GBTM: Community detection and network reconstruction for noisy and time-evolving data

Community detection and network reconstruction are two major concerns in network analysis. However, these two tasks are extremely challenging since most of the existing methods are not suitable for noisy and red time-evolving data, which are common in real world situations. To cope with this, we propose a novel method called the group-based binary time-evolving mixture (GBTM) model to detect communities and recover network structures jointly. This is the first to study address the challenges of community detection and network reconstruction in scenarios where data are dynamic and cannot be directly observed. In this work, the hidden Markov method is employed to capture the temporal evolution of node connections. In addition, we develop the grouped Baum-Welch algorithm for parameter estimation using a forward-backward procedure. Our GBTM model shows that conducting community detection and network reconstruction simultaneously can yield synergistic benefits. Furthermore, we introduce an innovative Bayesian information criterion (BIC) for determining the number of communities. The results of various simulations under different settings and two real -world networks show that the proposed GBTM model outperforms the existing community detection or network reconstruction methods and has great potential for solving time-evolving and noisy network problems.