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The effective representation, precessing, analysis, and visualization oflarge-scale structured data over graphs are gaining a lot of attention. So farmost of the literature has focused on real-valued signals. However, signals areoften sparse in the Fourier domain, and more informative and compactrepresentations for them can be obtained using the complex envelope of theirspectral components, as opposed to the original real-valued signals. Motivatedby this fact, in this work we generalize graph convolutional neural networks(GCN) to the complex domain, deriving the theory that allows to incorporate acomplex-valued graph shift operators (GSO) in the definition of graph filters(GF) and process complex-valued graph signals (GS). The theory developed canhandle spatio-temporal complex network processes. We prove that complex-valuedGCNs are stable with respect to perturbations of the underlying graph support,the bound of the transfer error and the bound of error propagation throughmultiply layers. Then we apply complex GCN to power grid state forecasting,power grid cyber-attack detection and localization.

Complex-Value Spatio-temporal Graph Convolutional Neural Networks and its Applications to Electric Power Systems AI