Convolutional Graph Neural Networks

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

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

3 Citations (Scopus)
11 Downloads (Pure)


Convolutional neural networks (CNNs) restrict the, otherwise arbitrary, linear operation of neural networks to be a convolution with a bank of learned filters. This makes them suitable for learning tasks based on data that exhibit the regular structure of time signals and images. The use of convolutions, however, makes them unsuitable for processing data that do not exhibit such a regular structure. Graph signal processing (GSP) has emerged as a powerful alternative to process signals whose irregular structure can be described by a graph. Central to GSP is the notion of graph convolutional filters which can be used to define convolutional graph neural networks (GNNs). In this paper, we show that the graph convolution can be interpreted as either a diffusion or aggregation operation. When combined with nonlinear processing, these different interpretations lead to different generalizations which we term selection and aggregation GNNs. The selection GNN relies on linear combinations of signal diffusions at different resolutions combined with node-wise non-linearities. The aggregation GNN relies on linear combinations of neighborhood averages of different depth. Instead of node-wise nonlinearities, the nonlinearity in aggregation GNNs is pointwise on the different aggregation levels. Both of these models particularize to regular CNNs when applied to time signals but are different when applied to arbitrary graphs. Numerical evaluations show different levels of performance for selection and aggregation GNNs.

Original languageEnglish
Title of host publicationConference Record - 53rd Asilomar Conference on Circuits, Systems and Computers, ACSSC 2019
EditorsMichael B. Matthews
Number of pages5
ISBN (Electronic)9781728143002
Publication statusPublished - 2019
Event53rd Asilomar Conference on Circuits, Systems and Computers, ACSSC 2019 - Pacific Grove, United States
Duration: 3 Nov 20196 Nov 2019

Publication series

NameConference Record - Asilomar Conference on Signals, Systems and Computers
ISSN (Print)1058-6393


Conference53rd Asilomar Conference on Circuits, Systems and Computers, ACSSC 2019
Country/TerritoryUnited States
CityPacific Grove

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.


  • graph convolutions
  • graph neural networks
  • graph signal processing
  • network data


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