Nonlinear PDEs and graph-based learning

Nonlinear PDEs and graph-based learning

Applied Math And Analysis Seminar

Jeff Calder (University of Minnesota)

Wednesday, November 6, 2019 -
12:00pm to 1:00pm
119 Physics

This talk will focus on recent connections between PDEs and regularization in graph-based learning. We will discuss graph-based semi-supervised learning, where graph Laplacian regularization is widely used. In the limit of vanishingly few labels, Laplacian learning is a discretization of an ill-posed PDE and gives poor results. We present a new rigorous analysis of this ill-posedness using random walks on graphs, and will also discuss new models for regularization in graph based learning that are provably well-posed with very few labels, and have connections to nonlinear elliptic PDEs, including the p-Laplace equation. We will also present some new results on error estimates for spectral convergence of the graph Laplacian to the Laplace-Beltrami operator on the data manifold that use a unique blend of variational methods and PDE techniques.

Last updated: 2019/11/21 - 2:34pm