Learning with Multigraph Convolutional Filters

TL;DR

This paper presents a novel convolutional neural network architecture designed for learning on multigraphs, utilizing algebraic signal processing to effectively process complex graph-structured data.

Contribution

It introduces a multigraph convolutional neural network framework based on algebraic signal processing, with efficient computation and dimensionality reduction techniques.

Findings

MGNNs outperform other architectures on resource allocation tasks

Proposed methods enable scalable processing of multigraph data

Efficient filter coefficient computation improves training speed

Abstract

In this paper, we introduce a convolutional architecture to perform learning when information is supported on multigraphs. Exploiting algebraic signal processing (ASP), we propose a convolutional signal processing model on multigraphs (MSP). Then, we introduce multigraph convolutional neural networks (MGNNs) as stacked and layered structures where information is processed according to an MSP model. We also develop a procedure for tractable computation of filter coefficients in the MGNN and a low cost method to reduce the dimensionality of the information transferred between layers. We conclude by comparing the performance of MGNNs against other learning architectures on an optimal resource allocation task for multi-channel communication systems.