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：多层网络的日益普及迫切需要考虑不同层之间的潜在依赖性，尤其是在以社区检测（网络分析中的一项基本学习任务）为目标时。我们提出了一种全贝叶斯混合模型，用于单层和多层网络中的社区检测。该模型的一个关键特征是将通常随网络数据一起提供的节点属性联合建模为潜空间上的空间过程。此外，针对多层网络，我们的模型允许各层在独特的潜位置结构中具有不同的依赖强度，并假设两个参与者之间（在某一层中）的关系概率取决于其潜位置之间的距离（乘以特定层的因子）以及节点属性之间的差异。在我们的先验设定下，参与者在潜空间中的位置来自有限高斯混合分布，每个组分对应一个聚类。模拟示例表明，我们的模型优于现有基准模型，并且在处理含缺失值的数据集时表现出显著更强的鲁棒性。该模型还应用于一个由律师事务所员工组成的真实三层网络。