Nonlinear State-Space Generalizations of Graph Convolutional Neural Networks

Luana Ruiz, Fernando Gama, Alejandro Ribeiro, Elvin Isufi

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Graph convolutional neural networks (GCNNs) learn compositional representations from network data by nesting linear graph convolutions into nonlinearities. In this work, we approach GCNNs from a state-space perspective revealing that the graph convolutional module is a minimalistic linear state-space model, in which the state update matrix is the graph shift operator. We show that this state update may be problematic because it is nonparametric, and depending on the graph spectrum it may explode or vanish. Therefore, the GCNN has to trade its degrees of freedom between extracting features from data and handling these instabilities. To improve such trade-off, we propose a novel family of nodal aggregation rules that aggregate node features within a layer in a nonlinear state-space parametric fashion allowing for a better trade-off. We develop two architectures within this family inspired by the recurrence with and without nodal gating mechanisms. The proposed solutions generalize the GCNN and provide an additional handle to control the state update and learn from the data. Numerical results on source localization and authorship attribution show the superiority of the nonlinear state-space generalization models over the baseline GCNN.
Original languageEnglish
Title of host publicationICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
Place of PublicationPiscataway
Number of pages5
ISBN (Electronic)978-1-7281-7605-5
ISBN (Print)978-1-7281-7606-2
Publication statusPublished - 2021
EventICASSP 2021: The IEEE International Conference on Acoustics, Speech, and Signal Processing - Virtual Conference/Toronto, Canada
Duration: 6 Jun 202111 Jun 2021


ConferenceICASSP 2021
CityVirtual Conference/Toronto

Bibliographical note

Accepted author manuscript


  • Graph neural networks
  • Graph signal processing
  • Nonlinear systems
  • State-space models

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