The paper introduces the DIverse MultiPLEx (DIMPLE) network model where all layers of the network have the same collection of nodes and are equipped with the Stochastic Block Models (SBM). In addition, all layers can be partitioned into groups with the same community structures, although the layers in the same group may have different matrices of block connection probabilities. The DIMPLE model generalizes a multitude of papers that study multilayer networks with the same community structures in all layers (which include the tensor block model and the checker-board model as particular cases), as well as the Mixture Multilayer Stochastic Block Model (MMLSBM), where the layers in the same group have identical matrices of block connection probabilities. Since the techniques from either of the above mentioned groups cannot be applied to the DIMPLE model, we introduce novel algorithms for the between-layer and the within-layer clustering. We study the accuracy of those algorithms, both theoretically and via computer simulations. Finally, we show how our between-layer clustering algorithm can be extended to the Heterogeneous Multiplex Random Dot-Product Graph model, which generalizes the COmmon Subspace Independent Edge (COSIE) random graph model developed in Arroyo et al. (Journ. Machine Learn. Res., 2021).
翻译:本文介绍了DIverse MultipPLEX( DIMPLE) 网络模型, 网络的所有层都有相同的节点集合, 并配有“ 碎块模型 ” ( SBM) 。 此外, 所有层可以分成为具有相同群落结构的组群, 尽管同一组的层可能具有块状连接概率的不同矩阵。 DIMPLE 模型将大量论文普遍化, 以所有层( 包括高压区块模型和棋盘模型等特定案例) 来研究具有相同群落结构的多层网络, 以及混合多层堆块模型( MMMLSBM) 。 此外, 同一组的层组的层可以按照相同的块状连接概率矩阵进行分解。 由于上述两个组中的两组的技术都无法应用于 DIMPLE 模型, 我们为层之间和层群集群集的算法提供了新的算法。 我们研究了这些算法的准确性, 包括理论和计算机模拟。 最后, 我们展示了我们的层群集组合算法如何扩展到 Heconomoleous 多重多层空间的模型, DoProgrodrodal- commaxal 。 ( commax 20I.