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Network Topology Inference from Spectral Templates

Friday, September 29, 2017, 11:00 AM
Woolf Hall Room 221

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Gonzalo Mateos
Assistant Professor, Electrical and Computer Engineering Department, University of Rochester

Abstract:
Advancing a holistic theory of networks necessitates fundamental breakthroughs in modeling, identification, and controllability of distributed network processes often conceptualized as signals defined on the vertices of a graph. Under the assumption that the signal properties are related to the topology of the graph where they are supported, the goal of graph signal processing (GSP) is to develop algorithms that fruitfully leverage this relational structure, and can make inferences about these relationships when they are only partially observed.

After presenting the fundamentals of GSP, we leverage these ideas to address the problem of network topology inference from graph signal observations. It is assumed that the unknown graph encodes direct relationships between signal elements, which we aim to recover from observable indirect relationships generated by a diffusion process on the graph. The innovative approach is to consider the Graph Fourier Transform of the acquired signals associated with an arbitrary graph and, among all the feasible networks, search for one that endows the resulting transforms with target spectral properties and the sought graph with appealing physical characteristics such as sparsity. Leveraging results from GSP and sparse recovery, efficient topology inference algorithms with theoretical guarantees are put forth. Numerical tests corroborate the effectiveness of the proposed algorithms when used to recover social and structural brain networks from synthetically-generated signals, as well as to identify the structural properties of proteins.

Gonzalo MateosBio: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. Dr. Mateos received the Best Student Paper Award at the 2012 IEEE Workshop on Signal Processing Advances in Wireless Communications (SPAWC) and the 2016 IEEE Statistical Signal Processing (SSP) Workshop as senior co-author, and was also a finalist of the Student Paper Contest at the 2011 IEEE DSP/SPE Workshop. 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.

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