Geometry Seminar

Date: March 22, 2024

Time: 4:00PM - 5:00PM

Location: BLOC 302

Speaker: Paulina Hoyos Restrepo, UT Austin

Title: Manifold Learning in the Presence of Symmetries

Abstract: Graph Laplacian-based algorithms for data lying on a manifold have proven effective for tasks such as dimensionality reduction, clustering, and denoising. Consider data sets whose data points lie on a manifold that is closed under the action of a known unitary matrix Lie group G. In this talk, I will show how to construct a G-invariant graph Laplacian (G-GL) by incorporating the distances between all the pairs of points generated by the action of G on the data set. The G-GL converges to the Laplace-Beltrami operator on the data manifold, with a significantly improved convergence rate compared to the standard graph Laplacian, which uses only the distances between the points in the given data set.