Nonlinear State-Space Generalizations of Graph Convolutional Neural Networks

TL;DR

This paper introduces a nonlinear state-space framework for graph convolutional neural networks, enhancing their stability and expressiveness by controlling state updates, with demonstrated improvements in source localization and authorship attribution tasks.

Contribution

It proposes a novel nonlinear state-space approach to generalize GCNNs, allowing better control over feature extraction and stability, which outperforms baseline models.

Findings

Nonlinear state-space models outperform baseline GCNNs in experiments.

The proposed architectures improve stability and feature learning.

Numerical results show superior performance in source localization and authorship attribution.

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.