In many scientific and engineering problems, the data of interest can be viewed as drawn from a mixture of geometric or statistical models instead of a single one. Such data are often referred to in different contexts as ``mixed,'' or ``multi-modal,'' or ``multi-model,'' or ``heterogeneous,'' or ``hybrid''. For instances, a natural image normally consists of multiple regions of different texture, a video sequence may contains multiple independently moving objects, and a hybrid dynamical system may arbitrarily switch among different subsystems.
Generalized Principal Component Analysis
(GPCA) is a general method for modeling and segmenting such mixed data using a collection of subspaces, also known in mathematics as a subspace arrangement. By introducing certain new algebraic models and techniques into data clustering, traditionally a statistical problem, GPCA offers a new spectrum of algorithms for data modeling and clustering that are in many aspects more efficient and effective than (or complementary to) traditional methods (e.g. Expectation Maximization and K-Means).
The goal of this site is to promote the use of the GPCA algorithm to improve segmentation performance in many application domains. Tutorials and sample code are provided to help researchers and practitioners decide if the algorithm can be applied to their application domain, and to help get their implementation set up quickly and correctly.
Browsing through the links on the left, you will find a brief overview of the fundamental concepts behind GPCA in the Introduction
section; numerical implementations of several variations of the GPCA algorithm in the Sample Code
section; examples of real applications in the areas of computer vision, image processing; and system identification in the Applications
section; and finally all the related literature in the Publications
This site is jointly developed and maintained by the research groups of
- Professor Yi Ma of the Electrical & Computer Engineering Department at the University of Illinois at Urbana-Champaign
- Professor Rene Vidal of the Biomedical Engineering Department at the Johns Hopkins University
- Professor Kun Huang of the Biomedical Informatics Department at the Ohio State University
Many graduate students have helped with developing and maintaining this website. They are Wei Hong, Shankar Rao, Andrew Wagner, John Wright, and Allen Yang.
© Copyright 2005 University of Illinois. To report bugs or to request help with the sample code provided, please contact the webmaster