FFHR：一种完全灵活的知识图谱完备化双曲表示方法
FFHR: Fully and Flexible Hyperbolic Representation for Knowledge Graph Completion
摘要：
知识图谱的双曲嵌入学习由于其在捕获层次结构方面的优势而受到越来越多的关注。然而，双曲空间中的一些重要运算仍然缺乏良好的定义，使得现有的方法无法充分利用双曲空间的优点。具体而言，它们受到两个主要限制：1）现有的双曲空间中的图卷积网络（GCN）方法依赖于切空间近似，这会在表示学习中产生近似误差; 2）由于双曲空间中缺乏内积运算定义，现有方法只能用双曲距离来度量事实（链接）的可扩展性，其难以捕获复杂的数据模式。在这项工作中，我们贡献：1）一个完整的庞加莱多关系GCN，实现了图信息传播在双曲空间，而不需要任何近似，和2）双曲推广的欧几里得内积，这是有益的，以捕捉层次和复杂的模式。在此基础上，我们进一步发展了一个\textbf{F} ully和\textbf{F} flexible \textbf{H}双曲\textbf{R}表示框架（\textbf{FFHR}），它能够将最近的基于欧几里得的进展转移到双曲空间。我们证明它通过实例化FFHR与四个代表性的KGC方法。在基准数据集上进行的大量实验验证了我们的FFHR比欧几里得算法以及最先进的双曲嵌入方法的优越性。
英文摘要：
Learning hyperbolic embeddings for knowledge graph (KG) has gained increasing attention due to its superiority in capturing hierarchies. However, some important operations in hyperbolic space still lack good definitions, making existing methods unable to fully leverage the merits of hyperbolic space. Specifically, they suffer from two main limitations: 1) existing Graph Convolutional Network (GCN) methods in hyperbolic space rely on tangent space approximation, which would incur approximation error in representation learning, and 2) due to the lack of inner product operation definition in hyperbolic space, existing methods can only measure the plausibility of facts (links) with hyperbolic distance, which is difficult to capture complex data patterns. In this work, we contribute: 1) a Full Poincaré Multi-relational GCN that achieves graph information propagation in hyperbolic space without requiring any approximation, and 2) a hyperbolic generalization of Euclidean inner product that is beneficial to capture both hierarchical and complex patterns. On this basis, we further develop a \textbf{F}ully and \textbf{F}lexible \textbf{H}yperbolic \textbf{R}epresentation framework (\textbf{FFHR}) that is able to transfer recent Euclidean-based advances to hyperbolic space. We demonstrate it by instantiating FFHR with four representative KGC methods. Extensive experiments on benchmark datasets validate the superiority of our FFHRs over their Euclidean counterparts as well as state-of-the-art hyperbolic embedding methods.
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