Hierarchical Stochastic Block Model for Community Detection in Multiplex Networks
Hierarchical Stochastic Block Model for Community Detection in Multiplex Networks
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DOI：
10.1214/22-ba1355
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发表时间：
2019-03
期刊：
影响因子：
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通讯作者：
M. Paez;A. Amini;Lizhen Lin
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文献类型：
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作者：
M. Paez;A. Amini;Lizhen Lin
多路网络在许多领域中已经变得越来越普遍，并且已经成为模拟真实网络复杂性的有力工具。迫切需要为多路网络开发能够考虑跨不同层的潜在依赖关系的推理模型，特别是当目标是社区检测时。在有限的文献基础上，我们提出了一种新的、高效的贝叶斯多路网络社区检测模型。我们方法的一个关键功能是能够在不同的网络层对不同的社区进行建模。相比之下，许多现有模型假定所有层都具有相同的社区。此外，我们的模型会自动获取每一层所需的社区数量(通过实际数据示例进行验证)。这很吸引人，因为确定社区的数量是社区检测的一个具有挑战性的方面，如果允许社区跨层变化，在多重环境中尤其如此。借鉴分层贝叶斯建模的思想，我们在跨层建模社区标签之前使用了分层Dirichlet，允许它们的结构中的依赖性。在给定社区标签的情况下，假设每一层都采用随机分块模型(SBM)。我们开发了一种高效的切片采样器，用于采样社区标签的后验分布以及社区之间的链接概率。在这样做的过程中，我们解决了SBM的复杂可能性与标签上先验的分层性质相结合所带来的一些独特的挑战。在模拟和真实数据上进行了广泛的经验验证，证明了该模型优于单层方案的性能，以及发现真实网络中有趣结构的能力。
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.