Joint Community Detection and Rotational Synchronization via Semidefinite Programming

TL;DR

This paper introduces semidefinite programming methods to simultaneously classify and synchronize rotated objects in heterogeneous data, achieving exact recovery under a new stochastic block model with a sharp phase transition.

Contribution

It develops novel semidefinite relaxations for joint community detection and rotational synchronization, extending existing models and providing theoretical guarantees for exact recovery.

Findings

Semidefinite relaxations achieve exact recovery under the extended stochastic block model.

Numerical experiments confirm the effectiveness and phase transition behavior of the proposed algorithms.

The methods outperform existing approaches in the joint detection and synchronization tasks.

Abstract

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.