Multilayer networks are a useful data structure for simultaneously capturing multiple types of relationships between a set of nodes. In such networks, each relational definition gives rise to a layer. While each layer provides its own set of information, community structure across layers can be collectively utilized to discover and quantify underlying relational patterns between nodes. To concisely extract information from a multilayer network, we propose to identify and combine sets of layers with meaningful similarities in community structure. In this paper, we describe the “strata multilayer stochastic block model” (sMLSBM), a probabilistic model for multilayer community structure. The central extension of the model is that there exist groups of layers, called “strata”, which are defined such that all layers in a given stratum have community structure described by a common stochastic block model (SBM). That is, layers in a stratum exhibit similar node-to-community assignments and SBM probability parameters. Fitting the sMLSBM to a multilayer network provides a joint clustering that yields node-to-community and layer-to-stratum assignments, which cooperatively aid one another during inference. We describe an algorithm for separating layers into their appropriate strata and an inference technique for estimating the SBM parameters for each stratum. We demonstrate our method using synthetic networks and a multilayer network inferred from data collected in the Human Microbiome Project.

中文翻译：

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使用 Strata 多层随机块模型对网络层进行聚类


多层网络是一种有用的数据结构，可同时捕获一组节点之间的多种类型的关系。在这样的网络中，每个关系定义都会产生一个层。虽然每一层都提供自己的信息集，但可以共同利用跨层的社区结构来发现和量化节点之间的底层关系模式。为了从多层网络中简洁地提取信息，我们建议识别并组合在社区结构中具有有意义的相似性的层集。在本文中，我们描述了“地层多层随机块模型”（sMLSBM），这是一种多层群落结构的概率模型。该模型的核心扩展是存在称为“层”的层组，这些层的定义使得给定层中的所有层都具有由通用随机块模型（SBM）描述的社区结构。也就是说，层中的各层表现出相似的节点到社区分配和 SBM 概率参数。将 sMLSBM 拟合到多层网络提供了一种联合聚类，可产生节点到社区和层到层的分配，这些分配在推理过程中相互协作。我们描述了一种将各层分成适当层的算法以及用于估计每个层的 SBM 参数的推理技术。我们使用合成网络和从人类微生物组项目收集的数据推断出的多层网络来演示我们的方法。