Detection of Representation Orbits of Compact Lie Groups from Point Clouds

Learn to detect and recover underlying Lie group representations from point cloud data in this conference talk that addresses the fundamental challenge of identifying continuous symmetries in data analysis. Explore how linear actions of compact Lie groups arise across diverse applications including image processing with Euclidean isometries, equivariant neural networks, and physical systems governed by Noether's theorem. Discover an innovative orbit-regression algorithm that reformulates the representation recovery problem at the Lie algebra level as a discrete-continuous optimization over the orthogonal group. Examine the theoretical foundations building on work by Cahill, Mixon and Parshall, and understand how this approach enables verification of the Lie linear orbit hypothesis while enhancing existing data analysis techniques. Gain insights into practical applications spanning computer vision, machine learning, and mathematical physics where recovering representations from observed orbits provides crucial structural understanding of underlying symmetries.