Codes and Expansions (CodEx) Seminar

Kathryn Beck (Tufts)
Frames for signal processing on Cayley graphs

A major focus of Graph Signal Processing (GSP) is to develop methods for processing data on a graph domain that take into account the underlying structure of the graph. We focus on developing techniques for Cayley graphs, which are algebraically-defined and highly symmetric in nature, making them a rich class of graphs for applications. For instance, the Cayley graph of the symmetric group is a natural model for ranked data analysis. The main tool used in GSP, the graph Fourier transform, relies on an appropriate choice of eigenbasis for the associated graph matrix. In order to better capture the symmetries in a Cayley graph, we present a spectral decomposition of the adjacency matrix based on the representation theory of the underlying group. We utilize this eigen-decomposition to construct frames that are suitable for signal processing on Cayley graphs. Specifically, we construct frames for which every frame atom belongs to the coefficient space of only one irreducible representation of the underlying group.