Multi-view data arises frequently in modern network analysis e.g. relations of multiple types among individuals in social network analysis, longitudinal measurements of interactions among observational units, annotated networks with noisy partial labeling of vertices etc. We study community detection in these disparate settings via a unified theoretical framework, and investigate the fundamental thresholds for community recovery. We characterize the mutual information between the data and the latent parameters, provided the degrees are sufficiently large. Based on this general result, (i) we derive a sharp threshold for community detection in an inhomogeneous multilayer block model \citep{chen2022global}, (ii) characterize a sharp threshold for weak recovery in a dynamic stochastic block model \citep{matias2017statistical}, and (iii) identify the limiting mutual information in an unbalanced partially labeled block model. Our first two results are derived modulo coordinate-wise convexity assumptions on specific functions -- we provide extensive numerical evidence for their correctness. Finally, we introduce iterative algorithms based on Approximate Message Passing for community detection in these problems.

翻译：多视角数据在现代网络分析中频繁出现，例如社交网络分析中个体间的多种类型关系、观测单元交互的纵向测量、以及带有噪声部分顶点标注的带注释网络等。我们通过统一的理论框架研究这些不同场景下的社区检测，并探究社区恢复的基本阈值。在度数足够大的条件下，我们刻画了数据与潜在参数之间的互信息。基于这一普遍结果，（i）推导了非齐次多层区块模型 \citep{chen2022global} 中社区检测的精确阈值，（ii）刻画了动态随机区块模型 \citep{matias2017statistical} 中弱恢复的精确阈值，（iii）确定了非平衡部分标记区块模型中的极限互信息。前两个结果是在特定函数坐标凸性假设下推导得出的——我们提供了大量数值证据支持其正确性。最后，我们引入基于近似消息传递的迭代算法来解决这些问题的社区检测。