For more information about this meeting, contact Fei Wang, Toan Nguyen, 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|
|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
|Date:||02 / 17 / 2014|
|Time:||12:20pm - 01:30pm|