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Mahya Ghandehari (University of Delaware)

Time: 10:00 am on Thursday, October 6th, 2022

Signal processing on large graphs; a noncommutative approach to the graphon Fourier transform

Signal analysis on graphs relies heavily on the graph Fourier transform, which is defined as the expansion of a signal with respect to an eigenbasis of the associated shift operator. Large graphs of similar structures may be represented by a graphon. Theoretically, graphons are limit objects of converging sequences of graphs. In this talk, we introduce the graphon Fourier transform as a higher dimensional transform, and show how it provides a common scheme for signal analysis of graphs that are similar in structure to a graphon. In the case of a Cayley graphon, we show that Fourier analysis of the underlying group enables the construction of a suitable eigen-decomposition for the graphon, which can be used as a common framework for signal processing on graphs sampled from the graphon.

This talk is based on joint work with Jeannette Janssen and Nauzer Kalyaniwalla.