Hyperbolic Ordinal Embedding
Hyperbolic Ordinal Embedding
复制标题
DOI：
--
复制
发表时间：
2019-10
期刊：
影响因子：
--
通讯作者：
Atsushi Suzuki;Jing Wang;Feng Tian;Atsushi Nitanda;K. Yamanishi
中科院分区：
文献类型：
--
作者：
Atsushi Suzuki;Jing Wang;Feng Tian;Atsushi Nitanda;K. Yamanishi
给定序数关系，例如对象i与j的相似性大于对象k与l的相似性，序数嵌入是将这些对象嵌入到一个低维空间中，并保留所有序数约束。虽然现有的方法保留了欧氏空间中的序关系，但欧氏空间是否与真实数据结构兼容在很大程度上被忽略了，尽管这对有效嵌入至关重要。由于真实的数据往往具有层次结构，欧几里德空间方法很难在低维情况下实现有效的嵌入，从而导致计算复杂度高或过拟合。本文提出了一种新的双曲序嵌入（HOE）方法来嵌入双曲空间中的对象。由于双曲空间的层次友好属性，HOE可以有效地捕获层次，以实现在极低维空间中的嵌入。我们不仅从理论上证明了双曲空间的优越性和欧氏空间嵌入层次数据的局限性，但也实验证明，HOE显着优于基于欧氏的方法。
Given ordinal relations such as the object i is more similar to j than k is to l, ordinal embedding is to embed these objects into a low-dimensional space with all ordinal constraints preserved. Although existing approaches have preserved ordinal relations in Euclidean space, whether Euclidean space is compatible with true data structure is largely ignored, although it is essential to effective embedding. Since real data often exhibit hierarchical structure, it is hard for Euclidean space approaches to achieve effective embeddings in low dimensionality, which incurs high computational complexity or overfitting. In this paper we propose a novel hyperbolic ordinal embedding (HOE) method to embed objects in hyperbolic space. Due to the hierarchy-friendly property of hyperbolic space, HOE can effectively capture the hierarchy to achieve embeddings in an extremely low-dimensional space. We have not only theoretically proved the superiority of hyperbolic space and the limitations of Euclidean space for embedding hierarchical data, but also experimentally demonstrated that HOE significantly outperforms Euclidean-based methods.