Entity alignment (EA) aims to match identical entities across different knowledge graphs (KGs). Graph neural network-based entity alignment methods have achieved promising results in Euclidean space. However, KGs often contain complex local and hierarchical structures, which are hard to represent in a single space. In this paper, we propose a novel method named as UniEA, which unifies dual-space embedding to preserve the intrinsic structure of KGs. Specifically, we simultaneously learn graph structure embeddings in both Euclidean and hyperbolic spaces to maximize the consistency between embeddings in the two spaces. Moreover, we employ contrastive learning to mitigate the misalignment issues caused by similar entities, where embeddings of similar neighboring entities become too close. Extensive experiments on benchmark datasets demonstrate that our method achieves state-of-the-art performance in structure-based EA. Our code is available at https://github.com/wonderCS1213/UniEA.

Quaternion contains one real part and three imaginary parts, which provided a more expressive hypercomplex space for learning knowledge graph. Existing quaternion embedding models measure the plausibility of a triplet either through semantic matching or distance scoring functions. However, it appears that semantic matching diminishes the separability of entities, while the distance scoring function weakens the semantics of entities. To address this issue, we propose a novel quaternion knowledge graph embedding model. Our model combines semantic matching with entity’s geometric distance to better measure the plausibility of triplets. Specifically, in the quaternion space, we perform a right rotation on the head entity and a reverse rotation on the tail entity to learn the rich semantic features. Then, we utilize distance adaptive translations to learn the geometric distance between entities. Furthermore, we provide mathematical proofs to demonstrate our model can handle complex logical relationships. Extensive experimental results and analyses show our model significantly outperforms previous models on well-known knowledge graph completion benchmark datasets. Our code is available at https://anonymous.4open.science/r/l2730.

Linear Graph Convolutional Networks (GCNs) are used to classify the node in the graph data. However, we note that most existing linear GCN models perform neural network operations in Euclidean space, which do not explicitly capture the tree-like hierarchical structure exhibited in real-world datasets that modeled as graphs. In this paper, we attempt to introduce hyperbolic space into linear GCN and propose a novel framework for Lorentzian linear GCN. Specifically, we map the learned features of graph nodes into hyperbolic space, and then perform a Lorentzian linear feature transformation to capture the underlying tree-like structure of data. Experimental results on standard citation networks datasets with semi-supervised learning show that our approach yields new state-of-the-art results of accuracy 74.7% on Citeseer and 81.3% on PubMed datasets. Furthermore, we observe that our approach can be trained up to two orders of magnitude faster than other nonlinear GCN models on PubMed dataset. Our code is publicly available at https://github.com/llqy123/LLGC-master.