JHU Vision, Dynamics and Learning Lab
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Teaching

Learning Theory II: Modeling and Segmentation of Multivariate Mixed Data

(BME 580.692, CS 600.462)

Instructor: René Vidal

Phone: 410-516-7306, E-mail: rvidal @ cis.jhu.edu

Time/Place: T-Th 4.30pm-6pm, Hodson 301

Office Hours: Mondays 5-6, 308B Clark Hall

The aim of this two-semester course is to study the foundations of computational methods for the statistical and dynamical modeling of multivariate data. The emphasis of Learning Theory I is to use probability theory to build models of data in the framework of regression, classification, and data reduction. The emphasis of Learning Theory II is to use methods from algebraic geometry, probability theory and dynamical systems theory to build models of data in the framework of linear and polynomial algebra and dynamical systems theory. Topics will include nonlinear dimensionality reduction (PCA, LLE, Isomap), unsupervised learning (central clustering, subspace clustering, Generalized PCA), and estimation and identification of dynamical systems (Kalman filtering, subspace identification, hybrid system identification). We will apply these tools to model data from computer vision, biomedical imaging, neuroscience, and computational biology.

Course Syllabus

Introduction (Chapter 1)

09/07 Course overview

Linear and Nonlinear Dimensionality Reduction (Chapter 2)

09/12 Principal Component Analysis (PCA)
09/14 Model Selection and Robust PCA
09/19 Nonlinear and Kernel PCA
09/21 Locally Linear Embedding (LLE)

Iterative Methods for Unsupervised Learning (Chapter 3)

09/26-28 Central Clustering: K-means, Expectation Maximization (EM)
10/03-05 Subspace Clustering: K-subspaces, EM for Mixtures of PCAs

Algebraic Methods for Unsupervised Learning (Chapter 4)

10/10-12 Line, plane, and hyperplane clustering
10/17-19 Subspace Clustering: Generalized Principal Component Analysis (GPCA)

Applications in Computer Vision

10/24-26 3-D Motion Segmentation (Chapter 8)
10/31-02 Spatial and Temporal Video Segmentation (Chapter 9)
11/7 Midterm

Estimation and Segmentation of Hybrid Dynamical Models (Chapters 10-11)

11/9 Linear systems: input/output (ARX) and state space (ARMA) representation
11/14-16 State estimation: observability, observer design, Kalman filter
11/21-28 Identification: linear parameter identification, subspace identification, recursive identification
11/30 Identification of hybrid systems
12/5-7: Presentation of projects

References

R. Vidal, Y. Ma, and S. Sastry. Generalized Principal Component Analysis. Springer Verlag, 2007. (In preparation)

Grading Policy

Homework (30%): Homework problems will include both analytical exercises as well as programming assignments in MATLAB.
Midterm (30%): There will be one midterm on November 7^th.
Project (40%): There will be a final project where each student will either apply techniques from the course to solve a real problem or solve an open research problem. Each student will submit a 1-page project description by October 19^th (5%), a 3-page progress report by November 16^th (5%), a 6-page final report by December 7^th (15%), and give a 20 minute presentation on December 5^th or 7^th (15%).

Honor system

Homeworks, midterms and projects will be individual. The strength of the university depends on academic and personal integrity. In this course, you must be honest and truthful. Ethical violations include cheating on exams, plagiarism, reuse of assignments, improper use of the Internet and electronic devices, unauthorized collaboration, alteration of graded assignments, forgery and falsification, lying, facilitating academic dishonesty, and unfair competition. All these will be severely penalized.

Announcements

First class will meet on Thursday 09/07. We can discuss change of time in the first class.

Handout

Homeworks: Please submit the code of your homework at Submit HW

Homework 1: Linear Algebra. Due Thursday September 21st, 2006, beginning of class.

Homework 2: Principal Component Analysis (PCA). Due Thursday September 28th, 2006, beginning of class.
Dataset (images and MATLAB functions).
Errata corrige
- The prototype of the function vector2image is [img]=vector2image(vectorimg,sz) instead of [vectorimg,sz]=vector2image(img).
- Improved the clarity for the description of the function reconstruct.
- In the second part (Experiments), question (f), "Set B" must be substituted with "Set A, Validation Set".
Thank you for reporting these errors.
Homework 3: Nonlinear Dimensionaliry Reduction (KPCA, LLE and Isomap). Due Thursday October 5th, 2006, beginning of class.
Dataset (images and MATLAB functions).
Clarifications

The code given for Matlab function handles was tested in Matlab 7.1. If your version is 6.5 or older, check help as you may have to use"feval" y=feval(kernel,x,var) .
When discussing classification rates, please give the percentage of correct classification in addition to any plots you may have.

Homework 4: Central and Subspace Clustering (K-means, EM and K-subspaces). Due Thursday October 12th, 2006, beginning of class.
Images for Intensity Segmentation
Images for texture Segmentation
Face Dataset
Note : Resize the images to 30 x 40 to run K-Subspaces, Please Run K-Subpaces on the Dataset (after resizing it) without dimensionality reduction and with reducing the dimension using PCA.
Errata
1.Question 2 modified
2.Mean added to the return value of K-subspaces algorithm.
Homework 5: EM, MPPCA, Polysegment Due Thursday October 19th, 2006, beginning of class.
Homework 6: Generalized PCA Due Thursday October 26th, 2006, beginning of class.
Test dataset for problem 5
Homework 7: Applications of GPCA Due Thursday November 2nd, 2006, beginning of class.
Kanatani1 Kanatani2 Kanatani3 three-cars canbook FaceData
Errata
1. mat files updated to include true classification. Please download the new version
Homework 8: Linear and Hybrid Systems Due Thursday November 30th, 2006, beginning of class.

Midterms:

Sample Midterm