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

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.

Citation Download Citation

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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