  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. To the best
of our knowledge, this is the first attempt to use Riemannian optimization for
community detection problem. Numerical experimental results on synthetic
benchmarks and real-world networks show that our algorithm is effective and
outperforms several state-of-art algorithms.
