Journal
IEEE SIGNAL PROCESSING MAGAZINE
Volume 37, Issue 6, Pages 128-138Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/MSP.2020.3016143
Keywords
Convolution; Finite impulse response filters; Autoregressive processes; Network topology; Information filters; Nonhomogeneous media; Graphical models
Categories
Funding
- National Science Foundation Computing and Communication Foundations [1717120]
- Army Research Office [W911NF1710438]
- Army Research Laboratory Distributed and Collaborative Intelligent Systems and Technology Collaborative Research Alliance [W911NF-17-2-0181]
- International Science and Technology Center-Wireless Autonomous Systems and Intel DevCloud
- U.S. Department of Defense (DOD) [W911NF1710438] Funding Source: U.S. Department of Defense (DOD)
- Division of Computing and Communication Foundations
- Direct For Computer & Info Scie & Enginr [1717120] Funding Source: National Science Foundation
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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.
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