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 can be collectively utilized to discover and quantify underlying relational patterns. To most 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 assumption of the model is that there exist groups of layers, that we call strata, with community structure described by a common stochastic block model (SBM). That is, layers in a stratum exhibit similar node-to-community assignments as well as SBM probability parameters. Fitting the sMLSBM to a multilayer network provides a joint clustering of nodes and layers with node-to-community and layer-to-strata assignments interactively aiding each other in inference. We describe an algorithm for separating layers into their appropriate strata and an inference technique for estimating the stochastic block model parameters describing each stratum. We demonstrate that our method works on synthetic networks and in a multilayer network inferred from human microbiome project data.
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