Topology meets Machine Learning: An Introduction using the Euler Characteristic Transform
It aims to enrich ML research by integrating topological concepts, though it is an introductory overview rather than a novel contribution.
This article introduces the Euler Characteristic Transform as a topological tool to enhance machine learning, showing it leads to more efficient models for analyzing point clouds, graphs, and meshes.
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.