Community Detection with a Subsampled Semidefinite Program
This work is an incremental theoretical validation of a computational speed-up technique for community detection, which benefits researchers working with large graphs.
This paper addresses the computational slowness of semidefinite programs (SDPs) in community detection by validating a subsampling technique. It provides a positive answer to a conjecture regarding the statistical limits of this technique for the stochastic block model with two balanced communities.
Semidefinite programming is an important tool to tackle several problems in data science and signal processing, including clustering and community detection. However, semidefinite programs are often slow in practice, so speed up techniques such as sketching are often considered. In the context of community detection in the stochastic block model, Mixon and Xie \cite{mixon2020sketching} have recently proposed a sketching framework in which a semidefinite program is solved only on a subsampled subgraph of the network, giving rise to significant computational savings. In this short paper, we provide a positive answer to a conjecture of Mixon and Xie about the statistical limits of this technique for the stochastic block model with two balanced communities.