A random projection method for large-scale community detection

In this work, we consider a random projection method for a large-scale community detection task. We introduce a random Gaussian matrix that generates several projections on the column space of the network adjacency matrix. The $k$-means algorithm is then applied with the low-dimensional projected matrix. The computational complexity is much lower than that of the classic spectral clustering methods. Furthermore, the algorithm is easy to implement and accessible for privacy preservation. We can theoretically establish a strong consistency result of the algorithm under the stochastic block model. Extensive numerical studies are conducted to verify the theoretical findings and illustrate the usefulness of the proposed method.