Community detection is the task of clustering objects based on their pairwise relationships. Most of the model-based community detection methods, such as the stochastic block model and its variants, are designed for networks with binary (yes/no) edges. In many practical scenarios, edges often possess continuous weights, spanning positive and negative values, which reflect varying levels of connectivity. To address this challenge, we introduce the heterogeneous block covariance model (HBCM) that defines a community structure within the covariance matrix, where edges have signed and continuous weights. Furthermore, it takes into account the heterogeneity of objects when forming connections with other objects within a community. A novel variational expectation-maximization algorithm is proposed to estimate the group membership. The HBCM provides provable consistent estimates of memberships, and its promising performance is observed in numerical simulations with different setups. The model is applied to a single-cell RNA-seq dataset of a mouse embryo and a stock price dataset. Supplementary materials for this article are available online.

翻译：社区检测是根据对象间的成对关系进行聚类的任务。大多数基于模型的社区检测方法，如随机块模型及其变体，都是为具有二元（是/否）边的网络设计的。在许多实际场景中，边通常具有连续权重，涵盖正值和负值，这反映了不同水平的连接强度。为应对这一挑战，我们引入了异质块协方差模型（HBCM），该模型在协方差矩阵内定义了一种社区结构，其中边具有带符号的连续权重。此外，该模型考虑了对象在社区内与其他对象形成连接时的异质性。我们提出了一种新颖的变分期望最大化算法来估计群体成员关系。HBCM 提供了可证明一致的成员关系估计，并在不同设置的数值模拟中观察到了其良好的性能。该模型被应用于小鼠胚胎的单细胞 RNA-seq 数据集和一个股票价格数据集。本文的补充材料可在线获取。