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 edge-varying 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.

本文利用图信号处理来表征图神经网络（GNNs）的表征空间，讨论了图卷积滤波器在GNNs中的作用，并展示了这类滤波器所建立的任何架构都具有置换等变性和对网络拓扑的稳定性的基本属性。然后，我们讨论了扩展了边变量和自回归移动平均图滤波器的GNNs以及它们的属性，并最终研究了在推荐系统和学习机器人群体的分散式控制器中使用GNNs的相关研究。

图表，卷积和神经网络：从图滤波器到图神经网络