DCNMF: Dynamic Community Discovery with Improved Convex-NMF in Temporal Networks

For its crucial importance in the study of temporal networks, techniques for detecting community structures and tracking evolutionary behaviors have been developed. Among these techniques, evolutionary clustering is an efficient method which unveils substructures in complex networks and models the evolution of a system. Most research works in this domain mainly employ Semi-NMF to discover evolving communities. However, in some cases, it can not jointly maintain the quality of community detection and track the temporal evolution infallibly. In this paper, we present a novel community discovery model based on an evolutionary clustering framework using convex non-negative matrix factorization (Convex-NMF), called DCNMF. It is an improvement of Semi-NMF when applied in temporal networks to detect and track evolutionary communities. The proposed model, with temporal smoothness constraint considering the Convex-NMF results, is more accurate and robust both than the evolutionary clustering method based on Semi-NMF and some other existing methods. Specifically, we adopt the gradient descent algorithm to optimize the objective function and prove the correctness and convergence of the algorithm. Experimental results on several synthetic benchmarks and real-world networks show the effectiveness of the proposed method in discovering communities and tracking evolution in dynamic networks.