Abstract
An online algorithm for missing data imputation for networks with signals defined on the edges is presented. Leveraging the prior knowledge intrinsic to real-world networks, we propose a bi-level optimization scheme that exploits the causal dependencies and the flow conservation, respectively via <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(i)</i> a sparse line graph identification strategy based on a group-Lasso and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(ii)</i> a Kalman filtering-based signal reconstruction strategy developed using simplicial complex (SC) formulation. The advantages of this first SC-based attempt for time-varying signal imputation have been demonstrated through numerical experiments using EPANET models of both synthetic and real water distribution networks.
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