Dynamic Graph Convolutional Networks Using the Tensor M-Product

TL;DR

This paper introduces TM-GCN, a novel tensor algebra-based graph neural network designed for dynamic graphs, demonstrating improved performance in real-world tasks like link prediction and early COVID-19 detection.

Contribution

The paper extends GCNs to dynamic graphs using tensor M-product, establishing a spectral connection and integrating spatial-temporal message passing.

Findings

Effective in edge classification and link prediction on dynamic graphs

Demonstrates utility in COVID-19 contact tracing for early detection

Theoretically links tensor methods with spectral graph convolution

Abstract

Many irregular domains such as social networks, financial transactions, neuron connections, and natural language constructs are represented using graph structures. In recent years, a variety of graph neural networks (GNNs) have been successfully applied for representation learning and prediction on such graphs. In many of the real-world applications, the underlying graph changes over time, however, most of the existing GNNs are inadequate for handling such dynamic graphs. In this paper we propose a novel technique for learning embeddings of dynamic graphs using a tensor algebra framework. Our method extends the popular graph convolutional network (GCN) for learning representations of dynamic graphs using the recently proposed tensor M-product technique. Theoretical results presented establish a connection between the proposed tensor approach and spectral convolution of tensors. The proposed method TM-GCN is consistent with the Message Passing Neural Network (MPNN) framework, accounting for both spatial and temporal message passing. Numerical experiments on real-world datasets demonstrate the performance of the proposed method for edge classification and link prediction tasks on dynamic graphs. We also consider an application related to the COVID-19 pandemic, and show how our method can be used for early detection of infected individuals from contact tracing data.