Seminars/Colloquia/Invited Talks

Seminars

Lawrence Saul

Statistics, Geometry, Computation: Searching for Low Dimensional Manifolds in High Dimensional Data

PLACE:	Clark 314
EVENT:	CIS Seminar Series
DATE:	April 18, 2006
TIME:	1:00 - 2:00

Abstract

How can we detect low dimensional structure in high dimensional data? If the data is mainly confined to a low dimensional subspace, then simple linear methods can be used to discover the subspace and estimate its dimensionality. More generally, though, if the data lies on (or near) a low dimensional manifold, then its structure may be highly nonlinear, and linear methods are bound to fail.
The last few years have witnessed several advances in the problem of nonlinear dimensionality reduction. Given high dimensional data sampled from a low dimensional manifold, we now have several frameworks for estimating the data's intrinsic dimensionality and computing a faithful low dimensional representation. Surprisingly, the main computations for "manifold learning" are based on highly tractable optimizations, such as nearest-neighbor searches, least squares fits, eigenvalue problems, and semidefinite programming.
Building on elementary ideas from convex optimization, spectral graph theory, and differential geometry, I will describe some recent approaches that we have developed for the problem of nonlinear dimensionality reduction, both for computing distance-preserving (isometric) and angle-preserving (conformal) low dimensional representations. The resulting algorithms can be understood in terms of simple physical intuitions. The algorithms appear especially useful for the analysis and visualization of high dimensional image data.

Brief Biography

Lawrence Saul received his A.B. in Physics from Harvard (1990) and his Ph.D. in Physics from M.I.T. (1994). He stayed at M.I.T. for two more years as a postdoctoral fellow in the Center for Biological and Computational Learning, then joined the Speech and Image Processing Center of AT&T Labs in Florham Park, NJ. In 1999, the MIT Technology Review recognized him as one of 100 top young innovators. He joined the faculty of the University of Pennsylvania in January 2002, where he is currently an Associate Professor in the Department of Computer and Information Science. He has received an NSF CAREER Award for work in statistical learning, and more recently he served as Program Chair and General Chair for the 2003-2004 conferences on Neural Information Processing Systems. He is currently serving on the Editorial Board for the Journal of Machine Learning Research. In July 2006, he will be joining the faculty of the Department of Computer Science and Engineering at UC San Diego.