Convolutional Neural Network Architectures for Signals Supported on Graphs

Fernando Gama*, Antonio G. Marques, Geert Leus, Alejandro Ribeiro

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

91 Citations (Scopus)
116 Downloads (Pure)


Two architectures that generalize convolutional neural networks (CNNs) for the processing of signals supported on graphs are introduced. We start with the selection graph neural network (GNN), which replaces linear time invariant filters with linear shift invariant graph filters to generate convolutional features and reinterprets pooling as a possibly nonlinear subsampling stage where nearby nodes pool their information in a set of preselected sample nodes. A key component of the architecture is to remember the position of sampled nodes to permit computation of convolutional features at deeper layers. The second architecture, dubbed aggregation GNN, diffuses the signal through the graph and stores the sequence of diffused components observed by a designated node. This procedure effectively aggregates all components into a stream of information having temporal structure to which the convolution and pooling stages of regular CNNs can be applied. A multinode version of aggregation GNNs is further introduced for operation in large-scale graphs. An important property of selection and aggregation GNNs is that they reduce to conventional CNNs when particularized to time signals reinterpreted as graph signals in a circulant graph. Comparative numerical analyses are performed in a source localization application over synthetic and real-world networks. Performance is also evaluated for an authorship attribution problem and text category classification. Multinode aggregation GNNs are consistently the best-performing GNN architecture.

Original languageEnglish
Article number8579589
Pages (from-to)1034-1049
Number of pages16
JournalIEEE Transactions on Signal Processing
Issue number4
Publication statusPublished - 2019

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project

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.


  • convolutional neural networks
  • Deep learning
  • graph filters
  • graph signal processing
  • pooling


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