Multi-Frequency Joint Community Detection and Phase Synchronization

This paper studies the joint community detection and phase synchronization problem on stochastic block model with relative phase , where each node is associated an unknown angle. problem, a variety of real-world applications, aims to recover cluster structure angles simultaneously. We show this exhibits xmlns:xlink="http://www.w3.org/1999/xlink">“multi-frequency” by closely examining its maximum likelihood estimation (MLE) formulation, whereas existing methods are not originated from perspective. To end, two simple yet efficient algorithms that leverage MLE formulation benefit information across multiple frequencies proposed. The former spectral method based novel multi-frequency column-pivoted QR factorization. factorization applied top eigenvectors observation matrix provides key about angles. second approach iterative generalized power method, iteration updates in matrix-multiplication-then-projection manner. Numerical experiments our proposed significantly improve ability exactly recovering accuracy estimated angles, compared state-of-the-art algorithms.