This paper considers a new framework to detect communities in a graph from the observation of signals at its nodes. We model the observed signals as noisy outputs of an unknown network process, represented as a graph filter that is excited by a set of unknown low-rank inputs/excitations. Application scenarios of this model include diffusion dynamics, pricing experiments, and opinion dynamics. Rather than learning the precise parameters of the graph itself, we aim at retrieving the community structure directly. The paper shows that communities can be detected by applying a spectral method to the covariance matrix of graph signals. Our analysis indicates that the community detection performance depends on an intrinsic ‘low-pass’ property of the graph filter. We also show that the performance can be improved via a low-rank matrix plus sparse decomposition method when the latent parameter vectors are known. Numerical results demonstrate that our approach is effective.

中文翻译：

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从图过滤器的低阶激励中进行盲社区检测

本文考虑了一种新框架，通过观察节点上的信号来检测图中的社区。我们将观察到的信号建模为未知网络过程的噪声输出，表示为由一组未知的低秩输入/激发激发的图滤波器。该模型的应用场景包括扩散动态、定价实验和意见动态。我们的目标不是学习图本身的精确参数，而是直接检索社区结构。该论文表明，可以通过将谱方法应用于图信号的协方差矩阵来检测社区。我们的分析表明，社区检测性能取决于图过滤器的内在“低通”属性。我们还表明，当潜在参数向量已知时，可以通过低秩矩阵加稀疏分解方法来提高性能。数值结果表明我们的方法是有效的。