ECE 586 YM

• Control Systems

A common problem in processing or modeling such hybrid data is how to simultaneously segment the data into homogeneous subsets and model each subset with a different parametric model. In other words, one needs to infer from the data a number of models and their individual parameters that best fit subsets of the data. In the past few years, many different methods and algorithms for solving this problem have been developed in different application domains, including but not limited to sparse image representation and compression in image processing; image and video segmentation in computer vision; hybrid system identification in systems theory; and data modeling and analysis in biomedicine. These methods have shown great potential of exceeding many conventional techniques.

In this course, we aim to provide a comprehensive and balanced coverage of the theory for the estimation of hybrid models. 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.

1. Graduate students in ECE/CS in the areas of computer vision, image processing, and pattern recognition interested in data modeling, clustering, and segmentation.
2. Graduate students in ECE or ME in the areas of control interested in estimation theory and (hybrid) system identification.
3. Graduate students in Mathematics interested in applications of commutative algebra or students in statistics interested in estimation of mixtures of models.

Grading policy: Weekly homework (60%) and Final Project (40%). The final project can be done in a group of 2 or 3 students. The project can be theoretical, experimental or a mixture of both. It consists of a midterm proposal, a final presentation (in class) and a web-based report.

Tentative Course Syllabus and Schedule:

1. Introduction (1.5 hours): data modeling, hybrid models, and model estimation.
2. Review of Data Modeling with a Single Subspace (3 hours): Principal Component Analysis (PCA) and its extensions.
3. Review of Iterative Methods for Multiple-Subspace Segmentation (4.5 hours): mathematical statistics, Maximum likelihood estimate, Expectation Maximization (EM) algorithm, minimax estimate and K-means algorithm, iterative subspace-segmentation algorithms.
4. Algebraic Methods for Multiple-Subspace Segmentation (7.5 hours): Special cases, Generalized Principal Component Analysis (GPCA), recursive GPCA, algebraic properties of subspace arrangements, Hilbert function and series for subspace arrangements.
5. Statistical Analysis and Robustness Issues (3 hours): Discriminative analysis, model selection criteria, and outliers in the context of subspace methods.
6. Extension to Arrangements of Nonlinear Surfaces (1.5 hours): Arrangements of quadratic surfaces, other nonlinear manifolds.
7. Midterm Project Proposal (1.5 hours)
8. Image Representation, Segmentation & Classification (3 hours)
9. Motion Segmentation in Computer Vision (6 hours): 2D motion segmentation from image partial derivatives, 3D motion segmentation from feature correspondence.
10. Dynamical Texture and Video Segmentation (3 hours)
11. Hybrid System Identification (3 hours): Switched linear systems, input-output models and statespace models.
12. Applications in System Biology and Bioengineering(3 hours)
13. Final Project Presentation (3 hours)

Topics:

Tentative Course Syllabus and Schedule:

1. Introduction (1.5 hours): data modeling, hybrid models, and model estimation.
2. Review of Data Modeling with a Single Subspace (3 hours): Principal Component Analysis (PCA) and its extensions.
3. Review of Iterative Methods for Multiple-Subspace Segmentation (4.5 hours): mathematical statistics, Maximum likelihood estimate, Expectation Maximization (EM) algorithm, minimax estimate and K-means algorithm, iterative subspace-segmentation algorithms.
4. Algebraic Methods for Multiple-Subspace Segmentation (7.5 hours): Special cases, Generalized Principal Component Analysis (GPCA), recursive GPCA, algebraic properties of subspace arrangements, Hilbert function and series for subspace arrangements.
5. Statistical Analysis and Robustness Issues (3 hours): Discriminative analysis, model selection criteria, and outliers in the context of subspace methods.
6. Extension to Arrangements of Nonlinear Surfaces (1.5 hours): Arrangements of quadratic surfaces, other nonlinear manifolds.
7. Midterm Project Proposal (1.5 hours)
8. Image Representation, Segmentation & Classification (3 hours)
9. Motion Segmentation in Computer Vision (6 hours): 2D motion segmentation from image partial derivatives, 3D motion segmentation from feature correspondence.
10. Dynamical Texture and Video Segmentation (3 hours)
11. Hybrid System Identification (3 hours): Switched linear systems, input-output models and statespace models.
12. Applications in System Biology and Bioengineering(3 hours)
13. Final Project Presentation (3 hours)

1. Graduate students in ECE/CS in the areas of computer vision, image processing, and pattern recognition interested in data modeling, clustering, and segmentation.
2. Graduate students in ECE or ME in the areas of control interested in estimation theory and (hybrid) system identification.
3. Graduate students in Mathematics interested in applications of commutative algebra or students in statistics interested in estimation of mixtures of models.

Grading policy: Weekly homework (60%) and Final Project (40%). The final project can be done in a group of 2 or 3 students. The project can be theoretical, experimental or a mixture of both. It consists of a midterm proposal, a final presentation (in class) and a web-based report.

Additional references will be provided to the students throughout the semester.