PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Fei Wang, Toan Nguyen, Stephanie Zerby, Mark Levi, Victor Nistor, Jinchao Xu, Ludmil Zikatanov, Chun Liu.

Title:Diffusion Maps for data-driven dimensionality reduction
Seminar:CCMA Luncheon Seminar
Speaker:Tyrus Berry, Penn State University
Abstract:
Diffusion Maps is an algorithm for finding and describing low-dimensional structure in high-dimensional data based on concepts from Riemannian geometry. Diffusion Maps relies on a geometric prior which assumes that the data set lies `near' a low-dimensional smooth manifold embedded in a high-dimensional Euclidean space. A theoretical result of Coifman and Lafon shows that, using only the data and with no other prior information about the manifold structure, the Diffusion Maps construction converges to the Laplace-Beltrami operator on the manifold in the limit of large data. Since the Laplace-Beltrami operator determines the Riemannian metric, the Diffusion Maps algorithm captures all aspects of the geometry in the limit of large data. In this talk I give a comprehensive overview of Diffusion Maps including an explanation of the algorithm along with visualizations and explanations of the intuition behind the steps. I will also review the key theoretical results and some applications as time permits.

Room Reservation Information

Room Number:MB114
Date:02 / 17 / 2014
Time:12:20pm - 01:30pm