融合四元数与对偶复数的知识图谱嵌入模型

doi:10.19678/j.issn.1000-3428.0252047

摘要/Abstract

摘要： 知识图谱嵌入（KGE）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，例如路径组合中因顺序调换导致语义变化的场景，两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问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。

关键词: 知识图谱, 知识图谱补全, 链接预测, 四元数, 对偶复数

Abstract: Knowledge Graph Embedding (KGE) techniques map complex semantic information into low-dimensional vector representations, thereby enabling tasks such as link prediction and knowledge completion. However, existing models are constrained by a single mathematical structure, making it difficult to simultaneously accommodate three-dimensional, direction-sensitive rotations and noncommutative compositions. This limits their ability to perform joint inferences over complex relational patterns. To overcome this problem, the TransQD KGE model, which integrates quaternions and dual complex embeddings, is proposed. To address the expressiveness bottleneck of single-structure methods, TransQD introduces a collaborative mechanism between quaternion embeddings and dual complex embeddings for the first time: the quaternion embedding component uses the Hamiltonian product to model three-dimensional, direction-sensitive rotations, capturing spatial interactions between entities; the dual complex embedding component employs noncommutative multiplication to rigorously represent order-dependent relations, such as scenarios where reordering path compositions leads to semantic changes. These two components complement each other through a weighted allocation mechanism, thereby covering a broader range of relational patterns. Finally, TransQD demonstrates outstanding performance in both link prediction and path query Q&A tasks across multiple public datasets, and the necessity of dual-component collaboration is verified through designed ablation experiments.

Key words: Knowledge Graph (KG), Knowledge Graph Completion (KGC), link prediction, quaternion, dual complex number

中图分类号:

TP391

潘银仓, 张东, 李冠宇, 陈恒. 融合四元数与对偶复数的知识图谱嵌入模型[J]. 计算机工程, 2026, 52(11): 130-141.

PAN Yincang, ZHANG Dong, LI Guanyu, CHEN Heng. Knowledge Graph Embedding Model Integrating Quaternions and Dual Complex Numbers[J]. Computer Engineering, 2026, 52(11): 130-141.

https://www.ecice06.com/CN/Y2026/V52/I11/130

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