# Meeting Details

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

Title: Diffusion Maps for data-driven dimensionality reduction CCMA Luncheon Seminar 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 02 / 17 / 2014 12:20pm - 01:30pm