Exact minimax optimality of spectral methods in phase synchronization and orthogonal group synchronization
相位同步与正交群同步中谱方法的精确极小极大最优性
We study the performance of the spectral method for the phase synchronization problem with additive Gaussian noises and incomplete data. The spectral method utilizes the leading eigenvector of the data matrix followed by a normalization step. We prove that it achieves the minimax lower bound of the problem with a matching leading constant under a squared ℓ2 loss. This shows that the spectral method has the same performance as more sophisticated procedures including maximum…