Estimation and Clustering in Popularity Adjusted Block Model
将流行度调整块模型推广到社区数量未知且可能随节点数增长的情形，提出概率矩阵和社区结构的估计量，并给出非渐近误差上界，使用稀疏子空间聚类方法划分网络，在蝴蝶相似网络和人脑功能网络上展示优势。
Abstract The paper considers the Popularity Adjusted Block model (PABM) introduced by Sengupta and Chen (Journal of the Royal Statistical Society Series B, 2018, 80, 365–386). We argue that the main appeal of the PABM is the flexibility of the spectral properties of the graph which makes the PABM an attractive choice for modelling networks that appear in biological sciences. We expand the theory of PABM to the case of an arbitrary number of communities which possibly grows with a number of nodes in the network and is not assumed to be known. We produce estimators of the probability matrix and of the community structure and, in addition, provide non-asymptotic upper bounds for the estimation and the clustering errors. We use the Sparse Subspace Clustering (SSC) approach for partitioning the network into communities, the approach that, to the best of our knowledge, has not been used for the clustering network data. The theory is supplemented by a simulation study. In addition, we show advantages of the PABM for modelling a butterfly similarity network and a human brain functional network.