A Magnetic Framelet-Based Convolutional Neural Network for Directed Graphs

Abstract

Recent years have witnessed the surging popularity among studies on directed graphs (digraphs) and digraph neural networks. With the unique capability of encoding directional relationships, digraphs have shown their superiority in modelling many real-life applications, such as citation analysis and website hyperlinks. Spectral Graph Convolutional Neural Networks (spectral GCNNs), a powerful tool for processing and analyzing undirected graph data, have been recently introduced to digraphs. Although spectral GCNNs typically apply frequency filtering via Fourier transform to obtain representations with selective information, research shows that model performance can be enhanced by framelet transform-based filtering. However, the massive majority of such research only considers spectral GCNNs for undirected graphs. In this thesis, we introduce Framelet-MagNet, a magnetic framelet-based spectral GCNN for digraphs. The model adopts magnetic framelet transform which decomposes the input digraph data to low-pass and high-pass frequency components in the spectral domain, forming a more sophisticated digraph representation for filtering. Digraph framelets are constructed with the complex-valued magnetic Laplacian, simultaneously leading to signal processing in both real and complex domains. To our best knowledge, this approach is the first attempt to conduct framelet-based convolution on digraph data in both real and complex domains. We empirically validate the predictive power of Framelet-MagNet via various tasks, including node classification, link prediction, and denoising. Besides, we show through experiment results that Framelet-MagNet can outperform the state-of-the-art approaches across several benchmark datasets.