Bridging the Gap between Spatial and Spectral Domains: A Survey on Graph Neural Networks

Deep learning's success has been widely recognized in a variety of machine learning tasks, including image classification, audio recognition, and natural language processing. As an extension of deep learning beyond these domains, graph neural networks (GNNs) are designed to handle the non-Euclidean graph-structure which is intractable to previous deep learning techniques. Existing GNNs are presented using various techniques, making direct comparison and cross-reference more complex. Although existing studies categorize GNNs into spatial-based and spectral-based techniques, there hasn't been a thorough examination of their relationship. To close this gap, this study presents a single framework that systematically incorporates most GNNs. We organize existing GNNs into spatial and spectral domains, as well as expose the connections within each domain. A review of spectral graph theory and approximation theory builds a strong relationship across the spatial and spectral domains in further investigation.