Community detection in sparse networks via Grothendieck's inequality

• 成果类型: Article
• 署名作者: Guedon, Olivier; Vershynin, Roman
• 署名单位: Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; University of Michigan System; University of Michigan
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-015-0659-z
• 发表日期: 2016
• 页码: 1025-1049
• 关键词: stochastic blockmodels; spectral techniques; maximum-likelihood; cut; approximation; eigenvectors; algorithms; NORM

摘要

We present a simple and flexible method to prove consistency of semidefinite optimization problems on random graphs. The method is based on Grothendieck's inequality. Unlike the previous uses of this inequality that lead to constant relative accuracy, we achieve any given relative accuracy by leveraging randomness. We illustrate the method with the problem of community detection in sparse networks, those with bounded average degrees. We demonstrate that even in this regime, various simple and natural semidefinite programs can be used to recover the community structure up to an arbitrarily small fraction of misclassified vertices. The method is general; it can be applied to a variety of stochastic models of networks and semidefinite programs.