The Shape of Data

6 Newer Applications of Geometry in Machine Learning

In Chapter 5, we explored the contributions of metric geometry to machine learning and its myriad uses in model measurements and input. However, geometry has provided many other contributions to machine learning; in this chapter, we’ll explore tangent-space-based approaches to model estimation, exterior calculus, tools related to the intersection of curves (which can be used to replace linear algebra in algorithms), and rank-based models that involve vector fields acting on datasets’ tangent spaces. We’ll see how these tools can help in supervised learning on small datasets, help communities ...