Learning Low-dimensional Multi-domain Knowledge Graph Embedding via Dual Archimedean Spirals (2024)

Abstract: Knowledge graph embedding (KGE) is extensively employed for link prediction by representing entities and relations as low-dimensional vectors. In real-world scenarios, knowledge graphs (KGs) usually encompass diverse domains, which poses challenges to KG representations. However, existing KGE methods rarely make domain constraints on the embedding distribution of multi-domain KGs, leading to the embedding overlapping of different domains and performance degradation of link prediction. To address this challenge, we propose Du al A rchimedean S piral Knowledge Graph E mbedding (DuASE), a low-dimensional KGE model for multi-domain KGs. DuASE is inspired by our discovery that relation types can distinguish entities from different domains. Specifically, DuASE encodes entities with the same relation on the same Archimedean spiral, allowing it to differentiate the entities from different domains. To avoid embedding overlapping across domains, DuASE further makes the head and the tail spirals in the same triplet cluster to their respective domain space by a regularization function. Thus, DuASE can better capture the domain information and the dependencies between entities when modeling the multi-domain KGs, leading to improved KG representations. We validate the effectiveness of DuASE on the novel multi-domain dataset ( n -MDKG) introduced in this study and three other benchmark datasets.

## introduction knowledge graphs (kgs) represent networks of real-world entities and describe the associations between them, which play a crucial role in various tasks, including large language models @xcite @xcite , information retrieval @xcite and ques-tion answering @xcite . nonetheless, the incompleteness of kgs will lead to unfavorable outcomes in related tasks. therefore, researchers propose many knowledge graph embedding (kge) approaches @xcite to predict the missing links based on the known triplets. since high-dimensional kge methods require large memory and high computation costs @xcite , the low-dimensional kge methods have gained popularity @xcite @xcite . however, most existing kge methods, including low-dimension methods, ignore the multi-domain characteristics of kgs, and mining multi-domain information within kgs is essential for enhancing link prediction performance. in the context of kg, the term "domain" is used to describe a specific subject area or category of knowledge that the kg encompasses or represents. in reality, most kgs span a variety of domains, including sports, medicine, law, history, etc. the ignorance of making domain distinctions in kge leads to the problem of embedding overlapping across different domains, consequently impairing the effectiveness of link prediction. as shown in figure 1 , there are overlaps among the embeddings learned by the complex, rotate, and roth on the 6-mdkg dataset with six domains. more details about embedding overlapping cross domains are computed via the jaccard index and discussed in appendix a. in fact, if the kge model takes into account the distinction between domains, it can reduce the errors in the link prediction section. this is because there are significant differences in the types of relationships between entities in different domains. to effectively model multi-domain kgs, this paper imposes domain constraints in kge and proposes a low-dimensional kge model duase, which avoids the embedding overlapping and improves the performance of link prediction. our motivation is based on the following two aspects. first, it is reasonable to distinguish different domains via the relations in the kg triplets. in kgs, the differences among domains are mainly in entity types and relation types. since entity type information is not available in most kgs, we mainly rely on relation types in knowledge triplets to accomplish domain knowledge differentiation. we list some domains and their relations: specifically, duase maps the entities in knowledge triplets onto the relation archimedean spiral. duase further enforces the dual spirals of the head and the tail entities in the same triplet to be as close as possible by a regularization function. this clusters the learned embedding into their respective domain space and avoids the embedding overlapping across different domains. thus, du-ase can better capture the domain information and the dependencies between entities when modeling the multi-domain kgs, leading to improved kg representations. figure 1 shows that the proposed duase can effectively model domain distinction. we validate the effectiveness of duase on our proposed multi-domain dataset (n-mdkg) and three other benchmark datasets. furthermore, benefiting from the proposed dual archimedean spirals, duase can capture impor-tant relation patterns (symmetry, antisymmetry, inversion and composition) in low-dimensional space. we provide formal proofs of such ability of our model in appendix b. it further reinforces the reliability and robustness of our model in capturing meaningful patterns and associations among entities. our contributions are summarized as follows: ## conclusion given the importance of mining domain information in multi-domain kge and the fact that relations play an important role in distinguishing different domains, this paper proposes a low-dimension kge model, named dual archimedean spirals knowledge graph embedding model (duase). du-ase maps entities with the same relation on the same archimedean spiral. different spirals can model various relations for domain distinguishing through parameter b, and different rotation angles (parameter θ) of the same spiral can model differ-ent entities. meanwhile, we propose the dual spiral regularizer to cluster the spirals into their respective domain space. the experimental results fully illustrate that duase can better model multi-domain kg than previous methods and avoid embedding overlapping. in addition, we construct the datasets n-mdkg for multi-domain kge.