Community Detection by a Riemannian Projected Proximal Gradient Method⁎⁎⁎This paper was partially supported by the U.S. National Science Foundation under grant DBI 1934157. The author WH was partially supported by the Fundamental Research Funds for the Central Universities (NO. 20720190060) and National Natural Science Foundation of China (NO. 12001455). Part of this work was performed while the author KG was a visiting professor at UC Louvain, funded by the Science and Technology Sector, with additional support by the Netherlands Organization for Scientific Research.

Community detection plays an important role in understanding and exploiting the structure of complex systems. Many algorithms have been developed for community detection using modularity maximization or other techniques. In this paper, we formulate the community detection problem as a constrained nonsmooth optimization problem on the compact Stiefel manifold. A Riemannian projected proximal gradient method is proposed and used to solve the problem. Numerical experimental results on synthetic benchmarks and real-world networks show that our algorithm is effective and outperforms several state-of-art algorithms.