Advanced Topics in Machine Learning: Modeling and Segmentation of Multivariate Mixed Data
(BME 580.692, CS 600.692) Instructor: Rene Vidal web e-mail

Class Hours: MWF 12:00-1:15 p.m., Shaffer 100

Office Hours: M 2-3 p.m. 302B Clark Hall

Course Description
This class will cover machine learning techniques for modeling and segmentation of multivariate mixed data. Topics will include subspace learning (PCA, Probabilistic PCA, Robust PCA, Sparse representation, Rank minimization), manifold learning (Kernel PCA, LLE, Isomap), subspace clustering (K-subspaces, Mixtures of PPCAs, Generalized PCA, Sparse subspace clustering), and manifold clustering (LLMC). These methods will be applied to several problems in computer vision, biomedical imaging, computational neuroscience, and computational biology.

Introduction (Chapter 1)

  • 01/25 Course overview

Subspace Learning: Linear Dimensionality Reduction (Chapter 2)

  • 01/25-29 Principal Component Analysis (PCA)
  • 01/29 Application of PCA (slides)
  • 02/01-03 Factor Analysis (FA) and Probabilistic PCA (PPCA)
  • 02/05 Robust PCA: missing data (Power Factorization)
  • 02/08-12: Shoveling
  • 02/15 Robust PCA: outliers
  • 02/17 Robust PCA via sparse representation and rank minimization: (RPCA) (slides)

Manifold Learning: Nonlinear Dimensionality Reduction (Chapter 2)

  • 02/19 Nonlinear and Kernel PCA (KPCA)
  • 02/22 Multidimensional Scaling (MDS), Isometric Embedding (Isomap) and Locally Linear Embedding (LLE) (slides)

Subspace Clustering: Iterative Methods (Chapter 4)

  • 02/26 K-means and K-Subspaces
  • 03/01 K-Subspaces and RANSAC

Subspace Clustering: Algebraic Methods (Chapter 3)

  • 03/03 Line, plane, and hyperplane clustering (slides)
  • 03/05 Midterm 1
  • 03/08 Generalized Principal Component Analysis (GPCA)
  • 03/10 Local Subspace Affinity (LSA) and Spectral Curvature Clustering (SCC)

Subspace Clustering: Robust Methods based on Sparse Representation (Chapter 5)

  • 03/12 Sparse Subspace Clustering (SSC) (slides)

Applications in Computer Vision

  • 03/22-24 Motion Segmentation from Multiple Affine Views (Chapter 8)
  • 03/26-04/02 Motion Segmentation from Two Perspective Views (Chapter 8)
  • 04/09 Spatial and Temporal Video Segmentation (Chapter 9) (slides)
  • 04/16 Image Representation and Segmentation (Chapter 6) (slides)

Manifold Clustering (Chapter 12)

  • 04/23-30 Locally Linear Manifold Clustering (LLMC) (slides)
  • 05/07 Midterm 2




Grading policy

  • Homework (30%): Homework problems will include both analytical exercises as well as programming assignments in MATLAB.
  • Exams (70%): There will be two exams on February 26th March 5th and April 30th May 7th.


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.



  • Class will meet MWF till March 12th and F thereafter.





Please submit your homework in one single ZIP file to the Homework Submission Website.