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, Jinchao Xu, Chun Liu.

Title:Diffusion Maps for data-driven dimensionality reduction
Seminar:CCMA Luncheon Seminar
Speaker:Tyrus Berry, Penn State University
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