Graph Neural Networks: Architectures, Stability, and Transferability

Graph neural networks (GNNs) are information processing architectures for signals supported on graphs. They are presented here as generalizations of convolutional neural networks (CNNs) in which individual layers contain banks of graph convolutional filters instead of banks of classical convolutiona...

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Bibliographic Details
Published in:Proceedings of the IEEE Vol. 109; no. 5; pp. 660 - 682
Main Authors: Ruiz, Luana, Gama, Fernando, Ribeiro, Alejandro
Format: Journal Article
Language:English
Published: New York IEEE 01.05.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Artificial neural networks
Communication networks
Convergence
Convolutional neural networks
Data processing
Deep learning
Equivariance
Filter banks
graph filters
Graph neural networks
graph neural networks (GNNs)
graph signal processing (GSP)
graphon neural networks
graphons
Graphs
Information filters
Information processing
Neural networks
Permutations
Probability distribution
Recommender systems
Signal processing
Stability
Stability analysis
Training data
transferability
Wireless communications
Wireless networks
ISSN:0018-9219, 1558-2256
Online Access:Get full text
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Summary:Graph neural networks (GNNs) are information processing architectures for signals supported on graphs. They are presented here as generalizations of convolutional neural networks (CNNs) in which individual layers contain banks of graph convolutional filters instead of banks of classical convolutional filters. Otherwise, GNNs operate as CNNs. Filters are composed of pointwise nonlinearities and stacked in layers. It is shown that GNN architectures exhibit equivariance to permutation and stability to graph deformations. These properties help explain the good performance of GNNs that can be observed empirically. It is also shown that if graphs converge to a limit object, a graphon, GNNs converge to a corresponding limit object, a graphon neural network. This convergence justifies the transferability of GNNs across networks with different numbers of nodes. Concepts are illustrated by the application of GNNs to recommendation systems, decentralized collaborative control, and wireless communication networks.
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ISSN:0018-9219
1558-2256
DOI:10.1109/JPROC.2021.3055400