Community detection via an efficient nonconvex optimization approach based on modularity

Abstract

Maximizing modularity is a widely used method for community detection, which is generally solved by approximate or greedy search because of its high complexity. In this paper, we propose a method, named MSM, for modularity maximization, which reformulates the modularity maximization problem as a subset identification problem and maximizes the surrogate of the modularity. The surrogate of the modularity is constructed by replacing the discontinuous indicator functions in the reformulated modularity function with the continuous truncated L1 function. This makes the NP-hard problem of maximizing the modularity function approximately become a non-convex optimization problem, which can be efficiently solved via the DC (Difference of Convex Functions) Programming. The proposed MSM method can be used for community detection when the number of communities is given, and it can also be applied to the situation where the number of communities is unknown. Then, we demonstrate the advantages of the proposed MSM method by some simulation results and real data analyses.