Phase transition for the generalized two-community stochastic block model

被引：0
|
作者：
Lee, Sunmin [1 ,2 ]
Lee, Ji Oon [1 ,2 ]
机构：
[1] Korea Adv Inst Sci & Technol KAIST, Daejeon, South Korea
[2] Korea Adv Inst Sci & Technol, Dept Math Sci, Daejeon 34141, South Korea
来源：
JOURNAL OF APPLIED PROBABILITY | 2024年 / 61卷 / 02期
基金：
新加坡国家研究基金会;
关键词：
BBP-type transition; empirical spectral distribution; Wigner-type matrix; hidden community model; unbalanced stochastic block model; LARGEST EIGENVALUE; DEFORMATION; COMMUNITY; LIMITS;
D O I：
10.1017/jpr.2023.44
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
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-Peche (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.
引用
收藏
页码：385 / 400
页数：16
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