On the interplay between topology and signals supported on graphs

Michael Rabbat

doi:10.1117/12.2024716

26 September 2013 On the interplay between topology and signals supported on graphs

Michael Rabbat

Author Affiliations +

Proceedings Volume 8858, Wavelets and Sparsity XV; 88581K (2013) https://doi.org/10.1117/12.2024716
Event: SPIE Optical Engineering + Applications, 2013, San Diego, California, United States

Abstract

Recent work has begun to develop a theory for the representation, processing, and approximation of signals supported on graphs. For signals supported on graphs, the eigenvectors of the graph Laplacian play a role analogous to the Fourier transform. We discuss recent results which develop uncertainty principles for signals supported on graphs, focusing on the role of the graph topology. We then conduct a series of experiments to explore how characteristics of the graph topology influence the extent to which a signal can have low graph spread and spectral spread, as quantified through the uncertainty curve. Through experiments with small-world random graphs, we find a correlation between the clustering coefficient of the graph, the second largest eigenvalue, and the shape of the uncertainty curve.

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Michael Rabbat "On the interplay between topology and signals supported on graphs", Proc. SPIE 8858, Wavelets and Sparsity XV, 88581K (26 September 2013); https://doi.org/10.1117/12.2024716

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