Networks and data supported on graphs have become ubiquitous in the sciences and engineering. This paper studies the ‘blind’ community detection problem, where we seek to infer the community structure of a graph model given the observation of independent graph signals on a set of nodes whose connections are unknown. We model each observation as filtered white noise, where the underlying network structure varies with every observation. These varying network structures are modeled as independent realizations of a latent planted partition model (PPM), justifying our assumption of a constant underlying community structure over all observations. Under certain conditions on the graph filter and PPM parameters, we suggest simple algorithms for determining (i) the number of latent communities and (ii) the associated partitions of the PPM. We then prove statistical guarantees in the asymptotic and non-asymptotic sampling cases. Numerical experiments on real and synthetic data demonstrate the efficacy of these algorithms.

中文翻译：

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从多个图上的信号进行精确的盲社区检测

图支持的网络和数据在科学和工程中无处不在。本文研究了“盲”社区检测问题，我们试图在给定连接未知的一组节点上观察独立图信号的情况下推断图模型的社区结构。我们将每个观察建模为过滤后的白噪声，其中底层网络结构随每次观察而变化。这些不同的网络结构被建模为潜在种植分区模型 (PPM) 的独立实现，证明了我们对所有观察结果的潜在社区结构不变的假设。在图过滤器和 PPM 参数的某些条件下，我们建议使用简单的算法来确定 (i) 潜在社区的数量和 (ii) PPM 的相关分区。然后我们证明渐近和非渐近采样情况下的统计保证。真实数据和合成数据的数值实验证明了这些算法的有效性。