Multi-Frequency Joint Community Detection and Phase Synchronization
share
This paper studies the joint community detection and phase synchronization problem on the stochastic block model with relative phase, where each node is associated with a phase. This problem, with a variety of real-world applications, aims to recover community memberships and associated phases simultaneously. By studying the maximum likelihood estimation formulation, we show that this problem exhibits a “multi-frequency” structure. To this end, two simple yet efficient algorithms that leverage information across multiple frequencies are proposed. The former is a spectral method based on the novel multi-frequency column-pivoted QR factorization, and the latter is an iterative multi-frequency generalized power method. Numerical experiments indicate our proposed algorithms outperform state-of-the-art algorithms, in recovering community memberships and associated phases.
READ FULL TEXT
