A Localized Geometric Method to Match Knowledge in Low-dimensional Hyperbolic Space

Proceedings of the 2022 Conference on Empirical Methods in Natural Language Processing, pages 2822 - 2832 December 7-11, 2022 ©2022 Association for Computational Linguistics A Localized Geometric Method to Match Knowledge in Low-dimensional Hyperbolic Space Bo Hui Auburn University bohui@auburn.edu Tian Xia Auburn University tianxia@auburn.edu Wei-Shinn Ku Auburn University weishinn@auburn.edu Abstract Matching equivalent entities across Knowledge graphs is a pivotal step for knowledge fusion. Previous approaches usually study the problem in Euclidean space. However, recent works have shown that hyperbolic space has a higher capacity than Euclidean space and hyperbolic embedding can represent the hierarchical struc- ture in a knowledge graph. In this paper, we propose a localized geometric method to find equivalent entities in hyperbolic space. Specif- ically, we use a hyperbolic neural network to encode the lingual information of entities and the structure of both knowledge graphs into a low-dimensional hyperbolic space. To address the asymmetry of structure on different KGs and the localized nature of relations, we learn an instance-specific geometric mapping func- tion based on rotation to match entity pairs. A contrastive loss function is used to train the model. The experiment verifies the power of low-dimensional hyperbolic space for entity matching and shows that our method outper- forms the state of the art by a large margin. 1 Introduction Knowledge graph (KG) is knowledge base that uses a graph-structured topology to integrate entities, re- lations, and metadata. Real-world KGs such as DBpedia, Wikidata, and Yago benefit a variety of downstream applications such as question answer- ing (Cui et al., 2017), and fact checking (Huynh and Papotti, 2019). In general, a KG is constructed from one single knowledge base or built in one single language. Thus it is impractical to reach full coverage of the domain (Zhao et al., 2020). To increase the completeness of the knowledge base, a conventional approach is fusion of multiple KGs. One pivotal step for fusion is to align equivalent entities across different KGs. Conventional entity alignment approaches mainly compare symbolic features of enti- ties (Lacoste-Julien et al., 2013) or reason the co- relations by ontology matching (Jiménez-Ruiz and Grau, 2011). With the prosperity of node embed- ding (Grover and Leskovec, 2016), recent works favor learning entity embeddings for alignment and compare entities using embedding distance met- rics. Existing embedding methods for entity align- ment can be classified into three types: attribute- based (Sun et al., 2017), relation-based (Chen et al., 2017; Mao et al., 2020) and graph-based (Wang et al., 2018; Sun et al., 2020b). However, these embedding-based works study the problem in Euclidean space, where the embed- dings are Euclidean vectors. Recent research has proven that Euclidean space does not provide the most powerful geometrical representations for com- plex data that exhibit a highly non-Euclidean latent anatomy (Bronstein et al., 2017; Hui and Ku, 2022). To tackle this challenge, a variety of remarkable embedding methods have been developed to repre- sent the data in hyperbolic space. The distinctive feature of hyperbolic spaces enables us to embed hierarchical data while …

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