Advanced Topics in Machine Learning: Modeling and Segmentation of Multivariate Mixed Data
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)
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)
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)
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
- 03/05 Midterm 1
- 03/08 Generalized Principal Component Analysis (GPCA)
- 03/10 Local Subspace Affinity
and Spectral Curvature Clustering
Subspace Clustering: Robust Methods based on Sparse Representation (Chapter 5)
- 03/12 Sparse Subspace Clustering (SSC)
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)
- 04/16 Image Representation and Segmentation (Chapter 6)
Manifold Clustering (Chapter 12)
- 04/23-30 Locally Linear Manifold Clustering (LLMC)
- 05/07 Midterm 2
(30%): Homework problems will include both analytical exercises as well
as programming assignments in MATLAB.
(70%): There will be two exams on
February 26th March 5th and
April 30th May 7th.
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.