persistent Homology in Machine Learning: Applied Sciences Review

Abstract

Topological Data Analysis (‘TDA’) has become a vibrant and quickly developing field in recent years, providing topology-enhanced data processing and Machine Learning (‘ML’) applications. Due to the novelty of the field, as well as the dissimilarity between the mathematics behind the classical ML and TDA, it might be complicated for a field newcomer to assess the feasibility of the approaches proposed by TDA and the relevancy of the possible applications. The current paper aims to provide an overview of the recent developments that relate to persistent homology, a part of the mathematical machinery behind the TDA, with a particular focus on applied sciences. We consider multiple areas, such as physics, healthcare, material sciences, and others, examining the recent developments in the field. The resulting summary of this paper could be used by field experts to expand their knowledge on recent persistent homology applications, while field newcomers could assess the applicability of this TDA approach for their research. We also point out some of the current restrictions on the use of persistent homology, as well as potential development trajectories that might be useful to the whole field.

Keywords

• algebraic topology
• persistent homology
• machine learning
• physics
• healthcare
• topological data analysis
• chemistry
• biology
• material sciences
• data processing