用任意几何区域建模层次结构，实现类双曲表达力
RegD: Hierarchical Embeddings via Dissimilarity between Arbitrary Euclidean Regions
- 用盒子、球等任意几何体做嵌入表示，灵活适应不同数据
- 在真实数据集上优于现有方法，支持指数级增长特性
- 适合需要融合语义关系的层次结构建模任务
层次数据在生命科学和电子商务等领域广泛存在，其嵌入表示至关重要。尽管双曲嵌入理论上能高效表示层次结构，但现有方法依赖特定几何构造，限制了通用性，并难以与建模语义关系（如本体嵌入）的技术结合。本文提出RegD，一种灵活的欧氏框架，支持使用任意几何区域（如盒子、球体）作为嵌入表示。尽管完全在欧氏空间运行，我们形式化证明其通过基于深度的区域间差异度量，可实现类双曲表达力，包括指数增长特性。在多种真实世界数据集上的实证评估表明，RegD持续优于当前最优方法，展现出在超越纯层次结构的应用（如本体嵌入）中的潜力。
原文摘要 · Abstract (English)
Hierarchical data is common in many domains like life sciences and e-commerce, and its embeddings often play a critical role. While hyperbolic embeddings offer a theoretically grounded approach to representing hierarchies in low-dimensional spaces, current methods often rely on specific geometric constructs as embedding candidates. This reliance limits their generalizability and makes it difficult to integrate with techniques that model semantic relationships beyond pure hierarchies, such as ontology embeddings. In this paper, we present RegD, a flexible Euclidean framework that supports the use of arbitrary geometric regions -- such as boxes and balls -- as embedding representations. Although RegD operates entirely in Euclidean space, we formally prove that it achieves hyperbolic-like expressiveness by incorporating a depth-based dissimilarity between regions, enabling it to emulate key properties of hyperbolic geometry, including exponential growth. Our empirical evaluation on diverse real-world datasets shows consistent performance gains over state-of-the-art methods and demonstrates RegD's potential for broader applications such as the ontology embedding task that goes beyond hierarchy.
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