| Paper ID | SPTM-11.5 |
| Paper Title |
NONLINEAR STATE-SPACE GENERALIZATIONS OF GRAPH CONVOLUTIONAL NEURAL NETWORKS |
| Authors |
Luana Ruiz, University of Pennsylvania, United States; Fernando Gama, University of California, Berkeley, United States; Alejandro Ribeiro, University of Pennsylvania, United States; Elvin Isufi, Delft University of Technology, United States |
| Session | SPTM-11: Graphs Neural Networks |
| Location | Gather.Town |
| Session Time: | Wednesday, 09 June, 16:30 - 17:15 |
| Presentation Time: | Wednesday, 09 June, 16:30 - 17:15 |
| Presentation |
Poster
|
| Topic |
Signal Processing Theory and Methods: [SIPG] Signal and Information Processing over Graphs |
| IEEE Xplore Open Preview |
Click here to view in IEEE Xplore |
| Virtual Presentation |
Click here to watch in the Virtual Conference |
| 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. |
