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Applied & Computational Harmonic Analysis on Graphs and Networks

Faculty Research Seminar

Speaker: Naoki Saito, UC Davis
Location: Zoom Zoom (see below)
Start time: Tue, Jan 25 2022, 12:10PM

Applied & Computational Harmonic Analysis (ACHA) deals with:

1) efficient and meaningful representations of data objects (e.g., signals, images, and more generally data measured on graphs & networks) and operators (e.g., Laplacians, singular integral operators, matrices, etc.);

2) fast computational algorithms to operate on them; and

3) their wide-range applications in data science and other fields.

After introducing a list of my current research projects and plans on ACHA, my talk will focus on one of them: multiscale graph basis dictionaries. These are the generalization of the classical wavelet packet and local cosine basis dictionaries for the graph setting. After briefly reviewing these classical basis dictionaries, I plan to describe the difficulties of lifting those to the graph setting, and how we could overcome them. There are two keys for their successful constructions: 1) hierarchical bipartition tree of a given graph; and 2) the concept of the "dual" domain of a graph. As concrete examples, I will discuss

a) the Hierarchical Graph Laplacian Eigen Transform (HGLET) and

b) the Natural Graph Wavelet Packets (NGWPs).

The HGLET is the simplest of all those multiscale basis dictionaries, and corresponds to the classical hierarchical block discrete cosine transform. The NGWPs utilize the "dual" domain of a given graph based on the geometry of graph Laplacian eigenvectors, and the classical Shannon wavelet packets. I will conclude my talk with my perspective on these tools and some open problems on which I want my future students to attack, and the information on our software package of these dictionaries, which is completely written in the Julia programming language.



This meeting will be on Zoom: https://ucdavis.zoom.us/j/96864394419?pwd=REppQWJK... Meeting ID: 968 6439 4419 Passcode: 631425