AUTHOR=Hensel Felix , Moor Michael , Rieck Bastian TITLE=A Survey of Topological Machine Learning Methods JOURNAL=Frontiers in Artificial Intelligence VOLUME=4 YEAR=2021 URL=https://www.frontiersin.org/journals/artificial-intelligence/articles/10.3389/frai.2021.681108 DOI=10.3389/frai.2021.681108 ISSN=2624-8212 ABSTRACT=

The last decade saw an enormous boost in the field of computational topology: methods and concepts from algebraic and differential topology, formerly confined to the realm of pure mathematics, have demonstrated their utility in numerous areas such as computational biology personalised medicine, and time-dependent data analysis, to name a few. The newly-emerging domain comprising topology-based techniques is often referred to as topological data analysis (TDA). Next to their applications in the aforementioned areas, TDA methods have also proven to be effective in supporting, enhancing, and augmenting both classical machine learning and deep learning models. In this paper, we review the state of the art of a nascent field we refer to as “topological machine learning,” i.e., the successful symbiosis of topology-based methods and machine learning algorithms, such as deep neural networks. We identify common threads, current applications, and future challenges.