Abstract: In this talk, I will present two recent results in random matrix theory. The first is on a condition for rank loss of an ensemble of structured random matrices. Each row in each of the considered matrices is scaled by a random number. This problem has an application in designing linear schemes for wireless interference networks with no channel state information at the transmitters. In this setting, each matrix represents a beamforming matrix and the random row scaling is due to the unknown channel coefficients. We use the obtained result to present conditions for the feasibility of alignment in these networks and characterize the symmetric degrees of freedom for arbitrary network topologies. In the second part of the talk, I will present a result on the spectral properties of the Laplacian matrix corresponding to a distance-based similarity graph consisting of points sampled from a Euclidean space. We use this result to analyze the recently introduced method of Band-limited Interpolation of Graph-signals (BIG) for semi-supervised learning. By analyzing the convergence of the bandwidth of the graph signal, we show that as the number of samples increases, the decision boundary recovered through the BIG approach is closely related to the low density separation problem. By analyzing the distribution of the graph eigenvalues, we derive the required number of labels by the BIG approach, and compare it with spectral clustering methods to highlight the value of labelled samples when clustering is not a good solution.
Bio: Aly El Gamal received the B.S. degree in Computer Engineering from Cairo University, Cairo, in 2007, the M.S. degree in Electrical Engineering from Nile University, Cairo, in 2009, the M.S. degree in Mathematics and the Ph.D. degree in Electrical and Computer Engineering from the University of Illinois at Urbana-Champaign in 2013 and 2014, respectively. He worked as an intern at the Office of the Chief Scientist of Qualcomm Inc. in 2012. He joined the research group of Prof. Salman Avestimehr at the Ming Hsieh Department of Electrical Engineering of the University of Southern California as a Post-doctoral Research Associate in 2014. His research interests include information, learning and graph theories.