Constrained common cluster based model for community detection in temporal and multiplex networks

Abstract

Abstract On one hand, the detection of tightly connected groups, also known as community detection in complex networks, is a prominent problem for network analysis and mining. On the other hand, almost all of social, biological, bibliographic, communication and computer systems are modeled as temporal networks, the topological structures of which evolve with time, or multiplex networks, each pair of nodes of which has multiple linked relations. Current methods of community detection for temporal networks are based on incremental, independent or evolutionary clustering, and for multiplex networks are based on fusion of the multiple links. However, all these methods ignore the common structure hidden in the networks, which is denoted as the common cluster here. So in this paper, we propose a constrained common cluster based model (C3 model) to analyze the temporal and multiplex networks, which can not only detect the community structure, but also identify the importance of each node based on the common cluster structure of both two classes of networks. The intrinsic assumption of the proposed model is that there are common or coincident clusters hidden in these networks. In detail, we first construct the Markov steady-state matrices of each snapshot of temporal network or each slice of multiplex network. Next, we propose the object function of C3 model by combining the Markov steady-state matrices, similarity matrices with community membership matrices of each snapshot or slice of the network. Last, a gradient descent algorithm based on non-negative matrix factorization is proposed for the object function. Experiments on both synthetic datasets and real-world networks demonstrate that the proposed C3 model has competitive performance based on the evaluation indexes NMI and error of community detection, otherwise, the proposed model could identify the importance of nodes of the temporal or multiplex networks.