Hyperbolic embeddings have recently gained attention in machine learning due to their ability to represent hierarchical data more accurately and succinctly than their Euclidean analogues. However, multi-relational knowledge graphs often exhibit multiple simultaneous hierarchies, which current hyperbolic models do not capture. To address this, we propose a model that embeds multi-relational graph data in the Poincar\'e ball model of hyperbolic space. Our Multi-Relational Poincar\'e model (MuRP) learns relation-specific parameters to transform entity embeddings by M\"obius matrix-vector multiplication and M\"obius addition. Experiments on the hierarchical WN18RR knowledge graph show that our multi-relational Poincar\'e embeddings outperform their Euclidean counterpart and existing embedding methods on the link prediction task, particularly at lower dimensionality.
翻译:超曲嵌入器最近在机器学习中受到关注, 因为它们能够比欧几里得模拟更准确、更简洁地代表等级数据。 但是, 多关系知识图往往显示多个同时存在的等级, 而当前双曲模型无法捕捉。 为了解决这个问题, 我们提出了一个模型, 将多关系图数据嵌入双曲空间的波因卡尔球模型中。 我们的多关系波因卡尔模型( MuRP) 学习特定关系参数, 以改变由 M\ “ obius 矩阵- Victor 乘法和 M\ “ obius 添加 ” 嵌入的实体。 WN18RR 知识图上的实验显示, 我们的多关系波因卡的嵌入模型超越了它们的 Euclidean 对应方和现有的嵌入方法, 特别是在低维度上 。