Applied Math Lecture
Wednesday, January 29, 2020 at 2:30pm to 3:30pm
Room 2-190 -- MIT - Department of Mathemaics,, 77 Mass. Ave., Cambridge, MA
SPEAKER: Tingran Gao (The University of Chicago)
TITLE: Manifold Learning on Fibre Bundles
Spectral geometry has played an important role in modern geometric data analysis, where the technique is widely known as Laplacian eigenmaps or diffusion maps. In this talk, we present a geometric framework that studies graph representations of complex datasets, where each edge of the graph is equipped with a non-scalar transformation or correspondence. This new framework models such a dataset as a fibre bundle with a connection, and interprets the collection of pairwise functional relations as defining a horizontal diffusion process on the bundle driven by its projection on the base. The eigenstates of this horizontal diffusion process encode the “consistency” among objects in the dataset, and provide a lens through which the geometry of the dataset can be revealed. We demonstrate an application of this geometric framework on evolutionary anthropology.