Including Co-Relation via Concatenate Operator for Static and Temporal Knowledge Graph Embedding

Knowledge Graph Completion (KGC) aims to complete KGs by predicting missing entities. A common solution for KGC is Knowledge Graph Embedding (KGE), which assumes that semantical similar entities or relationships should possess similar representations in high-dimensional space. In KGE, a heuristic score function of the head entity and its relation with different operators is required. A typical technique is regularization for tensor factorization, such as the Nuclear-p norm and the Frobenius norm of the query/entity embedding, which significantly improve the KGE model performance on the KGC task. However, the Co-Relations, including the association between tail entities (Co-Query Relation) and the association between queries (Co-Entity Relation), desirable for KGC are not fully considered in existing embedding regularization techniques. In this article, we theoretically interpret the role of Co-Relation in KGE and propose a novel ConR regularization approach to learn embedding that takes Co-Relations into account. Extensive experiments show that our model improves static and temporal KGC tasks over decomposition-based models, ComplEx and TuckER. Further analysis of the score cumulative distribution function and embedding visualization demonstrates the effectiveness of ConR.