Geometric Machine Learning

Abstract A cornerstone of machine learning is the identification and exploitation of structure in high‐dimensional data. While classical approaches assume that data lies in a high‐dimensional Euclidean space, geometric machine learning methods are designed for non‐Euclidean data, including graphs, strings, and matrices, or data characterized by symmetries inherent in the underlying system. In this article, we review geometric approaches for uncovering and leveraging structure in data and how an understanding of data geometry can lead to the development of more effective machine learning algorithms with provable guarantees.