PSEUDO-LIKELIHOOD METHODS FOR COMMUNITY DETECTION IN LARGE SPARSE NETWORKS

• 成果类型: Article
• 署名作者: Amini, Arash A.; Chen, Aiyou; Bickel, Peter J.; Levina, Elizaveta
• 署名单位: University of Michigan System; University of Michigan; Alphabet Inc.; Google Incorporated; University of California System; University of California Berkeley
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/13-AOS1138
• 发表日期: 2013
• 页码: 2097-2122
• 关键词: stochastic blockmodels; distributions; Consistency; prediction; successes; number; graphs; models

摘要

Many algorithms have been proposed for fitting network models with communities, but most of them do not scale well to large networks, and often fail on sparse networks. Here we propose a new fast pseudo-likelihood method for fitting the stochastic block model for networks, as well as a variant that allows for an arbitrary degree distribution by conditioning on degrees. We show that the algorithms perform well under a range of settings, including on very sparse networks, and illustrate on the example of a network of political blogs. We also propose spectral clustering with perturbations, a method of independent interest, which works well on sparse networks where regular spectral clustering fails, and use it to provide an initial value for pseudo-likelihood. We prove that pseudo-likelihood provides consistent estimates of the communities under a mild condition on the starting value, for the case of a block model with two communities.