Multiplex networks have become increasingly more prevalent in many fields, and have emerged as a powerful tool for modeling the complexity of real networks. There is a critical need for developing inference models for multiplex networks that can take into account potential dependencies across different layers, particularly when the aim is community detection. We add to a limited literature by proposing a novel and efficient Bayesian model for community detection in multiplex networks. A key feature of our approach is the ability to model varying communities at different network layers. In contrast, many existing models assume the same communities for all layers. Moreover, our model automatically picks up the necessary number of communities at each layer (as validated by real data examples). This is appealing, since deciding the number of communities is a challenging aspect of community detection, and especially so in the multiplex setting, if one allows the communities to change across layers. Borrowing ideas from hierarchical Bayesian modeling, we use a hierarchical Dirichlet prior to model community labels across layers, allowing dependency in their structure. Given the community labels, a stochastic block model (SBM) is assumed for each layer. We develop an efficient slice sampler for sampling the posterior distribution of the community labels as well as the link probabilities between communities. In doing so, we address some unique challenges posed by coupling the complex likelihood of SBM with the hierarchical nature of the prior on the labels. An extensive empirical validation is performed on simulated and real data, demonstrating the superior performance of the model over single-layer alternatives, as well as the ability to uncover interesting structures in real networks.
翻译:多式网络在许多领域越来越普遍,并已成为模拟真实网络复杂程度的强大工具。非常需要为多式网络开发能够考虑到不同层次潜在依赖性的多式网络推导模型,特别是在目标为社区探测的情况下。我们通过提出一种创新和高效的贝叶斯模式,在多式网络中进行社区探测,增加了有限的文献。我们的方法的一个重要特征是能够在不同网络层次上建模不同的社区。相比之下,许多现有模型在所有层次上都建模相同的社区。此外,我们的模型自动收集每个层次上的必要社区数目(经真实数据级实例验证 ) 。这很有吸引力,因为确定社区数目是社区探测的一个具有挑战性的方面,特别是在多式环境中,如果人们允许社区在多层网络中进行跨层间社区检测,我们用一种等级分级的Drichlet,然后建模社区模型,从各个层次上都具有依赖性。在每一层次上自动地设置一个可查的区块模型(SBM),在真实数据级网络上自动采集必要数量的社区数量。我们开发一个高效的级级级级结构,作为前级标签的比级链接,我们以展示了单一的比级结构的精确的比级结构。我们以展示了单一的比级结构的比级结构的比级结构。