Topology meets Machine Learning: An Introduction using the Euler Characteristic Transform

Abstract

This overview article makes the case for how topological concepts can enrich research in machine learning. Using the Euler Characteristic Transform (ECT), a geometrical-topological invariant, as a running example, I present different use cases that result in more efficient models for analyzing point clouds, graphs, and meshes. Moreover, I outline a vision for how topological concepts could be used in the future, comprising (1) the learning of functions on topological spaces, (2) the building of hybrid models that imbue neural networks with knowledge about the topological information in data, and (3) the analysis of qualitative properties of neural networks. With current research already addressing some of these aspects, this article thus serves as an introduction and invitation to this nascent area of research.