Slides for - Network Topology Inference from Spectral Templates

This webinar will address the problem of identifying the structure of an undirected graph from the observation of signals defined on its nodes. Fundamentally, 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. Our approach leverages concepts from convex optimization and stationarity of graph signals, in order to identify the graph shift operator (a matrix representation of the graph) given only its eigenvectors. These spectral templates can be obtained, e.g., from the sample covariance of independent graph signals diffused on the sought network. The novel idea is to find a graph shift that, while being consistent with the provided spectral information, endows the network with certain desired properties such as sparsity. To that end, we develop efficient inference algorithms stemming from provably tight convex relaxations of natural non-convex criteria.