Pair-wise or high-order? A self-adaptive graph framework for knowledge graph embedding

Knowledge graphs (KGs) depict entities as nodes and connections as edges, and they are extensively utilized in numerous artificial intelligence applications. However, knowledge graphs often suffer from incompleteness, which seriously affects downstream applications. Knowledge graph embedding (KGE) technology tackles this challenge by encoding entities and relations as vectors, allowing for inference and computations using these representations. Graph convolutional networks (GCNs) are essential knowledge graph embedding technology models. GCN methods capture the topological structure features of the KG by calculating the pair-wise relationships between entities and neighboring nodes. Although GCN models have achieved excellent performance, there are still three main challenges: (1) effectively solving the over-smoothing problem in multi-layer GCN models for knowledge graph representation learning, (2) obtaining high-order information between entities and neighboring nodes beyond the pair-wise relationships, and (3) effectively integrating pair-wise and high-order features of entities. To address these challenges, we proposed an adaptive graph convolutional network model called PHGCN (Pair-wise and High-Order Graph Convolutional Network), which can simultaneously integrate pair-wise and high-order features. PHGCN tackles the three challenges mentioned above in the following ways. (1) We propose a layer-aware GCN to overcome the over-smoothing problem while aggregating pair-wise relationships. (2) We employ simplicial complex neural networks to extract high-order topological features from knowledge graphs. (3) We introduce a self-adaptive aggregation mechanism that effectively integrates pair-wise and high-order features. Our experiments on four benchmark datasets showed that PHGCN outperforms existing methods, achieving state-of-the-art results. The performance improvement from using a simplicial complex neural network to extract high-order features is significant. On the FB15k-237 dataset, PHGCN achieved a 1.5% improvement, while on the WN18RR dataset, it improved by 6.1%.