Collaborative bi-aggregation for directed graph embedding

Directed graph is able to model asymmetric relationships between nodes and research on directed graph embedding is of great significance in downstream graph analysis and inference. Learning source and target embeddings of nodes separately to preserve edge asymmetry has become the dominant approach, but also poses challenge for learning representations of low or even zero in/out degree nodes that are ubiquitous in sparse graphs. In this paper, a collaborative bi-directional aggregation method (COBA) for directed graph embedding is proposed. Firstly, the source and target embeddings of the central node are learned by aggregating from the counterparts of the source and target neighbors, respectively; Secondly, the source/target embeddings of the zero in/out degree central nodes are enhanced by aggregating the counterparts of opposite-directional neighbors (i.e. target/source neighbors); Finally, source and target embeddings of the same node are correlated to achieve collaborative aggregation. Both the feasibility and rationality of the model are theoretically analyzed. Extensive experiments on real-world datasets demonstrate that COBA comprehensively outperforms state-of-the-art methods on multiple tasks and meanwhile validates the effectiveness of proposed aggregation strategies.& COPY; 2023 Elsevier Ltd. All rights reserved.