Abstract
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 language | English |
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Title of host publication | ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) |
Place of Publication | Piscataway |
Publisher | IEEE |
Pages | 5265-5269 |
Number of pages | 5 |
ISBN (Electronic) | 978-1-7281-7605-5 |
ISBN (Print) | 978-1-7281-7606-2 |
DOIs | |
Publication status | Published - 2021 |
Event | ICASSP 2021: The IEEE International Conference on Acoustics, Speech, and Signal Processing - Virtual Conference/Toronto, Canada Duration: 6 Jun 2021 → 11 Jun 2021 |
Conference
Conference | ICASSP 2021 |
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Country/Territory | Canada |
City | Virtual Conference/Toronto |
Period | 6/06/21 → 11/06/21 |
Bibliographical note
Accepted author manuscriptKeywords
- Graph neural networks
- Graph signal processing
- Nonlinear systems
- State-space models