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Fast Network Community Detection With Profile-Pseudo Likelihood Methods

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Version 2 2021-12-08, 14:00
Version 1 2021-10-23, 01:20
journal contribution
posted on 2021-12-08, 14:00 authored by Jiangzhou Wang, Jingfei Zhang, Binghui Liu, Ji Zhu, Jianhua Guo

The stochastic block model is one of the most studied network models for community detection, and fitting its likelihood function on large-scale networks is known to be challenging. One prominent work that overcomes this computational challenge is the fast pseudo-likelihood approach proposed by Amini et al. for fitting stochastic block models to large sparse networks. However, this approach does not have convergence guarantee, and may not be well suited for small and medium scale networks. In this article, we propose a novel likelihood based approach that decouples row and column labels in the likelihood function, enabling a fast alternating maximization. This new method is computationally efficient, performs well for both small- and large-scale networks, and has provable convergence guarantee. We show that our method provides strongly consistent estimates of communities in a stochastic block model. We further consider extensions of our proposed method to handle networks with degree heterogeneity and bipartite properties. Supplementary materials for this article are available online.

Funding

Wang, Liu and Guo’s research are supported by National Key R&D Program of China (no. 2020YFA0714102), NSFC (grants nos. 11690012 and 12171079), China Postdoctoral Science Foundation 2021M701588, the Special Fund for Key Laboratories of Jilin Province, China (grant no. 20190201285JC). Zhang’s research is supported by NSF (grant no. DMS-2015190) and Zhu’s research is supported by NSF (grant no. DMS-1821243).

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