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
ABSTRACT:
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.
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