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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| Vydáno v: | Journal of computational and graphical statistics Ročník 31; číslo 3; s. 887 - 906 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Alexandria
Taylor & Francis
03.07.2022
Taylor & Francis Ltd |
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| ISSN: | 1061-8600, 1537-2715 |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. 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. |
| Author | Zhang, Hai Guo, Xiao Chang, Xiangyu |
| Author_xml | – sequence: 1 givenname: Hai orcidid: 0000-0002-1104-8283 surname: Zhang fullname: Zhang, Hai organization: Center for Modern Statistics, School of Mathematics, Northwest University – sequence: 2 givenname: Xiao surname: Guo fullname: Guo, Xiao organization: Center for Modern Statistics, School of Mathematics, Northwest University – sequence: 3 givenname: Xiangyu surname: Chang fullname: Chang, Xiangyu organization: Center for Intelligent Decision-Making and Machine Learning, School of Management, Xi'an Jiaotong University |
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| SubjectTerms | Algorithms Clustering Community detection Eigenvalues Errors Network Random projection Random sampling Statistical analysis Stochastic models |
| Title | Randomized Spectral Clustering in Large-Scale Stochastic Block Models |
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