Community Detection in Multilayer Networks Via Semi-Supervised Joint Symmetric Nonnegative Matrix Factorization

Community detection plays an important role in network analysis and has attracted considerable interest from researchers. In the past few decades, various community detection algorithms have been developed for single networks. However, in the real world, relationships between nodes are often of multiple natures, such as friendship, kinship and common interests among people in social networks. These relationships can be modeled by a multilayer network. Thus, identifying communities in multilayer networks has become a challenging problem. The existing algorithms for multilayer networks only utilize the topological structure and ignore the prior information, thereby resulting in low accuracy. In this article, by combining the graph regularization with the prior information, we propose a semi-supervised joint symmetric nonnegative matrix factorization(SSJSNMF) algorithm for community detection in multilayer networks. We use graph regularization term to penalize the latent space dissimilarity of some nodes when prior information shows that these nodes belong to same community. Then, by fusing graph regularization into a joint symmetric nonnegative matrix factorization(NMF) model, the proposed model can utilize the topological structure information and prior information simultaneously. Furthermore, we develop effective multiplicative updating rules to solve the proposed model. Finally, numerical experiments demonstrate that SSSNMF outperforms some existing algorithms.