Non-Convex Joint Community Detection and Group Synchronization via Generalized Power Method

TL;DR

This paper introduces a Generalized Power Method for joint community detection and group synchronization, achieving faster exact recovery under the stochastic group block model than traditional semidefinite programming methods.

Contribution

The paper presents a novel non-convex algorithm that outperforms existing methods in efficiency and accuracy for simultaneous community detection and group synchronization.

Findings

GPM achieves exact recovery in O(n log^2 n) time.

GPM outperforms SDP in computational efficiency.

Theoretical bounds show GPM surpasses information-theoretic thresholds.

Abstract

This paper proposes a Generalized Power Method (GPM) to tackle the problem of community detection and group synchronization simultaneously in a direct non-convex manner. Under the stochastic group block model (SGBM), theoretical analysis indicates that the algorithm is able to exactly recover the ground truth in $O(n\log^2n)$ time, sharply outperforming the benchmark method of semidefinite programming (SDP) in $O(n^{3.5})$ time. Moreover, a lower bound of parameters is given as a necessary condition for exact recovery of GPM. The new bound breaches the information-theoretic threshold for pure community detection under the stochastic block model (SBM), thus demonstrating the superiority of our simultaneous optimization algorithm over the trivial two-stage method which performs the two tasks in succession. We also conduct numerical experiments on GPM and SDP to evidence and complement our theoretical analysis.