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 (online) topology inference algorithms with theoretical guarantees are put forth. Numerical tests corroborate de effectiveness of the proposed algorithms when used to recover social and structural brain networks from simulated signals, as well as to identify the structural properties of proteins.
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 2012, all in electrical engineering. He joined the University of Rochester, Rochester, NY, in 2014, where he is currently an Associate Professor with the Department of Electrical and Computer Engineering, as well as an Asaro Biggar Family Fellow in 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 complex data, network science, decentralized optimization, and graph signal processing, with applications in brain connectivity, 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 and 2020 IEEE Signal Processing Society Young Author Best Paper Awards (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.