@inproceedings{dong-etal-2024-dual,
    title = "Dual Complex Number Knowledge Graph Embeddings",
    author = "Dong, Yao  and
      Kong, Qingchao  and
      Wang, Lei  and
      Luo, Yin",
    editor = "Calzolari, Nicoletta  and
      Kan, Min-Yen  and
      Hoste, Veronique  and
      Lenci, Alessandro  and
      Sakti, Sakriani  and
      Xue, Nianwen",
    booktitle = "Proceedings of the 2024 Joint International Conference on Computational Linguistics, Language Resources and Evaluation (LREC-COLING 2024)",
    month = may,
    year = "2024",
    address = "Torino, Italia",
    publisher = "ELRA and ICCL",
    url = "https://aclanthology.org/2024.lrec-main.479",
    pages = "5391--5400",
    abstract = "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 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.
Dong, Yao Kong, Qingchao Wang, Lei Luo, Yin
Dual Complex Number Knowledge Graph Embeddings