Graphs, Convolutions, and Neural Networks

Graphs, Convolutions, and Neural Networks: From Graph Filters to Graph Neural Networks

Gama, F. (TU Delft Signal Processing Systems)
Isufi, E. (TU Delft Multimedia Computing)
Leus, G.J.T. (TU Delft Signal Processing Systems)
Ribeiro, Alejandro (University of Pennsylvania)

2020

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.

http://resolver.tudelft.nl/uuid:61a69e1e-1aa5-4c15-afed-9dec771a4dff

https://doi.org/10.1109/MSP.2020.3016143

2021-05-31

1053-5888

IEEE Signal Processing Magazine, 37 (6), 128-138

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Institutional Repository

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© 2020 F. Gama, E. Isufi, G.J.T. Leus, Alejandro Ribeiro