Bias-Adjusted Spectral Clustering in Multi-Layer Stochastic Block Models

• 成果类型: Article
• 署名作者: Lei, Jing; Lin, Kevin Z.
• 署名单位: Carnegie Mellon University; University of Pennsylvania
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2022.2054817
• 发表日期: 2023
• 页码: 2433-2445
• 关键词: consistent community detection; tail probabilities; blockmodels; INEQUALITY

摘要

We consider the problem of estimating common community structures in multi-layer stochastic block models, where each single layer may not have sufficient signal strength to recover the full community structure. In order to efficiently aggregate signal across different layers, we argue that the sum-of-squared adjacency matrices contain sufficient signal even when individual layers are very sparse. Our method uses a bias-removal step that is necessary when the squared noise matrices may overwhelm the signal in the very sparse regime. The analysis of our method relies on several novel tail probability bounds for matrix linear combinations with matrix-valued coefficients and matrix-valued quadratic forms, which may be of independent interest. The performance of our method and the necessity of bias removal is demonstrated in synthetic data and in microarray analysis about gene co-expression networks. Supplementary materials for this article are available online.