The increasing prevalence of multiplex networks has spurred a critical need to take into account potential dependencies across different layers, especially when the goal is community detection, which is a fundamental learning task in network analysis. We propose a full Bayesian mixture model for community detection in both single-layer and multi-layer networks. A key feature of our model is the joint modeling of the nodal attributes that often come with the network data as a spatial process over the latent space. In addition, our model for multi-layer networks allows layers to have different strengths of dependency in the unique latent position structure and assumes that the probability of a relation between two actors (in a layer) depends on the distances between their latent positions (multiplied by a layer-specific factor) and the difference between their nodal attributes. Under our prior specifications, the actors' positions in the latent space arise from a finite mixture of Gaussian distributions, each corresponding to a cluster. Simulated examples show that our model outperforms existing benchmark models and exhibits significantly greater robustness when handling datasets with missing values. The model is also applied to a real-world three-layer network of employees in a law firm.

翻译：随着多层网络的日益普及，亟需考虑不同层之间潜在的依赖关系，尤其是在以社区检测为目标时——这是网络分析中的一项基本学习任务。本文提出了一种用于单层及多层网络社区检测的完整贝叶斯混合模型。该模型的核心特点是将常伴随网络数据出现的节点属性，作为潜在空间上的空间过程进行联合建模。此外，我们的多层网络模型允许各层在独特的潜在位置结构中具有不同的依赖强度，并假设两个行动者（在某层中）产生关联的概率取决于其潜在位置之间的距离（乘以层特定因子）及其节点属性之间的差异。根据我们的先验设定，行动者在潜在空间中的位置来源于高斯分布的有限混合，每个混合成分对应一个簇。模拟实验表明，本模型优于现有基准模型，且在处理含缺失值的数据集时表现出显著更强的鲁棒性。该模型亦应用于一个律师事务所员工构成的三层现实网络。