Community detection in degree-corrected block models
Chao Gao, Zongming Ma, Anderson Y. Zhang, Harrison H. Zhou
The Annals of Statistics · 2018 · Volume 46 · Issue 5
Abstract
Community detection is a central problem of network data analysis. Given a network, the goal of community detection is to partition the network nodes into a small number of clusters, which could often help reveal interesting structures. The present paper studies community detection in Degree-Corrected Block Models (DCBMs). We first derive asymptotic minimax risks of the problem for a misclassification proportion loss under appropriate conditions. The minimax risks are shown to depend on degree-correction parameters, community sizes and average within and between community connectivities in an intuitive and interpretable way. In addition, we propose a polynomial time algorithm to adaptively perform consistent and even asymptotically optimal community detection in DCBMs.
Keywords
62C20, 62H30, 90B15, 91D30, clustering, Minimax rates, network analysis, spectral clustering, Stochastic block model
Enable JavaScript for citation tools and additional paper interactions.