# Non-Convex Exact Community Recovery in Stochastic Block Model

arXiv: https://arxiv.org/abs/2006.15843 · HTML: https://mlsanity.com/paper/2006.15843/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jun 2020.

## Built on by (most cited first, 5 of 5)

- [A Global Geometric Analysis of Maximal Coding Rate Reduction](https://mlsanity.com/paper/2406.01909/) (2024)
- [Convergence and Recovery Guarantees of the K-Subspaces Method for Subspace Clustering](https://mlsanity.com/paper/2206.05553/) (2022)
- [Exact Community Recovery over Signed Graphs](https://mlsanity.com/paper/2202.12255/) (2022)
- [Synthetic Principal Component Design: Fast Covariate Balancing with Synthetic Controls](https://mlsanity.com/paper/2211.15241/) (2022)
- [Dynamic angular synchronization under smoothness constraints](https://mlsanity.com/paper/2406.04071/) (2024)

## Abstract (arXiv)

Community detection in graphs that are generated according to stochastic block models (SBMs) has received much attention lately. In this paper, we focus on the binary symmetric SBM -- in which a graph of n vertices is randomly generated by first partitioning the vertices into two equal-sized communities and then connecting each pair of vertices with probability that depends on their community memberships -- and study the associated exact community recovery problem. Although the maximum-likelihood formulation of the problem is non-convex and discrete, we propose to tackle it using a popular iterative method called projected power iterations. To ensure fast convergence of the method, we initialize it using a point that is generated by another iterative method called orthogonal iterations, which is a classic method for computing invariant subspaces of a symmetric matrix. We show that in the logarithmic sparsity regime of the problem, with high probability the proposed two-stage method can exactly recover the two communities down to the information-theoretic limit in O(nlog2n/loglog n) time, which is competitive with a host of existing state-of-the-art methods that have the same recovery performance. We also conduct numerical experiments on both synthetic and real data sets to demonstrate the efficacy of our proposed method and complement our theoretical development.