Tracking and detecting dynamic communities with node popularity preservation

Temporal networks are increasingly prevalent in modern data, and the analysis of such networks can uncover the important phenomenon and characterize the properties of networks of dynamical units. This paper presents a new community detection model using nonnegative matrix factorization (NMF) which is capable of detecting and tracking dynamic communities in temporal networks. A novel temporal smoothness constraint by preserving the expected node popularity of two consecutive time-slices is proposed, and the community membership transition matrices are introduced to capture the sudden changes in network topologies in dynamic cases. We then propose a gradient descent algorithm to optimize objective function and prove its correctness and convergence. Experimental results on some synthetic and real benchmarked networks show the effectiveness of the proposed new method in detecting communities as well as finding their changes in dynamic networks.