Graph Signal Processing: Foundational Advances for Learning from Network Data

Abstract: Coping with the challenges found at the intersection of Network Science and Big Data necessitates fundamental breakthroughs in modeling, identification, and controllability of distributed network processes – often conceptualized as signals defined on graphs. For instance, graph-supported signals can model vehicle trajectories over road networks; economic activity observed over a network of production flows between industrial sectors; infectious states of individuals susceptible to an epidemic disease spreading on a social network; gene expression levels defined on top of gene regulatory networks; brain activity signals supported on brain functional connectivity networks; and media cascades that diffuse on online social networks, to name a few. There is an evident mismatch between our scientific understanding of signals defined over regular domains (time or space) and graph-valued signals. Knowledge about time series was developed over the course of decades and boosted by real needs in areas such as communications, speech, or control. On the contrary, the prevalence of network-related information processing problems and the access to quality network data are recent events. The time has come for pushing the frontiers of knowledge in how we process information in network settings, and make progress towards understanding the inherent complexities of strongly coupled systems such as the brain.

Under the natural assumption that the signal properties are related to the topology of the graph where they are supported, the emerging field of graph signal processing (GSP) aims at developing data science 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 and motivating the study of graph signals, we leverage these ideas to offer a fresh look at the problem of network topology inference from graph signal observations, also know as graph learning. Focus in this talk is placed on building a judicious network model of the data facilitating efficient signal representation, visualization, prediction, (nonlinear) dimensionality reduction, and (spectral) clustering. Throughout, we illustrate the developed methods and results on various application domains including computational biology, the economy, network neuroscience, and online social media.

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 Associate Editor for the IEEE Transactions on Signal Processing, the EURASIP Journal on Advances in Signal Processing, 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), and the Best Paper Awards at ICASSP 2018, SSP Workshop 2016, and SPAWC 2012. 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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