A Fused G romov- W asserstein Framework for Unsupervised Knowledge Graph Entity Alignment (2023)

Abstract: Entity alignment is the task of identifying corresponding entities across different knowledge graphs (KGs). Although recent embedding-based entity alignment methods have shown significant advancements, they still struggle to fully utilize KG structural information. In this paper, we introduce FGWEA, an unsupervised entity alignment framework that leverages the Fused Gromov-Wasserstein (FGW) distance, allowing for a comprehensive comparison of entity semantics and KG structures within a joint optimization framework. To address the computational challenges associated with optimizing FGW, we devise a three-stage progressive optimization algorithm. It starts with a basic semantic embedding matching, proceeds to approximate cross-KG structural and relational similarity matching based on iterative updates of high-confidence entity links, and ultimately culminates in a global structural comparison between KGs. We perform extensive experiments on four entity alignment datasets covering 14 distinct KGs across five languages. Without any supervision or hyper-parameter tuning, FGWEA surpasses 21 competitive baselines, including cutting-edge supervised entity alignment methods. Our code is available at https://github.com/squareRoot3/FusedGW-Entity-Alignment .

## introduction knowledge graph (kg) is one of structured data representations that characterizes real-world concepts (also known as entities) with their relationships and attributes. recent years have witnessed the proliferation of kgs in various areas, ranging from the general ones such as dbpedia @xcite and conceptnet @xcite , to those in specific domains such as healthcare @xcite , education @xcite , and e-commerce @xcite . as the information contained in each individual kg is limited and biased, entity alignment (ea) is proposed for linking equivalent entities across two kgs from different sources or languages, and integrating them into a new holistic-view kg. ea task has received a lot of attentions in the computational linguistics community, due to its ability to improve the completeness and fairness of kgs, and enhance a wide range of knowledge-driven downstream applications like question-answering @xcite and dialogue systems @xcite . figure 1 illustrates a toy example of cross-lingual ea between an english kg and a japanese kg. the main challenge of this task is to leverage the variety of information in kg, such as entity semantics and relations. in the deep learning era, embedding-based approaches have become the mainstream for ad-dressing the ea task, which primarily follows the "embedding-learning-and-matching" paradigm. as shown in the middle of figure 1 , the embedding module encodes entities from two kgs into a shared latent space. the matching module then infers equivalent entities from the embeddings. the basic principle behind embedding-based ea is that equivalent entities in different kgs share similar neighborhood information. graph neural networks @xcite have been widely adopted as kg encoders, which are usually trained by margin-based losses that encourage equivalent entities to have similar embeddings. however, the design of the matching module has been overlooked in embedding-based ea. many existing methods use a greedy strategy that matches entity embeddings to their closest counterparts in another kg, which only relies on the embedding module to incorporate structural information. unfortunately, even the most powerful kg embedding models and graph neural networks fail to fully preserve structural information. although some recent methods have attempted to improve the matching module by treating it as a global assignment problem @xcite or an optimal transport problem @xcite , they still fall into the scope of embedding alignment and have limitations in utilizing kg structural information. to overcome the above issue, we propose fg-wea, an unsupervised ea framework based on the fused gromov-wasserstein (fgw) distance @xcite , which fuses entity embedding alignment (via the wasserstein distance) and kg structure alignment (via the gromov-wasserstein distance) into a joint optimization framework. as shown in figure 1 , instead of only comparing entity embeddings as most embeddingbased ea methods did in the literature, the proposed fgwea jointly incorporates both kg semantics and structure information. in fact, fg-wea considers cross-kg structural and relational consistencies in optimization objectives to better exploit structural information, rather than implicitly encoding it into embeddings. moreover, after shifting the inclusion of structural information to the matching module and relieving the workload of embedding module, fgwea is more compatible with pre-trained language models, which only acts as a main tool for encoding semantic information. as directly optimizing fgw leads to inefficiency and inferior performance, fgwea executes a three-stage progressive optimization algorithm, which begins with a relatively simple semantic comparison and then moves on to a more challenging structural comparison. we further develop a fast approximation algorithm and an iterative multiview ot alignment module to efficiently compare the various kg information. experiments on four cross-lingual and cross-source ea datasets demonstrate that fgwea outperforms 21 existing ea methods, including both supervised and unsupervised state-of-the-art approaches. ## the proposed method we present an unsupervised ea framework, fg-wea, that performs entity matching based on the fgw distance. as shown in figure 2 , it comprises a semantic embedding module and a three-stage entity matching module. to address the aforementioned challenges, we propose a three-step progressive optimization algorithm. first, fgwea performs the straightforward semantic embedding matching to obtain high-confidence aligned entity pairs as anchors (section 3.1). building on these anchors, fgwea employs a fast approximation of gwd to compute cross-kg structural and relational similarities, which are then used for iterative multi-view ot alignment (section 3.2). upon achieving a better initial point for the coupling matrix, fgwea proceeds to comparing the global structures of kgs by optimizing gwd, the most challenging component in fgw (section 3.3). ## conclusion in this paper, we propose an unsupervised entity alignment framework named fgwea. instead of following the "embedding-learning-andmatching" paradigm, we invoke the fused gromov-wasserstein distance to realize a more explicit and comprehensive comparison of structural and semantic information between knowledge graphs. to realize the benefits of fgwea, we present a threestage progressive optimization algorithm to address the challenge of optimizing the fgw objective. experimental results show that fgwea outperforms both supervised and unsupervised state-of-the-art entity alignment methods. and srprs en_fr . the observation is consistent with section 4.5. two curves are highly correlated and the iteration corresponding to the minimum fgw objective value is approximately that to the maximum hit1 score.