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arXiv · 2112.14204

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

Sijin Chen·Xiwei Cheng·Anthony Man-Cho So
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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.

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Sijin Chen, Xiwei Cheng, Anthony Man-Cho So. 2021-12-28. Non-Convex Joint Community Detection and Group Synchronization via Generalized Power Method. https://arxiv.org/abs/2112.14204

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