用几何方法建模关系数据中的层次、循环和逻辑结构。
Geometric Relational Embeddings
- 基于几何空间表示关系数据，保留符号结构特性。
- 在知识图谱中有效捕捉层级与环状模式。
- 适合需要逻辑约束的智能系统设计者。
关系表示学习将关系数据转化为连续且低维的向量表示。然而，传统的向量表示难以捕捉关系数据中复杂的符号性特征。本文提出几何关系嵌入（Geometric Relational Embeddings），一种尊重底层符号结构的关系嵌入范式。具体而言，该论文引入多种几何关系嵌入模型，能够捕捉：1）网络与知识图谱中的复杂结构模式，如层级关系和环路；2）本体中的逻辑结构及可用于约束机器学习模型输出的逻辑约束；3）实体与关系之间的高阶结构。在基准数据集与真实世界数据上的实验结果表明，几何关系嵌入能有效捕捉关系数据中固有的离散、符号化与结构化特性。
原文摘要 · Abstract (English)
Relational representation learning transforms relational data into continuous and low-dimensional vector representations. However, vector-based representations fall short in capturing crucial properties of relational data that are complex and symbolic. We propose geometric relational embeddings, a paradigm of relational embeddings that respect the underlying symbolic structures. Specifically, this dissertation introduces various geometric relational embedding models capable of capturing: 1) complex structured patterns like hierarchies and cycles in networks and knowledge graphs; 2) logical structures in ontologies and logical constraints applicable for constraining machine learning model outputs; and 3) high-order structures between entities and relations. Our results obtained from benchmark and real-world datasets demonstrate the efficacy of geometric relational embeddings in adeptly capturing these discrete, symbolic, and structured properties inherent in relational data.
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