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ECE 586YM: Generalized Principal Component Analysis:
Estimation and Segmentation of Hybrid Models

Spring 2006, ECE, University of Illinois at Urbana-Champaign

 

 "A knowledge of statistics is like a knowledge of
  foreign languages or of algebra; it may prove of
  use at any time under any circumstances."      

                                   -- A. L. Bowley

[Administrative | Homeworks | Handouts | Final Projects | Online Resource]

Administrative Information

 Instructor: Professor Yi Ma
Lectures: TuTh 1:30pm-2:50pm, 106B6 Engineering Hall
Office hours: Tu3:00pm-5:00pm, 145 CSL
Office: 145 CSL, Phone: 244-0871
Email: yima(at)uiuc.edu
Appointments: through email.

Announcements:


Brief Description:
In this course, we aim to provide a comprehensive and balanced coverage of the theory for the estimation of hybrid models (linear, nonlinear, or dynamical). We will cover both algebraic and statistical approaches to this problem, study and compare algebraic and statistical algorithms for the estimation of hybrid models from (possibly noisy and corrupted) data, and apply the theory and algorithms to a wide spectrum of engineering problems in image processing, computer vision, system identification and bioengineering.

The course is to follow closely the table of content of a new book on GPCA that the instructor has been working on. Draft of the book will be distributed in class.
Prerequisites:
This is an advanced course, and it can be considered as a follow-up course to either the computer vision course ECE549, or the image processing course ECE547, or the "Pattern Recognition" course offered by Narendra Ahuja as ECE598, or the linear system course ECE515, or the random processes course ECE534, or the estimation theory course ECE561.
*This course does require background in linear algebra (Math415/426) and statistics (ECE413).
*Familiarity with Matlab is recommended . If you have never used it before, it only takes a couple of weeks to learn (say from Matlab Primer).
*Some familiarity with abstract algebra (Math417) or mathematical statistics (Stat510) will certainly increase your appreciation but not crucial nor required. Some background in image/video processing, computer vision, machine learning, or systems theory may help you identify applications of your own interest (for the final project?).

Required Text:
*Generalized Principal Component Analysis: Estimation and Segmentation of Hybrid Models, a working book draft by Rene Vidal, Yi Ma, and S. Sastry, to be distributed by the instructor. Here is the table of content of the book.

Other References:
* Principal Component Analysis, I.T. Jolliffe, Springer, 2002.
* The Elements of Statistical Learning, T. Hastie, R. Tibshirani, and J. Friedman, Springer, 2001.
* The Nature of Statistical Learning Theory, V.N. Vapnik, Springer, 1995.
*Mathematical Statistics, P.J. Bickel and K.A. Doksum, Prentice Hall, 1977.
* More references on algebra and statistics will be throughout the course.

Grading Policy: Homework (60%) and Final Project (40%).
*Homework: You are allowed to discuss on the homework in small groups, but you must write the solution independently to hand in. No late homework will be accepted (unless an extension is granted by the instructor to the whole class).
*Final Project: The final project can be done in a group of 2 or 3 students - depending on the final size of the class. The project can be theoretical, experimental or a mix of both. It consists of a midterm proposal, a final presentation (in class) and a report. With the instructor's approval, the final project can be related to the student's own graduate research.

Homeworks & Programming Exercises

Handouts & Supplementary Notes

 The draft of the textbook will be constantly updated throughout the semester. I therefore will post one chapter after another so that you may the most recent version:

Course Final Projects

Online Resource Links
Yi Ma
Last modified: Sat May 13 17:39:09 CDT 2006