论文标题
不同的多重网络模型中的稀疏子空间聚类
Sparse Subspace Clustering in Diverse Multiplex Network Model
论文作者
论文摘要
本文考虑了在Pensky和Wang（2021）中引入的各种多重（Dimple）网络模型，其中该网络的所有层都具有相同的节点集合，并配备了随机块模型。此外，尽管同一组中的层可能具有不同的块连接概率矩阵，但所有层都可以分为具有相同社区结构的组。 Dimple模型概括了许多论文，这些论文在所有层中研究具有相同社区结构的多层网络，以及混合物多层随机块模型（MMLSBM），同一组中的层具有相同的块连接概率。尽管Pensky和Wang（2021）将光谱聚类应用于邻接张量的代理，但本文使用稀疏的子空间聚类（SSC）来识别具有相同社区结构的层组。在轻度条件下，后者导致层间聚类非常一致。此外，SSC允许比Pensky和Wang（2021）的方法处理更大的网络，并且非常适合应用并行计算。
The paper considers the DIverse MultiPLEx (DIMPLE) network model, introduced in Pensky and Wang (2021), where all layers of the network have the same collection of nodes and are equipped with the Stochastic Block Models. 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, as well as the Mixture Multilayer Stochastic Block Model (MMLSBM), where the layers in the same group have identical matrices of block connection probabilities. While Pensky and Wang (2021) applied spectral clustering to the proxy of the adjacency tensor, the present paper uses Sparse Subspace Clustering (SSC) for identifying groups of layers with identical community structures. Under mild conditions, the latter leads to the strongly consistent between-layer clustering. In addition, SSC allows to handle much larger networks than methodology of Pensky and Wang (2021), and is perfectly suitable for application of parallel computing.
