ECE Departmental Seminar
Digraph Signal Processing: Orthonormal transforms and inverse problems on directed networks
Prof. Gonzalo Mateos
University of Rochester
Tuesday, 2/18/20, 11:00am
Light Engineering 250
Abstract: We discuss the problem of constructing a graph Fourier transform (GFT) for directed graphs (digraphs), which decomposes graph signals into different modes of variation with respect to the underlying network. Accordingly, to capture low, medium, and high frequencies we seek a digraph (D)GFT such that the orthonormal frequency components are as spread as possible in the graph spectral domain. To that end, we advocate a two-step design whereby we find the maximum directed variation (i.e., a novel notion of frequency on a digraph) a candidate basis vector can attain; and minimize a smooth spectral dispersion function over the achievable frequency range to obtain the desired spread DGFT basis. Both steps involve non-convex, orthonormality-constrained optimization problems, which are tackled via a feasible optimization method on the Stiefel manifold that provably converges to a stationary solution. We also outline a data-adaptive variant whereby a sparsifying orthonormal transform is learnt to also yield parsimonious representations of bandlimited signals. If time allows, we will also present some recent results on solving inverse problems arising with source localization on networks, as well as with topology inference from nodal observations generated by linear diffusion dynamics on the sought digraph.
Bio: Gonzalo Mateos earned the B.Sc. degree from Universidad de la Republica, Uruguay, in 2005, and the M.Sc. and Ph.D. degrees from the University of Minnesota, Twin Cities, in 2009 and 2011, all in electrical engineering. He joined the University of Rochester, Rochester, NY, in 2014, where he is currently an Assistant Professor with the Department of Electrical and Computer Engineering, as well as a member of the Goergen Institute for Data Science. During the 2013 academic year, he was a visiting scholar with the Computer Science Department at Carnegie Mellon University. From 2004 to 2006, he worked as a Systems Engineer at Asea Brown Boveri (ABB), Uruguay. His research interests lie in the areas of statistical learning from Big Data, network science, decentralized optimization, and graph signal processing, with applications in dynamic network health monitoring, social, power grid, and Big Data analytics. He currently serves as Senior Area Editor for the IEEE Transactions on Signal Processing, is an Associate Editor for the IEEE Transactions on Signal and Information Processing over Networks, and is a member of the IEEE SigPort Editorial Board. Dr. Mateos received the NSF CAREER Award in 2018, the 2017 IEEE Signal Processing Society Young Author Best Paper Award (as senior co-author), the 2019 IEEE Signal Processing Society Outstanding Editorial Board Award, and Best Paper Awards at SPAWC 2012, SSP 2016, as well as ICASSP 2018 and 2019. His doctoral work has been recognized with the 2013 University of Minnesota's Best Dissertation Award (Honorable Mention) across all Physical Sciences and Engineering areas.