MAT 280 Harmonic Analysis on Graphs & Networks Syllabus Page (Spring 2012)
Course: MAT 280 Harmonic Analysis on Graphs & Networks
Credit Units: 3
Class: MW 5:10pm-6:30pm, 2112 Math. Sci. Bldg.
Instructor: Naoki Saito
Office: 2142 MSB
Email: saito@math dot ucdavis dot edu
Office Hours: By appointment
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; non-local means denoising algorithms,
MAT 129, 167, 271, or consent of the instructor.
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 Rd
- Basics of Graph Theory: Graph Laplacians
- How to Contruct Graphs from Given Datasets?
- Distances and Weights of Graphs
- Spectral Clustering of Massive Data
- Review on PCA & MDS
- Laplacian Eigenmaps & Diffusion Maps
- Graph Partitioning
- Fast Algorithms on Graphs
- Wavelets on Graphs
- Spectral Graph Wavelet Transform (Hammond et al)
- Haar-like Transform on Datasets (Coifman-Gavish-Nadler)
- Interpolating Wavelets on Graphs (Rustamov)
- Graph Embeddings
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 may be useful as general introductory references
in this field.
Class Web Page:
- For Laplacians on graphs:
- 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.
- F. R. K. Chung: Spectral Graph Theory, AMS, 1997.
- A. E. Brouwer and W. H. Haemers: Spectra of Graphs,
- For Laplacians on Euclidean domains:
- W. A. Strauss: Partial Differential Equations: An Introduction,
2nd Ed., Chap. 10 & 11, John Wiley & Sons, 2008.
- R. Courant and D. Hilbert: Methods of Mathematical Physics, Vol.I, Chap. V, VI, & VII, Wiley-Interscience, 1953.
- For Laplacians on Riemannian manifolds:
- S. Rosenberg: The Laplacian on a Riemannian Manifold, Vol. 31, London Mathematical Society Student Texts, Cambridge Univ. Press, 1997.
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.
Class Mailing List:
The class mailing list was created.
Important announcement will be communicated through this mailing list.
You can also submit your public comments, suggestions, and questions on HW,
and/or some useful information related to the class to this mailing
list. Once you send your email to this list, however, everyone will receive it.
So, please use this wisely and politely. Its name is: firstname.lastname@example.org.
- 100% Attendance
- If you are interested in conducting research and writing a short
report using the ideas and techniques covered in this course, then I am
happy to give you additional credit units as MAT 299 (Individual Study).
Please email me if you
have any comments or questions!
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