Geodesic Regression

Riemannian Geometry can be safely tagged as a “revolutionary” theory in mathematics. Firstly, the theory put forward a radical view of space and geometry by generalizing the “flat” Euclidean space to curved manifolds. Later, it was the basis for a major Physics revolution when Albert Einstein made use of the theory to explain space and gravity which we know as the “Theory of General Relativity”. There have been uses of Riemannian geometry in Machine Learning as well. In this article, we will learn about Geodesic Regression which is an extension of Linear Regression to Riemannian space. It is assumed that readers have a good understanding of the least squares linear regression model and some knowledge of Riemannian geometry. Before diving into the subject matter, it is worth discussing the basics of geometry. The explanation will be in simple terms just required for understanding the subject matter and we are not going into fine details of geometry. Hence we may have a casual explanation that may not conform precisely to standard mathematical definitions. <a href="https://towardsdatascience.com/geodesic-regression-d0334de2d9d8">Read More</a>