Space-Time Graph Neural Networks
This work addresses the challenge of modeling dynamic networks for applications like control systems, though it appears incremental as it builds on existing GNN concepts with a focus on stability.
The paper tackles the problem of processing time-varying network data by introducing a space-time graph neural network (ST-GNN) architecture, which is proven stable to small perturbations in graphs and time domains, with numerical experiments demonstrating its effectiveness in decentralized control systems.
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.