Space-Time Graph Neural Networks

TL;DR

This paper introduces space-time graph neural networks (ST-GNNs) that process dynamic network data by combining space and time convolutions, demonstrating stability and effectiveness in control systems.

Contribution

The paper proposes a novel ST-GNN architecture with a generic convolution definition and stability analysis for dynamic graph data.

Findings

ST-GNNs are stable to small graph and time perturbations.

Numerical experiments confirm effectiveness in control systems.

The architecture generalizes existing GNNs to dynamic settings.

Abstract

We introduce space-time graph neural network (ST-GNN), a novel GNN architecture, tailored to jointly process the underlying space-time topology of time-varying network data. The cornerstone of our proposed architecture is the composition of time and graph convolutional filters followed by pointwise nonlinear activation functions. We introduce a generic definition of convolution operators that mimic the diffusion process of signals over its underlying support. On top of this definition, we propose space-time graph convolutions that are built upon a composition of time and graph shift operators. We prove that ST-GNNs with multivariate integral Lipschitz filters are stable to small perturbations in the underlying graphs as well as small perturbations in the time domain caused by time warping. Our analysis shows that small variations in the network topology and time evolution of a system does not significantly affect the performance of ST-GNNs. Numerical experiments with decentralized control systems showcase the effectiveness and stability of the proposed ST-GNNs.