Graphs, Convolutions, and Neural Networks: From Graph Filters to Graph Neural Networks

Abstract

Network data can be conveniently modeled as a graph signal, where data values are assigned to nodes of a graph that describes the underlying network topology. Successful learning from network data is built upon methods that effectively exploit this graph structure. In this work, we leverage graph signal processing to characterize the representation space of graph neural networks (GNNs). We discuss the role of graph convolutional filters in GNNs and show that any architecture built with such filters has the fundamental properties of permutation equivariance and stability to changes in the topology. These two properties offer insight about the workings of GNNs and help explain their scalability and transferability properties which, coupled with their local and distributed nature, make GNNs powerful tools for learning in physical networks. We also introduce GNN extensions using edge-varying and autoregressive moving average graph filters and discuss their properties. Finally, we study the use of GNNs in recommender systems and learning decentralized controllers for robot swarms.

Submitted to IEEE SPM Special Issue on Graph Signal Processing: Foundations and Emerging Directions

Cited by in corpus (9)

• Bayesian Estimation of Graph Signals
• Finite Impulse Response Filters for Simplicial Complexes
• Stochastic Graph Neural Networks
• Distributed Training of Graph Convolutional Networks
• Widely-Linear MMSE Estimation of Complex-Valued Graph Signals
• On Local Distributions in Graph Signal Processing
• Graph Neural Networks with Parallel Neighborhood Aggregations for Graph Classification
• Learning Stochastic Graph Neural Networks with Constrained Variance
• Learning to Navigate in Turbulent Flows with Aerial Robot Swarms: A Cooperative Deep Reinforcement Learning Approach