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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.09793 |
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| _version_ | 1866929628387475456 |
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| author | Fraiman, Nicolas Nisenzon, Michael |
| author_facet | Fraiman, Nicolas Nisenzon, Michael |
| contents | Spectral clustering is a widely used method for community detection in networks. We focus on a semi-supervised community detection scenario in the Partially Labeled Stochastic Block Model (PL-SBM) with two balanced communities, where a fixed portion of labels is known. Our approach leverages random walks in which the revealed nodes in each community act as absorbing states. By analyzing the quasi-stationary distributions associated with these random walks, we construct a classifier that distinguishes the two communities by examining differences in the associated eigenvectors. We establish upper and lower bounds on the error rate for a broad class of quasi-stationary algorithms, encompassing both spectral and voting-based approaches. In particular, we prove that this class of algorithms can achieve the optimal error rate in the connected regime. We further demonstrate empirically that our quasi-stationary approach improves performance on both real-world and simulated datasets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_09793 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Semi-Supervised Community Detection via Quasi-Stationary Distributions Fraiman, Nicolas Nisenzon, Michael Statistics Theory Social and Information Networks Physics and Society 05C80, 60J20, 60B20, 62H30, Spectral clustering is a widely used method for community detection in networks. We focus on a semi-supervised community detection scenario in the Partially Labeled Stochastic Block Model (PL-SBM) with two balanced communities, where a fixed portion of labels is known. Our approach leverages random walks in which the revealed nodes in each community act as absorbing states. By analyzing the quasi-stationary distributions associated with these random walks, we construct a classifier that distinguishes the two communities by examining differences in the associated eigenvectors. We establish upper and lower bounds on the error rate for a broad class of quasi-stationary algorithms, encompassing both spectral and voting-based approaches. In particular, we prove that this class of algorithms can achieve the optimal error rate in the connected regime. We further demonstrate empirically that our quasi-stationary approach improves performance on both real-world and simulated datasets. |
| title | Semi-Supervised Community Detection via Quasi-Stationary Distributions |
| topic | Statistics Theory Social and Information Networks Physics and Society 05C80, 60J20, 60B20, 62H30, |
| url | https://arxiv.org/abs/2412.09793 |