A Magnetic Framelet-Based Convolutional Neural Network for Directed Graphs
This work addresses a gap in spectral GCNNs for directed graphs, which is important for domains like social networks or biological systems, but it is incremental as it extends existing framelet methods to digraphs.
The paper tackles the problem of applying spectral graph convolutional networks to directed graphs by introducing Framelet-MagNet, a magnetic framelet-based model that uses complex-valued magnetic Laplacian for signal processing, and it empirically shows superior predictive power in node classification, link prediction, and denoising tasks.
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.