Speaker: Antonio G. Marques

Time and Date: 15:30-17:00 pm, April 12, 2019

Place: Room B415 of Computing Center Building, Handan Campus, Fudan University

Abstract:

The problem addressed in this talk is that of learning an unknown network from nodal observations, which are modeled as graph signals generated by linear diffusion dynamics that depend on the topology of the sought graph. We assume that the observed diffused signals can be modeled as the output of a linear graph filter, applied to a set of independent input graph signals with arbitrarily-correlated components. In this context, we first rely on observations of the output signals along with prior statistical information on the inputs to identify the diffusion filter. Critical to this end is the formulation of the problem as the solution of a system of quadratic equations. Then, we leverage that linear graph filters are polynomials of the so-called graph-shift operator (a matrix representation of the network topology) to recover the graph via a convex optimization problem. We address three cases of increasing complexity: undirected networks with white inputs, undirected networks with colored inputs, and directed networks with arbitrary inputs. The resultant problems can be recast as sparse recovery problem with either Boolean constraints (for the undirected case) or manifold constraints (for the directed case). Numerical tests corroborating the effectiveness of the proposed algorithms in recovering synthetic and real-world directed graphs are provided.

Biography:

Antonio G. Marques received the telecommunications engineering degree and the Doctorate degree, both with highest honors, from the Carlos III University of Madrid, Spain, in 2002 and 2007, respectively. In 2007, he became a faculty of the Department of Signal Theory and Communications, King Juan Carlos University, Madrid, Spain, where he currently develops his research and teaching activities as an Associate Professor and serves as Deputy of the President for Strategic Policies. From 2005 to 2007 he was a visiting Ph.D. student at the University of Minnesota, Minneapolis, and, from 2008 to 2015, he held different visiting research and faculty positions there. In 2015, 2016 and 2017 he was a visitor scholar at the University of Pennsylvania, Philadelphia. His current research focuses on nonlinear and stochastic optimization of wireless and power networks, signal processing for graphs, and data science for networks, areas where he has written more than 100 journal and conference papers. Dr. Marques has served the IEEE in a number of posts (currently, he is an Associate Editor of the Signal Process. Letters, a member of the IEEE Signal Process. Theory and Methods Tech. Comm., a member of the IEEE Signal Process. Big Data Special Interest Group, the Technical Co-Chair of the 2019 IEEE CAMSAP Workshop, and the General Co-chair of the 2019 IEEE Data Science Workshop). His work has been awarded in several venues, with recent ones including IEEE SSP 2016, IEEE SAM 2016 and Asilomar 2015.