ECE 586 YM - Topics in Decision and Control: Estimation and Segmentation of Hybrid Models

Official Description

Lectures and discussions related to advanced topics and new areas of interest in decision and control theory: hybrid, sampled-data, and fault tolerant systems; control over networks; vision-based control; system estimation and identification; dynamic games. Course Information: May be repeated up to 12 hours within a term, and up to 20 hours total for the course. Credit towards a degree from multiple offerings of this course is not given if those offerings have significant overlap, as determined by the ECE department. Prerequisite: As specified each term. It is expected that each offering will have a 500-level course as prerequisite or co-requisite.

Subject Area

Control Systems

Course Director

Description

In many scientific and engineering problems, the data of interest can be viewed as drawn from a mixture of models instead of a single one. Such data are often referred to in different contexts as ?mixed,? or ?heterogenous,? or ?multi-modal,? or ?hybrid.? For instance, a natural image normally consists of different textural regions, a traffic surveillance video consists of multiple independently moving cars, and an ultrasonic video of a beating heart consists of multiple phases.

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.

Notes

Target Audience: The course targets at the following students:
  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.

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)

Detailed Description and Outline

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)
Target Audience: The course targets at the following students:
  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.

Texts

Generalized Principal Component Analysis: Estimation and Segmentation of Hybrid Models, Rene Vidal, Yi Ma, and S. Sastry, book draft will be made available as lecture notes.

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

Last updated

2/13/2013