In this work, we study the problem of community detection in the stochastic block model with adversarial node corruptions. Our main result is an efficient algorithm that can tolerate an $\epsilon$-fraction of corruptions and achieves error $O(\epsilon) + e^{-\frac{C}{2} (1 \pm o(1))}$ where $C = (\sqrt{a} - \sqrt{b})^2$ is the signal-to-noise ratio and $a/n$ and $b/n$ are the inter-community and intra-community connection probabilities respectively. These bounds essentially match the minimax rates for the SBM without corruptions. We also give robust algorithms for $\mathbb{Z}_2$-synchronization. At the heart of our algorithm is a new semidefinite program that uses global information to robustly boost the accuracy of a rough clustering. Moreover, we show that our algorithms are doubly-robust in the sense that they work in an even more challenging noise model that mixes adversarial corruptions with unbounded monotone changes, from the semi-random model.
翻译：在这项工作中,我们研究的是使用对抗节点腐败的随机区块模型中的社区探测问题。我们的主要结果是一个高效的算法,它能够容忍美元/欧元的腐败,并实现错误$O(\\ epsilon) + e ⁇ -\\\\\ fsc{C ⁇ 2} (1\\ pm o(1)) 美元,其中,美元= (cqrt{a} -\ sqrt{b}}) =2美元是信号对音比,美元/美元/美元和美元/美元/美元/美元/美元是社区之间和社区内部联系的概率。这些界限基本上符合SBM的微缩速率,而没有腐败。我们还为$\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
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