MAT 280 Harmonic Analysis on Graphs & Networks Syllabus Page (Fall 2019)
Synopsis:
Graphs and networks have been successfully used in a variety of
fields (e.g., machine learning, data mining, image analysis, sensor networks,
social sciences, etc.) that are confronted with the analysis and modeling of
high-dimensional datasets. Harmonic analysis tools originally developed for
Euclidean spaces and regular lattices are now being transferred to the general
settings of graphs and networks in order to analyze geometric and topological
structures, and data and signals measured on them. In this course, we shall
discuss a variety of important theories and interesting applications employing
harmonic analysis of and on graphs and networks.
Topics include: graph Laplacians, their eigenvalues and eigenvectors for
structural/morphological analysis; wavelets on graphs; random walks and
diffusion on graphs; spectral clustering; community detection; etc.
Prerequisite:
MAT 129, 167, 271, or consent of the instructor.
Topics:
I plan to cover the following (subject to change):
Overture: motivations, scope and structure of the course
Prelude to Analysis on Graphs: Laplacian Eigenfunctions on General
Shape Domains in R^{d}
Basics of Graph Theory: Graph Laplacians
How to Construct Graphs from Given Datasets?
Distances and Weights of Graphs
Spectral Clustering of Massive Data
Review on PCA & MDS
Laplacian Eigenmaps & Diffusion Maps
Graph Partitioning
Community Detection
Fast Algorithms on Graphs
Wavelets on Graphs
Graph Embeddings
Textbooks/References:
No textbook is required. Many journal papers will be discussed in the class and
their links will be posted in the comments, handouts, and reference page.
Yet, the following books and papers may be useful as general introductory references in this field.
For general introduction to graphs and networks and significant applications:
D. Cvetković, P. Rowlinson, and S. Simić: An Introduction to the Theory of Graph Spectra, Vol. 75, London Mathematical Society Student Texts, Cambridge Univ. Press, 2010.
I will maintain the Web pages for this course (one of which you are
looking at now). In particular, please read the comments, handouts, and reference page often.
After each class, I will put relevant comments and references as well as
most of my handouts in class in this page that should
serve as a guide to further understanding of the class material.
Grading Scheme:
100% Final Report (due 5pm, Thursday, Dec. 12, 2019)
Final Report:
Your grade will be determined by your final report.
My suggestion for writing your report is the following:
Describe how some of the methods you learned in this course will be
used in your research; or
Find out a practical application dealing with data analysis on a graph
or network yourself (not copying from papers/books) using the methods you
learned in this course; describe how to use them; describe the importance of
that application; what impact would you expect if you are successful?
I will be available for further individual discussions for you to determine the contents of your final report.