Quaternion contains one real part and three imaginary parts, which provided a more expressive hypercomplex space for learning knowledge graph. Existing quaternion embedding models measure the plausibility of a triplet either through semantic matching or geometric distance scoring functions. However, it appears that semantic matching diminishes the separability of entities, while the distance scoring function weakens the semantics of entities. To address this issue, we propose a novel quaternion knowledge graph embedding model. Our model combines semantic matching with entity's geometric distance to better measure the plausibility of triplets. Specifically, in the quaternion space, we perform a right rotation on head entity and a reverse rotation on tail entity to learn rich semantic features. Then, we utilize distance adaptive translations to learn geometric distance between entities. Furthermore, we provide mathematical proofs to demonstrate our model can handle complex logical relationships. Extensive experimental results and analyses show our model significantly outperforms previous models on well-known knowledge graph completion benchmark datasets. Our code is available at https://github.com/llqy123/DaBR.

This paper presents translation-based knowledge graph completion method via efficient relation rotation (TransERR), a straightforward yet effective alternative to traditional translation-based knowledge graph completion models. Different from the previous translation-based models, TransERR encodes knowledge graphs in the hypercomplex-valued space, thus enabling it to possess a higher degree of translation freedom in mining latent information between the head and tail entities. To further minimize the translation distance, TransERR adaptively rotates the head entity and the tail entity with their corresponding unit quaternions, which are learnable in model training. The experiments on 7 benchmark datasets validate the effectiveness and the generalization of TransERR. The results also indicate that TransERR can better encode large-scale datasets with fewer parameters than the previous translation-based models. Our code is available at: \url{https://github.com/dellixx/TransERR}.