Directional Graph Attention Networks

In recent years, graph neural networks (GNNs) have become a promising method for analyzing data structured in graph format. By considering connections between entities in a graph, GNNs are able to extract valuable insights. One notable variation of GNN is the graph attention network (GAT), which employs the attention mechanism and has demonstrated promising performance in various applications. However, its ability to incorporate feature information from nodes beyond the immediate neighborhood is limited, leading to degraded performance on heterophilic data. To address this limitation, this thesis proposes a novel attention-based model, namely the Directional Graph Attention Network (DGAT). This model combines the feature-based attention with the global directional information extracted from the graph topology, as inspired by the Directional Graph Network (DGN). A new class of Laplacian matrices is proposed and an existing theoretical result on DGN is extended. This extension bridges a gap in the literature. The experimental results presented in the thesis, based on nine real-world benchmarks and ten synthetic data sets, demonstrate the superiority of the proposed DGAT model compared to the GAT baseline model. Particularly on heterophilic data sets, DGAT showed a notable average increase of approximately 35% in node classification tasks across all heterophilic real-world data sets. In addition, DGAT outperforms GAT by an average margin of around 51% in all ten synthetic data sets with various levels of heterophily