广义两群体随机块体模型的相变

Pub Date : 2023-07-31 DOI:10.1017/jpr.2023.44

Sunmin Lee, J. Lee

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引用次数: 0

摘要

我们研究了从具有两个群落的广义随机块模型（G2-SBM）中检测群落结构的问题。基于对经验谱分布的Stieljtes变换的分析，我们证明了G2-SBM最大特征值的Baik–Ben Arous–Péché（BBP）型跃迁。对于特定的模型，如隐藏社区模型和不平衡随机块模型，我们提供了两个最大特征值的精确公式，建立了BBP型转换中的间隙。

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Phase transition for the generalized two-community stochastic block model

We study the problem of detecting the community structure from the generalized stochastic block model with two communities (G2-SBM). Based on analysis of the Stieljtes transform of the empirical spectral distribution, we prove a Baik–Ben Arous–Péché (BBP)-type transition for the largest eigenvalue of the G2-SBM. For specific models, such as a hidden community model and an unbalanced stochastic block model, we provide precise formulas for the two largest eigenvalues, establishing the gap in the BBP-type transition.

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