Convolutional Learning on Multigraphs

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.

References in corpus (21)

• Diffusion dynamics on multiplex networks
• MAGNN: Metapath Aggregated Graph Neural Network for Heterogeneous Graph Embedding
• Discrete Signal Processing on Graphs: Sampling Theory
• Representation Learning for Attributed Multiplex Heterogeneous Network
• Efficient Sampling Set Selection for Bandlimited Graph Signals Using Graph Spectral Proxies
• Signals on Graphs: Uncertainty Principle and Sampling
• Optimal Wireless Resource Allocation with Random Edge Graph Neural Networks
• Convolutional Neural Network Architectures for Signals Supported on Graphs
• Stability Properties of Graph Neural Networks
• A multilayer perspective for the analysis of urban transportation systems
• Achieving Global Optimality for Weighted Sum-Rate Maximization in the K-User Gaussian Interference Channel with Multiple Antennas
• Joint predictions of multi-modal ride-hailing demands: a deep multi-task multigraph learning-based approach
• Multiplex Heterogeneous Graph Convolutional Network
• A Note on Over-Smoothing for Graph Neural Networks
• Graphon Signal Processing
• Retweet communities reveal the main sources of hate speech
• Algebraic Neural Networks: Stability to Deformations
• Diffusion geometry of multiplex and interdependent systems
• CS-MLGCN : Multiplex Graph Convolutional Networks for Community Search in Multiplex Networks
• Extracting the multimodal fingerprint of urban transportation networks
• Simultaneous Block Diagonalization of Matrices of Finite Order