Bridging the Gap between Spatial and Spectral Domains: A Theoretical Framework for Graph Neural Networks

During the past decade, deep learning's performance has been widely recognized in a variety of machine learning tasks, ranging from image classification, speech recognition to natural language understanding. Graph neural networks (GNN) are a type of deep learning that is designed to handle non-Euclidean issues using graph-structured data that are difficult to solve with traditional deep learning techniques. The majority of GNNs were created using a variety of processes, including random walk, PageRank, graph convolution, and heat diffusion, making direct comparisons impossible. Previous studies have primarily focused on classifying current models into distinct categories, with little investigation of their internal relationships. This research proposes a unified theoretical framework and a novel perspective that can methodologically integrate existing GNN into our framework. We survey and categorize existing GNN models into spatial and spectral domains, as well as show linkages between subcategories within each domain. Further investigation reveals a strong relationship between the spatial, spectral, and subgroups of these domains.