The University of Texas at Austin
Computer Science Department

Computer Science 395T
Spectral Graph Theory for Visual Computing

Spring 2022

General Information:

Time: Tuesdays and Thursdays 3:30PM-5:00PM
Place: JES A303A
Instructor: Qixing Huang
Office hour: Fridays 3pm-5pm at GDC 5422.

The course covers the mathematics of applications of spectral graph theory, broaderly defined. Grading is based on homeworks (60%) and the final project (40%).

A partial list of applications to be covered:

  • Spectral Graph Theory.
  • Graph Neural Networks.
  • Spectral Clustering.
  • Spectral Map Synchronization.
  • Spectral Shape Matching.
  • Spectral Vector-Field Design.
  • Spectral Parameterization.

    • Prereqs: The course assumes a good knowledge of linear algebra and probability. Please talk to me or email me if you are unsure if the course is a good match for your background.

    Schedule:

    Date Topics Reading Notes
    Jaunary 18th Introduction
    January 20th Adjacency Matrix, Laplacian Matrix, and Spectral Graph Drawing
    January 25th Normalized Adjacency Matrix and Laplacian Matrix Homework 1 out.
    January 27th Fast Power Iterations
    Feburary 1st Cheeger's Inequality (Discrete)
    Feburary 3th Cheeger's Inequality (Continuous)
    Feburary 8th Random walk, Diffusion distance and Heat kernel Homework 1 due. Homework 2 out.
    Feburary 10th Spectral Theory of Random Graphs I
    Feburary 15th Spectral Theory of Random Graphs II.
    Feburary 17th Expanders, interlacing polynomials, and Ramanujan Graphs I
    Feburary 22th Expanders, interlacing polynomials, and Ramanujan Graphs II Homework 2 due. Homework 3 out.
    Feburary 24th Spectral Sparsification I
    March 1st Spectral Sparsification II
    March 3rd Spectral Theory of Directed Graphs I Perron-Frobenius Theorem Final project proposal Due.
    March 8th Spectral Theory of Directed Graphs II Homework 3 due. Homework 4 out.
    March 10th Laplacian Operators of Triangular Meshes (Guest Lecture)
    March 22th Spectral Vector-Field Design I
    March 24th Spectral Vector-Field Design II
    March 29th Spectral Surface Parameterization I
    March 31th Spectral Surface Parameterization II Homework 4 due. Homework 5 out.
    April 5th Normalized Cut and Spectral Shape Segmentation I
    April 7th Normalized Cut and Spectral Shape Segmentation II
    April 12th Spectral Graph Matching and Spectral Shape Matching
    April 14th Functional Maps
    April 19th Functional Map Networks Homework 5 due. Homework 6 out.
    April 21th Spectral Map Synchronization I
    April 26th Spectral Map Synchronization II
    April 28th Spectral Graph Neural Networks and Geometric Deep Learning I
    May 3rd Spectral Graph Neural Networks and Geometric Deep Learning II Homework 6 due.
    May 5th Course Wrapup Final project report due.

    Final Project:

    The final project is done in groups of 2-3 students. Each project should have an initial proposal, a final report, and a final poster presentation. The project proposal shall describe four key components of a research project (namely Motivation, Technical Merit, Broader Impact, and Project Plan). The final report should be written as an academic research article. A more detailed instruction will be given later.