In the era of data deluge, the development of methods for discovering structure in high-dimensional data is becoming increasingly important. This course will cover state-of-the-art methods from algebraic geometry, sparse and low-rank representations, and statistical learning for modeling and clustering high-dimensional data. The first part of the course will cover methods for modeling data with a single low-dimensional subspace, such as PCA, Robust PCA, Kernel PCA, and manifold learning techniques. The second part of the course will cover methods for modeling data with multiple subspaces, such as algebraic, statistical, sparse and low-rank subspace clustering techniques. The third part of the course will cover applications of these methods in image processing, computer vision, and biomedical imaging.

1. Background
• Introduction (Chapter 1)
• Basic Facts from Linear Algebra
2. Modeling Data with a Single Subspace (Part I)
• Principal Component Analysis (Chapter 2)
• Statistical View
• Geometric View
• Model Selection
• Applications in Face Recognition
• Robust Principal Component Analysis (Chapter 3)
• PCA with Missing Entries
• PCA with Corrupted Entries
• PCA with Outliers
• Applications in Face Recognition
• Nonlinear and Nonparametric Extensions (Chapter 4)
• Laplacian Eigenmaps
• Spectral Clustering
• Applications in Face Recognition
3. Modeling Data with Multiple Subspaces (Part II)
• Sparse and Low-Rank Methods (Chapter 8)
• Low-Rank Subspace Clustering
• Sparse Subspace Clustering
• Applications in Face Clustering

R. Vidal, Y. Ma, and S. Sastry. "Generalized Principal Component Analysis." Springer-Verlag New York, 2016.

06/10/17: Salle C315: Syllabus + Introduction + Basics of Linear Algebra + Statistical View of PCA

13/10/17: Amphi Fonteneau ENS Cachan: Geometric View of PCA + Rank Minimization View of PCA + Model Selection for PCA

20/10/17: Amphi Fonteneau ENS Cachan: PCA with Missing Entries via Convex Optimization

10/11/17: Salle C315: PCA with Corrupted Entries via Convex Optimization +PCA with Outliers via Convex Optimization (L21)

17/11/17: Salle des Conferences Pavillon des Jardins ENS Cachan: Laplacian Eigenmaps (LE)

24/11/17: Salle C315: Spectral Clustering + K-subspaces

01/12/17: Salle Condorcet: Sparse Subspace Clustering Challenge

• Slides on Subspace Clustering

• Example Exam1 from JHU

• Solutions Example Exam1 from JHU

• Example Exam2 from JHU

• Solutions Example Exam2 from JHU

1. Exams (40%):
• Exam: 08/12/2017, 09h00-12h00, Amphi Marie Curie.
2. Projects (60%):
• Project 1: Due 24/11/2017 @ 23h59: Face Completion and Movie Recommendation Challenge
• Project 2: Due 22/12/2017 @ 23h59: Face Clustering and Motion Segmentation Challenge

• Late policy:
• Homeworks and projects are due on the specified dates.
• No late homeworks or projects will be accepted.
• Honor policy:

  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.

• Homeworks and exams are strictly individual
• Projects can be done in teams of three students