Orthogonal Symmetric Nonnegative Matrix Factorization With Low-Rank Tensor Representation for Multilayer Network Community Detection

Multilayer networks community detection plays an important role in data mining. It can discover the latent representations of network structures for effectively completing downstream tasks. However, existing community detection methods rarely consider the relationships between multilayer networks. In addition, the noise contained in the networks always leads to the degradation of detection performance. To address the above issues, this article proposes an orthogonal symmetric nonnegative matrix factorization (SNMF) with low-rank tensor representation (OSNMFTR) for multilayer networks community detection. Specifically, the proposed approach obtains the latent representation of each network via orthogonal SNMF, then a clean self-representation tensor is got based on subspace learning. Finally, to discover the high-order relationships among each network, a weighted tensor nuclear norm is utilized to constrain the tensor to make it low-rank. An algorithm based on the alternating direction method of multipliers (ADMMs) is designed to solve the OSNMFTR model. The experiments on nine datasets show the superior performance of the proposed approach.