Publication Type
Working Paper
Version
publishedVersion
Publication Date
10-2017
Abstract
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.
Keywords
Clustering, community detection, degree-corrected stochastic block model, k-means, regularization, strong consistency
Discipline
Econometrics
Research Areas
Econometrics
First Page
1
Last Page
52
City or Country
Singapore
Citation
SU, Liangjun; WANG, Wuyi; and ZHANG, Yichong.
Strong consistency of spectral clustering for stochastic block models. (2017). 1-52.
Available at: https://ink.library.smu.edu.sg/soe_research/2102
Copyright Owner and License
Authors
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Additional URL
http://arxiv.org/pdf/1710.06191.pdf