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 $L_1$ 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.

最大化模块化是一种广泛使用的社区检测方法，由于其复杂性高，通常可以通过近似或贪婪搜索来解决。在本文中，我们提出了一种名为MSM的模块化最大化方法，该方法将模块化最大化问题重新定义为子集标识问题，并最大化了模块化的替代性。模块化的替代方法是通过用连续的截断代替新格式的模块化函数中的不连续指标函数${\mathrm{大号}}_{\mathrm{1个}}$功能。这使得最大化模块化函数的NP难题大约变成了非凸优化问题，可以通过DC（凸函数之差）编程有效地解决该问题。给出社区数量时，提出的MSM方法可用于社区检测，也可用于社区数量未知的情况。然后，通过一些仿真结果和实际数据分析，证明了所提出的MSM方法的优点。