A Magnetic Framelet-Based Convolutional Neural Network for Directed Graphs

TL;DR

This paper introduces Framelet-MagNet, a novel spectral graph convolutional network for directed graphs that leverages magnetic framelet transforms to improve representation and filtering capabilities in both real and complex domains.

Contribution

It presents the first magnetic framelet-based spectral GCNN for directed graphs, enhancing graph signal processing with complex-valued transforms.

Findings

Outperforms state-of-the-art models in node classification.

Achieves superior results in link prediction.

Effective in graph denoising tasks.

Abstract

Spectral Graph Convolutional Networks (spectral GCNNs), a powerful tool for analyzing and processing graph data, typically apply frequency filtering via Fourier transform to obtain representations with selective information. Although research shows that spectral GCNNs can be enhanced by framelet-based filtering, the massive majority of such research only considers undirected graphs. In this paper, we introduce Framelet-MagNet, a magnetic framelet-based spectral GCNN for directed graphs (digraphs). The model applies the framelet transform to digraph signals to form a more sophisticated representation for filtering. Digraph framelets are constructed with the complex-valued magnetic Laplacian, simultaneously leading to signal processing in both real and complex domains. We empirically validate the predictive power of Framelet-MagNet over a range of state-of-the-art models in node classification, link prediction, and denoising.