Determining the number of communities in degree-corrected stochastic block models

• Main Authors: MA, Shujie, SU, Liangjun, ZHANG, Yichong
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2021
• Subjects: Clustering; community detection; degree-corrected stochastic block model; K-means; regularization; Computer Sciences; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/2485; https://ink.library.smu.edu.sg/context/soe_research/article/3484/viewcontent/20_037_pvoa.pdf
• Institution: Singapore Management University

We propose to estimate the number of communities in degree-corrected stochastic block models based on a pseudo likelihood ratio. For estimation, we consider a spectral clustering together with binary segmentation method. This approach guarantees an upper bound for the pseudo likelihood ratio statistic when the model is over-fitted. We also derive its limiting distribution when the model is under-fitted. Based on these properties, we establish the consistency of our estimator for the true number of communities. Developing these theoretical properties require a mild condition on the average degree: growing at a rate faster than log(n), where n is the number of nodes. Our proposed method is further illustrated by simulation studies and analysis of real-world networks. The numerical results show that our approach has satisfactory performance when the network is sparse and/or has unbalanced communities.