Consistent community detection in multi-layer network data

• 成果类型: Article
• 署名作者: Lei, Jing; Chen, Kehui; Lynch, Brian
• 署名单位: Carnegie Mellon University; Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asz068
• 发表日期: 2020
• 页码: 6173
• 关键词: stochastic blockmodels

摘要

We consider multi-layer network data where the relationships between pairs of elements are reflected in multiple modalities, and may be described by multivariate or even high-dimensional vectors. Under the multi-layer stochastic block model framework we derive consistency results for a least squares estimation of memberships. Our theorems show that, as compared to single-layer community detection, a multi-layer network provides much richer information that allows for consistent community detection from a much sparser network, with required edge density reduced by a factor of the square root of the number of layers. Moreover, the multi-layer framework can detect cohesive community structure across layers, which might be hard to detect by any single-layer or simple aggregation. Simulations and a data example are provided to support the theoretical results.