Fast algorithm on stochastic block model for exploring general communities

Abstract

A stochastic block model can produce a wide variety of networks with different structures (named as general community, including traditional community, bipartite structure, hierarchical structure and etc); it also can detect general community in networks according to the rules of stochastic equivalence. However, the simple stochastic block model has some problems in modeling the generation of the networks and learning the models, showing poor results in fitting the practical networks. The GSB (general stochastic block) model is an extension of the stochastic block model, which is based on the idea of link community and is provided to detect general communities. But its complexity limits its applications in medium and large networks. In order to explore the latent structures of networks with different scales without prior knowledge about networks, a fast algorithm on the GSB model (FGSB) is designed to explore general communities in networks faster. FGSB dynamically learns the parameters related to the network structure in the process of iterations. It reduces the storage memory by reorganizing parameters to cut down unnecessary parameters, and saves the running time by pruning the related parameters of converging nodes and edges to decrease the computing time of each iteration. FGSB has the same ability of structure detection as the GSB model, but its complexities of time and storage are lower. Tests on synthetic benchmarks and real-world networks have demonstrated that FGSB not only can run faster than the algorithm of the GSB model in the similar accuracy, but also can detect general communities for large networks. ©Copyright 2013, Institute of Software, the Chinese Academy of Sciences.