Abstract: Abstract: In recent years, deterministic knowledge graph embedding research has advanced to a mature stage, whereas uncertain knowledge graph embedding has emerged as a new focus. Unlike deterministic knowledge graph embedding, uncertain knowledge graph embedding must not only capture semantic interactions between entities and relations but also precisely quantify the credibility of each triple. Existing methods have made preliminary progress in this direction but still have significant limitations, particularly in modeling complex relations. The UKGE framework, for example, can only model simple relation patterns such as symmetry. Although the RotatE model, which uses complex-plane rotations, is efficient and can model multiple relation facts, its expressiveness is constrained by the two-dimensional complex space, making it difficult to model high-dimensional rotations. It is also prone to the "deadlock" problem, which limits further modeling of complex relations. To address these limitations, this study proposes a novel uncertain knowledge graph embedding model based on quaternions, termed UQuatE. In UQuatE, entities are represented as four-dimensional quaternion vectors, and relations are modeled as rotation operators in quaternion space. The scoring function leverages the Hamilton product to achieve quaternion rotations, thereby systematically capturing a variety of complex relation patterns, including symmetry, asymmetry, inverse relations, commutativity, and non-commutativity. The three-dimensional rotational property of quaternions in UQuatE effectively alleviates the "deadlock" problem in high-dimensional rotations and significantly enhances the modeling capacity for complex relations. To verify the effectiveness of UQuatE, five comparative experiments were designed across three public uncertain knowledge graph datasets. The results demonstrate that UQuatE significantly outperforms existing baseline models in core tasks such as confidence prediction and relation fact ranking, providing new methodological insights and supporting further research in uncertain knowledge graph embedding.

Key words: uncertainty knowledge graph embedding, quaternion, complex relation modeling, rotation

摘要： 摘 要: 近年来，确定性知识图谱嵌入的研究已趋于成熟，而不确定性知识图谱嵌入正逐渐成为新的关注焦点。相较于前者，不确定知识图谱嵌入不仅需要刻画实体与关系之间的语义关联，还必须对每条三元组的可信度进行精准量化。现有方法在这一方向上取得了初步进展，但仍存在诸多不足，尤其在对复杂关系的建模方面表现有限。UKGE框架仅能刻画对称等简单关系模式，复数平面上的旋转模型RotatE虽能借助复数旋转刻画多关系事实，简洁而高效，但其表达能力受限于二维复数空间，难以刻画高维旋转，且易出现“死锁”现象，制约了对复杂关系的进一步刻画。针对上述局限，提出一种基于四元数的不确定性知识图谱嵌入模型UQuatE，该模型将实体表示为四维四元数向量，并将关系建模为四元数空间中的旋转算子。在评分函数层面，利用实体与关系的汉密尔顿积计算方法实现四元数旋转，从而能够系统地表征对称、反对称、逆关系、可交换及不可交换等复杂关系模式。四元数的三维旋转特性有效缓解了高维旋转中的“死锁”问题，并显著提升了对复杂关系的刻画能力。为验证UQuatE的有效性，在三个公开不确定性知识图谱数据集上设计了五项对比实验。实验结果表明，UQuatE在置信度预测、关系事实排序等核心任务上整体上显著优于现有基线模型，为不确定性知识图谱嵌入的进一步研究提供了新的思路与方法论支撑。

关键词: 不确定知识图谱嵌入, 四元数, 复杂关系建模, 旋转