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Graph Neural Networks (GNNs) have emerged as a notorious alternative toaddress learning problems dealing with non-Euclidean datasets. However,although most works assume that the graph is perfectly known, the observedtopology is prone to errors stemming from observational noise, graph-learninglimitations, or adversarial attacks. If ignored, these perturbations maydrastically hinder the performance of GNNs. To address this limitation, thiswork proposes a robust implementation of GNNs that explicitly accounts for thepresence of perturbations in the observed topology. For any task involvingGNNs, our core idea is to i) solve an optimization problem not only over thelearnable parameters of the GNN but also over the true graph, and ii) augmentthe fitting cost with a term accounting for discrepancies on the graph.Specifically, we consider a convolutional GNN based on graph filters and followan alternating optimization approach to handle the (non-differentiable andconstrained) optimization problem by combining gradient descent and projectedproximal updates. The resulting algorithm is not limited to a particular typeof graph and is amenable to incorporating prior information about theperturbations. Finally, we assess the performance of the proposed methodthrough several numerical experiments.

Robust Graph Neural Network based on Graph Denoising