Community preserving mapping for network hyperbolic embedding

Abstract

Hyperbolic embedding aims to reveal the hidden space by capturing most of the properties observed in real networks. Most existing hyperbolic embedding models map to learn the representation vectors while preserving the microscopic adjacency, which cannot accurately represent the mesoscopic community structures. To this end, this study proposes a Community Preserving Hyperbolic Embedding model (CPHE). Specifically, we regularize the likelihood function of hyperbolic embedding by adding to the community co-occurrence relation (CCR). We then construct a closed loop for node embedding and community detection. Thus, the representation vectors and CCR alternately update. Finally, to avoid the distortion of the representing community, an equivalent majorization based on the sum of linear ratios programming is achieved for the numerical solution. Application experiments are implemented on both synthetic and real-world networks to evaluate the embedding performance. The accuracy and normalized mutual information (NMI) of community detection improved by approximately 3% and 2.4%, respectively, and the area under the receiver operating characteristic curve (AUROC) of link prediction improved by approximately 1.3%, demonstrating the advantages of the proposed model.