Graphs, Convolutions, and Neural Networks

Network data can be conveniently modeled as a graph signal, where data values are assigned to nodes of a graph that describes the underlying network topology. Successful learning from network data is built upon methods that effectively exploit this graph structure. In this work, we overview graph convolutional filters, which are linear, local and distributed operations that adequately leverage the graph structure. We then discuss graph neural networks (GNNs), built upon graph convolutional filters, that have been shown to be powerful nonlinear learning architectures. We show that GNNs are permutation equivariant and stable to changes in the underlying graph topology, allowing them to scale and transfer. We also introduce GNN extensions using edgevarying and autoregressive moving average graph filters, and discuss their properties. Finally, we study the use of GNNs in learning decentralized controllers for robot swarm and in addressing the recommender system problem. I. INTRODUCTION Data generated by networks are increasingly common in power grids, robotics, biological, social and economic networks, and recommender systems among others. The irregular and complex nature of these network data poses unique challenges, therefore, making successful learning possible only by incorporating the structure into the inner-working mechanisms of the model [1]. Work in this paper is supported by NSF CCF 1717120, ARO W911NF1710438, ARL DCIST CRA W911NF-17- 2-0181, ISTC-WAS and Intel DevCloud. E. Isufi is with the Multimedia Computing Group and G. Leus is with the Circuits and Systems Group, Delft Univ. of Technology, The Netherlands.