Colloquium: Tingran Gao (U. Chicago)

When:
February 20, 2020 @ 3:00 pm – 4:00 pm
2020-02-20T15:00:00-10:00
2020-02-20T16:00:00-10:00
Where:
Keller 401


Speaker: Tingran Gao (U. 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.