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首页> 外文期刊>IEEE Signal Processing Magazine >Graphs, Convolutions, and Neural Networks: From Graph Filters to Graph Neural Networks
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Graphs, Convolutions, and Neural Networks: From Graph Filters to Graph Neural Networks

机译：图形，卷曲和神经网络：从图形过滤器到图形神经网络

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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 article, we leverage graph signal processing (GSP) to characterize the representation space of graph neural networks (GNNs). We discuss the role of graph convolutional filters in GNNs and show that any architecture built with such filters has the fundamental properties of permutation equivariance and stability to changes in the topology. These two properties offer insight about the workings of GNNs and help explain their scalability and transferability properties, which, coupled with their local and distributed nature, make GNNs powerful tools for learning in physical networks. We also introduce GNN extensions using edge-varying and autoregressive moving average (ARMA) graph filters and discuss their properties. Finally, we study the use of GNNs in recommender systems and learning decentralized controllers for robot swarms.
机译：网络数据可以方便地建模为曲线图信号，其中数据值被分配给描述底层网络拓扑的图表的节点。在有效利用此图形结构的方法上建立了从网络数据的成功学习。在本文中，我们利用图形信号处理（GSP）来表征图形神经网络（GNN）的表示空间。我们讨论了Graph卷积滤波器在GNNS中的作用，并表明使用此类滤波器构建的任何体系结构都具有置换设备的基本属性和拓扑变化的稳定性。这两个属性提供了有关GNN的运作的洞察力，并帮助解释其可扩展性和可转换性属性，即与其本地和分布式性质相结合，使GNNS强大的工具在物理网络中学习。我们还使用边缘变化和自回归移动平均（ARMA）图形过滤器来介绍GNN扩展，并讨论其属性。最后，我们研究了GNNS在推荐系统中使用GNN和学习机器人群的分散控制器。

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