Network embedding on metric of relation

Network embedding maps the nodes of a given network into a low-dimensional space such that the semantic similarities among the nodes can be effectively inferred. Most existing approaches use inner-product of node embeddings to measure the similarity between nodes leading to the fact that they lack the capacity to capture complex relationships among nodes. Moreover, they take only structural information but not semantical information when deciding paths in the embedding. In this paper, We propose a novel method called Network Embedding on the Metric of Relation, abbreviated as NEMR, which can learn the embeddings of nodes in a relational metric space efficiently. It first models the relationships among nodes in a metric space with deep learning methods including variational inference that maps the relationship of nodes to a gaussian distribution so as to capture the uncertainties, then infers the embeddings of the nodes by considering not only the equivalence of multiple-paths in order to capture the multiple relationships among nodes that should have the same semantical distance, e.g., age, hobby and profession, but also the natural order of nodes along the path in calculating similarity distance. Experimental results on several public datasets show that the NEMR outperforms the state-of-the-art methods on relevant inference tasks including link prediction and node classification.