论文标题
具有依赖层的多个关系稀疏网络的最佳恢复条件的一般社区检测
General Community Detection with Optimal Recovery Conditions for Multi-relational Sparse Networks with Dependent Layers
论文作者
论文摘要
近期，多层网络和多重网络正在成为常见的网络数据集。我们考虑确定一种称为多关系网络的特殊类型的多层网络的共同社区结构的问题。我们考虑用于多关系网络的光谱聚类方法的扩展，并提供理论保证，即光谱聚类方法恢复了社区结构，即使网络层之间的依赖性，也从随机和程度校正的块模型的多层版本中生成的多层网络始终如一地恢复了社区结构。该方法显示在最佳条件下在网络的学位参数下起作用，以检测具有误差比例消失的误差比例的分类和分离的社区结构，即使多关系网络的各个层的网络结构低于社区可检测性阈值。我们也通过模拟增强了理论结果的有效性。
Multilayer and multiplex networks are becoming common network data sets in recent times. We consider the problem of identifying the common community structure for a special type of multilayer networks called multi-relational networks. We consider extensions of the spectral clustering methods for multi-relational networks and give theoretical guarantees that the spectral clustering methods recover community structure consistently for multi-relational networks generated from multilayer versions of both stochastic and degree-corrected block models even with dependence between network layers. The methods are shown to work under optimal conditions on the degree parameter of the networks to detect both assortative and disassortative community structures with vanishing error proportions even if individual layers of the multi-relational network has the network structures below community detectability threshold. We reinforce the validity of the theoretical results via simulations too.
