Convolutional Learning on Multigraphs

TL;DR

This paper introduces convolutional multigraph neural networks (MGNNs) that effectively model complex data structures with multiple edge types, enhancing performance in applications like wireless resource allocation and hate speech detection.

Contribution

It formalizes convolutional signal processing on multigraphs and develops a novel MGNN architecture with a sampling method to handle complex dynamics and reduce computational costs.

Findings

Improved performance over traditional GNNs in targeted applications

Effective modeling of complex dynamics in multigraphs

Reduced computational complexity through sampling

Abstract

Graph convolutional learning has led to many exciting discoveries in diverse areas. However, in some applications, traditional graphs are insufficient to capture the structure and intricacies of the data. In such scenarios, multigraphs arise naturally as discrete structures in which complex dynamics can be embedded. In this paper, we develop convolutional information processing on multigraphs and introduce convolutional multigraph neural networks (MGNNs). To capture the complex dynamics of information diffusion within and across each of the multigraph's classes of edges, we formalize a convolutional signal processing model, defining the notions of signals, filtering, and frequency representations on multigraphs. Leveraging this model, we develop a multigraph learning architecture, including a sampling procedure to reduce computational complexity. The introduced architecture is applied towards optimal wireless resource allocation and a hate speech localization task, offering improved performance over traditional graph neural networks.