提出可处理有符号连续边权的社区检测模型，适合复杂网络分析。
Community Detection with Heterogeneous Block Covariance Model
- 基于协方差矩阵建模社区结构，支持正负连续边权。
- 在模拟数据中实现成员归属的可证明一致估计。
- 适用于单细胞测序和股票价格等真实复杂网络数据。
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）仅适用于二值边（有/无）的网络。但在许多实际场景中，边常具有连续权重，包含正负值，反映不同程度的连接强度。为此，本文提出异质块协方差模型（HBCM），在协方差矩阵中定义社区结构，允许边具有带符号的连续权重，并考虑对象间连接的异质性。提出一种新颖的变分期望-最大化算法以估计群体归属。理论证明该模型能提供成员归属的一致估计；数值模拟显示其在多种设置下表现优异。模型应用于小鼠胚胎单细胞RNA-seq数据集与股票价格数据集，验证了实用性。补充材料在线可获取。
原文摘要 · Abstract (English)
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.
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