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

Displaying course information from Spring 2006.

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 Prerequisites
Course Directors Yi Ma
Detailed Description and Outline


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.

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