摘要： 知识图谱的嵌入技术旨在将复杂的语义信息映射为易于计算的低维向量形式，从而支持高效的链接预测、知识补全等任务。然而,现有模型因受限于单一数学结构，难以同时兼顾三维方向敏感旋转与非交换组合特性，导致现有方法无法有效覆盖复杂关系模式的联合推理需求。为此提出融合四元数与对偶复数的TransQD知识图谱嵌入模型，针对因单一数学结构导致的表达瓶颈，TransQD首次引入四元数嵌入与对偶复数嵌入的协同机制：四元数嵌入部分通过汉密尔顿乘积建模三维方向敏感的旋转操作，捕捉实体间空间方向性交互；对偶复数嵌入部分利用其非交换性乘法运算严格表征顺序依赖关系，例如路径组合中顺序调换导致语义变化的场景，二者通过权重分配实现互补，从而覆盖更全面的关系模式。最后，TransQD在多个公开数据集上进行的链接预测与路径查询回答任务中均表现出卓越性能，同时设计并进行消融实验验证了双组件协同的必要性。

Abstract: Knowledge graph embedding techniques map complex semantic information into low-dimensional vector representations, enabling like link prediction and knowledge completion. However, Models are constrained by a single mathematical structure, making it difficult to simultaneously accommodate three-dimensional, direction-sensitive rotations and non-commutative composition. This limits effective joint inference of complex relational patterns. To overcome this, we propose the TransQD knowledge graph embedding model, which integrates quaternion and dual complex embeddings. Addressing the expressiveness bottleneck of single-structure methods, TransQD introduces a collaborative mechanism between quaternion and dual complex embeddings: the quaternion component uses the Hamiltonian product to model three-dimensional, direction-sensitive rotations, capturing spatial interactions between entities; the dual complex component employs non-commutative multiplication to rigorously represent order-dependent relations—such as when reordering in path compositions causes semantic shifts. By weighting each component, the model achieves a complementary effect, covering a broader range of relational patterns. Finally, TransQD demonstrates outstanding performance in link prediction and path query tasks on multiple public datasets, with ablation experiments confirming the necessity of dual-component collaboration.