Joint Community Detection and Rotational Synchronization via Semidefinite Programming
This addresses the challenge of simultaneously clustering and aligning rotated objects in multi-category data, representing an incremental advance by extending the stochastic block model to a new setting.
The paper tackles the joint problem of community detection and rotational synchronization in heterogeneous data, proposing semidefinite relaxations and proving exact recovery with a sharp phase transition, as confirmed by numerical experiments.
In the presence of heterogeneous data, where randomly rotated objects fall into multiple underlying categories, it is challenging to simultaneously classify them into clusters and synchronize them based on pairwise relations. This gives rise to the joint problem of community detection and synchronization. We propose a series of semidefinite relaxations, and prove their exact recovery when extending the celebrated stochastic block model to this new setting where both rotations and cluster identities are to be determined. Numerical experiments demonstrate the efficacy of our proposed algorithms and confirm our theoretical result which indicates a sharp phase transition for exact recovery.