The community detection problem requires to cluster the nodes of a network into a small number of well-connected "communities". There has been substantial recent progress in characterizing the fundamental statistical limits of community detection under simple stochastic block models. However, in real-world applications, the network structure is typically dynamic, with nodes that join over time. In this setting, we would like a detection algorithm to perform only a limited number of updates at each node arrival. While standard voting approaches satisfy this constraint, it is unclear whether they exploit the network information optimally. We introduce a simple model for networks growing over time which we refer to as streaming stochastic block model (StSBM). Within this model, we prove that voting algorithms have fundamental limitations. We also develop a streaming belief-propagation (StreamBP) approach, for which we prove optimality in certain regimes. We validate our theoretical findings on synthetic and real data.

中文翻译：

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用于社区检测的流式信念传播

社区检测问题需要将网络节点聚集成少数连接良好的“社区”。最近在描述简单随机块模型下社区检测的基本统计限制方面取得了重大进展。然而，在实际应用中，网络结构通常是动态的，随着时间的推移节点会加入。在此设置中，我们希望检测算法在每个节点到达时仅执行有限数量的更新。虽然标准投票方法满足这一限制，但尚不清楚它们是否以最佳方式利用网络信息。我们为随时间增长的网络引入了一个简单的模型，我们将其称为流式随机块模型 (StSBM)。在这个模型中，我们证明投票算法具有根本的局限性。我们还开发了一种流式信念传播 (StreamBP) 方法，我们证明了在某些情况下的最优性。我们在合成数据和真实数据上验证了我们的理论发现。