In this paper we prove the strong consistency of several methods based on thespectral clustering techniques that are widely used to study the communitydetection problem in stochastic block models (SBMs). We show that under someweak conditions on the minimal degree, the number of communities, and theeigenvalues of the probability block matrix, the K-means algorithm applied tothe Eigenvectors of the graph Laplacian associated with its first few largesteigenvalues can classify all individuals into the true community uniformlycorrectly almost surely. Extensions to both regularized spectral clustering anddegree-corrected SBMs are also considered. We illustrate the performance ofdifferent methods on simulated networks.
Clustering, community detection, degree-corrected stochastic block model, k-means, regularization, strong consistency
Singapore Management University Economics & Statistics Working Papers, No. 16-2017
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SU, Liangjun; WANG, Wuyi; and ZHANG, Yichong.
Strong consistency of spectral clustering for stochastic block models. (2017). 1-53. Research Collection School Of Economics.
Available at: http://ink.library.smu.edu.sg/soe_research/2102
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