Directed Knowledge Graph Embedding Using a Hybrid Architecture of Spatial and Spectral GNNs

Knowledge graph embedding has been identified as an effective method for node-level classification tasks in directed graphs, the objective of which is to ensure that nodes of different categories are embedded as far apart as possible in the feature space. The directed graph is a general representation of unstructured knowledge graphs. However, existing methods lack the ability to simultaneously approximate high-order filters and globally pay attention to the task-related connectivity between distant nodes for directed graphs. To address this limitation, a directed spectral graph transformer (DSGT), a hybrid architecture model, is constructed by integrating the graph transformer and directed spectral graph convolution networks. The graph transformer leverages multi-head attention mechanisms to capture the global connectivity of the feature graph from different perspectives in the spatial domain, which bridges the gap between frequency responses and, further, naturally couples the graph transformer and directed graph convolutional neural networks (GCNs). In addition to the inherent hard inductive bias of DSGT, we introduce directed node positional and structure-aware edge embedding to provide topological prior knowledge. Extensive experiments demonstrate that the DSGT exhibits state-of-the-art (SOTA) or competitive node-level representation capabilities across datasets of varying attributes and scales. Furthermore, the experimental results indicate that the homophily and degree of correlation of the nodes significantly influence the classification performance of the model. This finding opens significant avenues for future research.