We investigate the widely encountered problem of detecting communities in multiplex networks, such as social networks, with an unknown arbitrary heterogeneous structure. To improve detectability, we propose a generative model that leverages the multiplicity of a single community in multiple layers, with no prior assumption on the relation of communities among different layers. Our model relies on a novel idea of incorporating a large set of generic localized community label constraints across the layers, in conjunction with the celebrated Stochastic Block Model (SBM) in each layer. Accordingly, we build a probabilistic graphical model over the entire multiplex network by treating the constraints as Bayesian priors. We mathematically prove that these constraints/priors promote existence of identical communities across layers without introducing further correlation between individual communities. The constraints are further tailored to render a sparse graphical model and the numerically efficient Belief Propagation algorithm is subsequently employed. We further demonstrate by numerical experiments that in the presence of consistent communities between different layers, consistent communities are matched, and the detectability is improved over a single layer. We compare our model with a “correlated model” which exploits the prior knowledge of community correlation between layers. Similar detectability improvement is obtained under such a correlation, even though our model relies on much milder assumptions than the correlated model. Our model even shows a better detection performance over a certain correlation and signal to noise ratio (SNR) range. In the absence of community correlation, the correlation model naturally fails, while ours maintains its performance.

中文翻译：

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多路复用网络中的社区检测和改进的可检测性

我们调查了在具有未知任意异构结构的多重网络（例如社交网络）中检测社区的广泛遇到的问题。为了提高可检测性，我们提出了一种生成模型，该模型利用多层中单个社区的多样性，而无需事先假设不同层之间的社区关系。我们的模型依赖于一种新颖的想法，即在各层中结合大量通用本地化社区标签约束，并结合每一层中著名的随机块模型 (SBM)。因此，我们通过将约束视为贝叶斯先验，在整个多路复用网络上构建概率图模型。我们在数学上证明了这些约束/先验促进了跨层相同社区的存在，而不会在各个社区之间引入进一步的相关性。进一步调整约束以呈现稀疏图形模型，随后采用数值有效的置信传播算法。我们通过数值实验进一步证明，在不同层之间存在一致社区的情况下，一致社区是匹配的，并且在单层上提高了可检测性。我们将我们的模型与利用层之间社区相关性的先验知识的“相关模型”进行比较。在这种相关性下获得了类似的可检测性改进，即使我们的模型依赖于比相关模型更温和的假设。我们的模型甚至在一定的相关性和信噪比 (SNR) 范围内显示出更好的检测性能。在没有社区相关性的情况下，相关性模型自然会失败，而我们的模型保持其性能。