Semi-Supervised Community Detection via Quasi-Stationary Distributions

Nicolas Fraiman; Michael Nisenzon

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arXiv · 2412.09793

Semi-Supervised Community Detection via Quasi-Stationary Distributions

Nicolas Fraiman·Michael Nisenzon

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Abstract

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.

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BibTeX RIS

Nicolas Fraiman, Michael Nisenzon. 2024-12-13. Semi-Supervised Community Detection via Quasi-Stationary Distributions. https://arxiv.org/abs/2412.09793

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