Randomized Spectral Clustering in Large-Scale Stochastic Block Models

Spectral clustering has been one of the widely used methods for community detection in networks. However, large-scale networks bring computational challenges to the eigenvalue decomposition therein. In this paper, we study the spectral clustering using randomized sketching algorithms from a statisti...

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Bibliographic Details
Published in:Journal of computational and graphical statistics Vol. 31; no. 3; pp. 887 - 906
Main Authors: Zhang, Hai, Guo, Xiao, Chang, Xiangyu
Format: Journal Article
Language:English
Published: Alexandria Taylor & Francis 03.07.2022
Taylor & Francis Ltd
Subjects:
Algorithms
Clustering
Community detection
Eigenvalues
Errors
Network
Random projection
Random sampling
Statistical analysis
Stochastic models
ISSN:1061-8600, 1537-2715
Online Access:Get full text
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Summary:Spectral clustering has been one of the widely used methods for community detection in networks. However, large-scale networks bring computational challenges to the eigenvalue decomposition therein. In this paper, we study the spectral clustering using randomized sketching algorithms from a statistical perspective, where we typically assume the network data are generated from a stochastic block model that is not necessarily of full rank. To do this, we first use the recently developed sketching algorithms to obtain two randomized spectral clustering algorithms, namely, the random projection-based and the random sampling-based spectral clustering. Then we study the theoretical bounds of the resulting algorithms in terms of the approximation error for the population adjacency matrix, the misclassification error, and the estimation error for the link probability matrix. It turns out that, under mild conditions, the randomized spectral clustering algorithms lead to the same theoretical bounds as those of the original spectral clustering algorithm. We also extend the results to degree-corrected stochastic block models. Numerical experiments support our theoretical findings and show the efficiency of randomized methods. A new R package called Rclust is developed and made available to the public. Supplementary materials for this article are available online.
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ISSN:1061-8600
1537-2715
DOI:10.1080/10618600.2022.2034636