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2018 Community detection by $L_{0}$-penalized graph Laplacian
Chong Chen, Ruibin Xi, Nan Lin
Electron. J. Statist. 12(1): 1842-1866 (2018). DOI: 10.1214/18-EJS1445


Community detection in network analysis aims at partitioning nodes into disjoint communities. Real networks often contain outlier nodes that do not belong to any communities and often do not have a known number of communities. However, most current algorithms assume that the number of communities is known and even fewer algorithm can handle networks with outliers. In this paper, we propose detecting communities by maximizing a novel model free tightness criterion. We show that this tightness criterion is closely related with the $L_{0}$-penalized graph Laplacian and develop an efficient algorithm to extract communities based on the criterion. Unlike many other community detection methods, this method does not assume the number of communities is known and can properly detect communities in networks with outliers. Under the degree corrected stochastic block model, we show that even for networks with outliers, maximizing the tightness criterion can extract communities with small misclassification rates when the number of communities grows to infinity as the network size grows. Simulation and real data analysis also show that the proposed method performs significantly better than existing methods.


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Chong Chen. Ruibin Xi. Nan Lin. "Community detection by $L_{0}$-penalized graph Laplacian." Electron. J. Statist. 12 (1) 1842 - 1866, 2018.


Received: 1 December 2017; Published: 2018
First available in Project Euclid: 12 June 2018

zbMATH: 06886387
MathSciNet: MR3813599
Digital Object Identifier: 10.1214/18-EJS1445

Primary: 62-09
Secondary: 62P10

Keywords: consistency , degree corrected stochastic block model , gene regulatory network , outlier , Social network , spectral clustering


Vol.12 • No. 1 • 2018
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