Robust Generalized Principal Component Analysis

and Its Applications

PLACE:	Clark 314
EVENT:	CIS Seminar Series
DATE:	October 19, 2004
TIME:	1:00 - 2:00

Abstract

Many problems in computer vision, image processing, system identification, and data mining require to group a large data set, typically embedded in a high-dimensional space, into multiple subsets so that each subset can be fit with a low-dimensional parametric model. Recently, it has been shown that if the underlying models are a mixture of linear subspaces (or other simple algebraic varieties), the segmentation and model-estimation problem can be solved non-iteratively via an algebraic geometric means based on a generalization of Principal Component Analysis (PCA), now known as Generalized Principal Component Analysis (GPCA). This method clearly reveals the algebraic nature of the above problems
and provides an elegant solution when the number of models is known. However, in practice, we often face the situation in which the number of linear subspaces is unknown and there are both noises and outliers in the given data set. To deal with these difficult situations, we introduce the notion of the GPCA algorithm.
The robust GPCA algorithm is found extremely powerful and efficient in solving many traditional or new problems in computer vision, image processing, and systems theory. In this talk, we will demonstrate with applications such as image/video segmentation, image representation/compression with sparse components, and hybrid systems identification. Since GPCA presents a novel approach to data modeling, more general and powerful than traditional PCA, we expect to find more important applications in the processing, modeling, and analysis of other data types such as genomic data, biomedical images, and even acoustic signals in the future.

Brief biography

Kun Huang received the two Bachelors’ degree in Biology and Computer Science from Tsinghua University, Beijing, China, in 1996. From 1996 to 2004, he studied in the University of Illinois at Urbana-Champaign (UIUC) where he obtained the Master of Science degrees in Physiology, Electrical Engineering, and mathematics and the Ph.D. degree in Electrical and Computer Science. Currently he is an Assistant Professor in
the Department of Biomedical Informatics in Ohio State University. His research interests include computer vision, machine learning, medical imaging, and computational biology.