EE 290A: Generalized Principal Component Analysis with Applications to Vision, Image Processing and System Identification


Time:
 Tu & Th, 3:40-5:00. Spring, 2011.
Location:
 Room 254, Sutardja Dai Hall. This course will be recorded and webcast to UC Merced concurrently.
Webcasting: mms://media.citris.berkeley.edu/eecs290a
Units: Three (3)
Instructors: S. Shankar Sastry and Allen Y. Yang.
Course/
Homework Email:		 ucb.gpca.spring2011@gmail.com
UCM students are encouraged to participate in discussion by sending messages to this account.
Instructor Emails: { sastry, yang } @ eecs
Office Hour: Thursday 2:00-3:30 (Sastry) and Friday 12:30-2 (Yang), by appointment only.
Office Phone:
 643-5798 (Yang)


Goal: In many modern scientific and engineering problems, the data are often drawn from a mixture of hybrid models instead of from a unimodal distribution. For instance, a natural image normally consists of different textural regions; a traffic surveillance video consists of multiple independently moving cars; and the dynamics of human/humanoid body movements consists of multiple phases. This course addresses a common problem in modeling such hybrid data, namely, how to simultaneously segment the data into homogeneous subsets and model each subset with a unique parametric model.

The lectures aim to provide a comprehensive and balanced coverage of the fundamental theory for the estimation of hybrid models. We will cover both algebraic and statistical approaches to this problem, and study algebraic and statistical algorithms for the estimation of hybrid models from possibly noisy and corrupted data. The theory will be applied to a wide spectrum of engineering problems in image processing, computer vision, system identification, and system biology.


Required Textbook:

Prepring: Estimation and Segmentation of Hybrid Models, by Rene Vidal, Yi Ma, and Shankar Sastry.

The book draft will be made available as lecture material during the class.


Grading Policy:

There will be approximately 5 problem sets (60% credit)  and a final project (40% credit) for the class,  Participation in the class is expected from the registered students. Homework is due at the beginning of the class on the due date.


Course Projects Final Reports: TBA


Course Progress: --> Course Video

Date

Topics

 Lecture Notes

HW

Week 1

(1-18; 1-20)

Introduction,
PCA

 syllabus, lecture 1,
lecture 2.

 

Week 2

(1-27)

(No class on 1-25)
PCA and extensions.

 lecture 3

HW1

Week 3

(2-1; 2-3)

Algebraic methods

lecture 4
lecture 5

 

Week 4

(2-8; 2-10)

Iterative methods
for estimating subspace
arrangements

lecture 6,
lecture 7

HW2

Week 5

(2-15; 2-17)

Robust statistical
analysis

lecture 8,
lecture 9


Week 6

(2-22; 2-24)

Robust PCA

lecture 10,
lecture 11

 HW3

Week 7

(3-1; 3-3)

 Algebraic Properties of
subspace arrangements

lecture 12,
lecture 13


Week 8

(3-8; 3-10)

Extensions to arrangements
of nonlinear surfaces,
Mid-term project proposal

lecture 14

HW4

Week 9

(3-15; 3-17)

Applications:
Motion Segmentation

lecture 15,
lecture 16

 

Week 10

Spring Recess (No class)



Week 11

(3-29; 3-31)

Applications:
Motion Segmentation

lecture 17,
lecture 18


Week 12

(4-5; 4-7)

Applications:
Dynamic texture and
video segmentation

lecture 19,
lecture 20


Week 13

(4-12; 4-14)

Applications:
Hybrid system identieifcation

lecture 21,
lecture 22


Week 14

(4-19; 4-21)

Applications:
system biology and
bioengineering

lecture 23,
lecture 24

 

Week 15

(4-26; 4-28)

Final project presentation



 


Additional Material:

  1. GPCA Website at Illinois (most current papers and MATLAB code): http://perception.csl.uiuc.edu/gpca/