Generalized Principal Components Analysis

Rene Vidal, Johns Hopkins University

July 25, 2007


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Abstract

Over the past two decades, we have seen tremendous advances on the simultaneous segmentation and estimation of a collection of models from sample data points, without knowing which points correspond to which model. Most existing segmentation methods treat this problem as "chicken-and-egg", and iterate between model estimation and data segmentation. This lecture will show that for a wide variety of data segmentation problems (e.g. mixtures of subspaces), the "chicken-and-egg" dilemma can be tackled using an algebraic geometric technique called Generalized Principal Component Analysis (GPCA). This technique is a natural extension of classical PCA from one to multiple subspaces. The lecture will touch upon a few motivating applications of GPCA in computer vision, such as image/video segmentation, 3-D motion segmentation or dynamic texture segmentation, but will mainly emphasize the basic theory and algorithmic aspects of GPCA.

Biography

Professor Vidal received his B.S. degree in Electrical Engineering (highest honors) from the Pontificia Universidad Catolica de Chile in 1997 and his M.S. and Ph.D. degrees in Electrical Engineering and Computer Sciences from the University of California at Berkeley in 2000 and 2003, respectively. He was a research fellow at the National ICT Australia since September 2003 and joined The Johns Hopkins University in January 2004 as an Assistant Professor in the Department of Biomedical Engineering and the Center for Imaging Science. His areas of research are biomedical imaging (DTI registration and clustering, heart motion analysis), computer vision (segmentation of static and dynamic scenes, multiple view geometry, omnidirectional vision), machine learning (generalized principal component analysis GPCA, kernel GPCA, dynamic GPCA), vision-based coordination and control of unmanned vehicles, and hybrid systems identification and control.

Dr. Vidal is recipient of the 2005 NFS CAREER Award and the 2004 Best Paper Award Honorable Mention (with Prof. Yi Ma) for his work on "A Unified Algebraic Approach to 2-D and 3-D Motion Segmentation" presented at the European Conference on Computer Vision. He also received the 2004 Sakrison Memorial Prize for "completing an exceptionally documented piece of research", the 2003 Eli Jury award for "outstanding achievement in the area of Systems, Communications, Control, or Signal Processing", the 2002 Student Continuation Award from NASA Ames, the 1998 Marcos Orrego Puelma Award from the Institute of Engineers of Chile, and the 1997 Award of the School of Engineering of the Pontificia Universidad Catolica de Chile to the best graduating student of the school. He is a program chair for PSIVT 2007 and area chair for CVPR 2005 and ICCV 2007.arning, and the European Conference on Principles and Practice of Knowledge Discovery in Databases.