Knowledge graph embedding, which aims to learn representations of entities and relations in large scale knowledge graphs, plays a crucial part in various downstream applications. The performance of knowledge graph embedding models mainly depends on the ability of modeling relation patterns, such as symmetry/antisymmetry, inversion and composition (commutative composition and non-commutative composition). Most existing methods fail in modeling the non-commutative composition patterns. Several methods support this kind of pattern by modeling in quaternion space or dihedral group. However, extending to such sophisticated spaces leads to a substantial increase in the amount of parameters, which greatly reduces the parameter efficiency. In this paper, we propose a new knowledge graph embedding method called dual complex number knowledge graph embeddings (DCNE), which maps entities to the dual complex number space, and represents relations as rotations in 2D space via dual complex number multiplication. The non-commutativity of the dual complex number multiplication empowers DCNE to model the non-commutative composition patterns. In the meantime, modeling relations as rotations in 2D space can effectively improve the parameter efficiency. Extensive experiments on multiple benchmark knowledge graphs empirically show that DCNE achieves significant performance in link prediction and path query answering.

Knowledge graph embedding, which aims to learn representations of entities and relations in knowledge graphs, finds applications in various downstream tasks. The key to success of knowledge graph embedding models are the ability to model relation patterns including symmetry/antisymmetry, inversion, commutative composition and non-commutative composition. Although existing methods fail in modeling the non-commutative composition patterns, several approaches support this pattern by modeling beyond Euclidean space and complex space. Nevertheless, expanding to complicated spaces such as quaternion can easily lead to a substantial increase in the amount of parameters, which greatly reduces the computational efficiency. In this paper, we propose a new knowledge graph embedding method called RotateCT, which first transforms the coordinates of each entity, and then represents each relation as a rotation from head entity to tail entity in complex space. By design, RotateCT can infer the non-commutative composition patterns and improve the computational efficiency. Experiments on multiple datasets empirically show that RotateCT outperforms most state-of-the-art methods on link prediction and path query answering.