CIS 515, Fall 2016

Brief description:

The goal of this course is to provide firm foundations in linear algebra and optimization techniques that will enable students to analyze and solve problems arising in various areas of computer science, especially computer vision, robotics, machine learning, computer graphics, embedded systems, and market engineering and systems. The students will acquire a firm theoretical knowledge of these concepts and tools. They will also learn how to use these tools in practice by tackling various judiciously chosen projects (from computer vision, etc.). This course will serve as a basis to more advanced courses in computer vision, convex optimization, machine learning, robotics, computer graphics, embedded systems, and market engineering and systems.

Topics covered include: Fundamentals of linear algebra: Basic concepts; solving linear systems; eigenvalues and eigenvectors; introduction to the finite elements method; singular value decomposition, pseudo-inverses, PCA. Basics of quadratic optimization; the Rayleigh-Ritz ratio. Methods for computing eigenvalues (power iteration, QR method, etc.). Elementary spectral graph theory. Applications to graph clustering using normalized cuts

If time permits, I will discuss Methods using Krylov subspaces (Arnoldi, Lanczos); Hadamard matrices and applications; Basics of optimization: review of analysis (derivatives, gradient, Hessian, Lagrange multipliers).

Syllabus:

(*) means: if time permits.
  1. Linear Algebra;
  2. (*) Basics of Optimization;
  3. Elementary spectral graph theory
    Applications to graph clustering using normalized cuts

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Jean Gallier