Community Detection using Nonnegative Matrix Factorization with Orthogonal Constraint

Community structure is one of the most important properties for understanding the topology and function of a complex network. Recently, the rank reduction technique, non-negative matrix factorization (NMF), has been successfully used to uncover communities in complex networks. In the machine learning literature, the algorithm Alternating Constraint Least Squares (ACLS) is developed to perform NMF with sparsity constraint for clustering data and showed good performance, but it is not used in detecting communities in networks. In this study, we first test the ACLS algorithm on several synthetic and real networks to show its performance on community detection. Then we extend ACLS to orthogonal nonnegative matrix factorization, propose ALSOC, in which orthogonality constraint is added into NMF to discovery communities. The experimental results show that NMF with orthogonality constraint is able to improve the performance of community detection, meanwhile it has ability to maintain the sparsity of matrix factors.