Dual-based Online Learning of Dynamic Network Topologies

Abstract: We investigate online network topology identification from smooth nodal observations acquired in a streaming fashion. Different from non-adaptive batch solutions, our distinctive goal is to track the (possibly) dynamic adjacency matrix with affordable memory and computational costs by processing signal snapshots online. To this end, we leverage and truncate dual-based proximal gradient (DPG) iterations to solve a composite smoothness-regularized, time-varying inverse problem. Numerical tests with synthetic and real electrocorticography data showcase the effectiveness of the novel lightweight iterations when it comes to tracking slowly-varying network connectivity. We also show that the online DPG algorithm converges faster than a primal-based baseline of comparable complexity. Aligned with reproducible research practices, we share the code developed to produce all figures included in this paper.