Topics in Spectral Graph Methods

Instructor: Michael Mahoney
  • Email: mmahoney ATSYMBOL
  • Office hours: By appointment.
  • Location: Office is in the AMPLab, fourth floor of Soda Hall.
  • Teaching Assistant: Di Wang
  • Email: wangd ATSYMBOL
  • Office hours: By appointment.
  • Class time and Location:
  • Tue-Thu 9:30-11:00AM, in 320 Soda (First meeting is Thu Jan 22, 2015.)

  • Notes:
  • (5/31) My scribed version of the class lectures are available below. Feedback welcome!
  • (1/29) I'll be posting notes on Piazza, not here.
  • (1/15) All students, including auditors, are requested to register for the class. Auditors should register S/U; an S grade will be awarded for class participation and satisfactory scribe notes.

    Course description: Spectral graph methods use eigenvalues and eigenvectors of matrices associated with a graph, e.g., adjacency matrices or Laplacian matrices, in order to understand the properties of the graph. They have a rich algorithmic and statistical theory, including connections with random walks, inference, and expanders; and they are useful in applications ranging from parallel computing to computer vision to social network analysis. The course will cover advanced topics in the underlying algorithmic and statistical theory, with a bias toward theoretical aspects of methods that are practically useful in modern machine learning and data analysis. Topics to include a subset of:
  • underlying theory, including Cheeger's inequality and its connections with partitioning, isoperimetry, and expansion;
  • algorithmic and statistical consequences, including explicit and implicit regularization and connections with other graph partitioning methods;
  • applications to semi-supervised and graph-based machine learning;
  • applications to clustering and related community detection methods in statistical network analysis;
  • local and locally-biased spectral methods and personalized spectral ranking methods;
  • applications to graph sparsification and fast solving linear systems; etc.
    Appropriate for advanced graduate students in statistics, computer science, and mathematics, as well as computationally-inclined students from application domains.
  • Prerequisites: General mathematical sophistication; and a solid understanding of Algorithms, Linear Algebra, and Probability Theory, at the advanced undergraduate or beginning graduate level, or equivalent.

    Course requirements: Most likely, three homeworks (ca. 15-20% each), scribe two lectures (ca. 10%), and a major project (ca. 40%).

    Primary references: We will be reading reviews and primary sources. Here are several things to get started. Additional articles for particular topics and particular classes are listed below. Individual Lectures: Here are readings for each class as well as lecture notes.