Applications of diffusion maps in dynamical systems

Speaker: 
Tim Sauer, George Mason University
Date: 
Sep 29 2014 - 4:30pm
Event type: 
PACM Colloquium
Room: 
Fine 214
Abstract: 

There is great current interest in the use of diffusion maps for dimension reduction. We discuss some examples of diffusion methods applied to understanding dynamical data, in particular combining spectral approaches with delay coordinates. In addition, we extend the usual diffusion map construction by introducing local kernels, a generalization of the standard isotropic kernel. In fact, for data lying on a manifold, any Riemannian geometry can be generated by an appropriate local kernel. This work is joint with Tyrus Berry.