Community Detection in Multi-Relational Data Through Multi-Layer Stochastic Blockmodel

• Activity Number: 126
• Type: Topic Contributed
• Date/Time: Monday, August 10, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Subhadeep Paul* and Yuguo Chen
• Companies: University of Illinois at Urbana-Champaign and University of Illinois at Urbana-Champaign
• Keywords: Stochastic blockmodel ; Variational EM ; Multi-layer networks ; Consistent community detection ; Restricted maximum likelihood inference

Abstract

In recent years there has been an increased interest in statistical analysis of data with multiple types of relations among a set of entities, mainly driven by applications in biology, social sciences, e-commerce and marketing. For community detection in such multi-relational graphs we consider a random graph model, multi-layer stochastic blockmodel (MLSBM) which is an extension of the well known stochastic block model. In this connection we also propose a model with a restricted parameter space, regularized multi-layer stochastic blockmodel (RMLSBM) for applications where either the network layers are sparse or the number of communities are large or both. We derive consistency results for community assignments through both methods where MLSBM is assumed to be the true model and either the number of nodes or the number of types of edges or both grow. We compare the two methods both in terms of performance in simulation and asymptotic performance under different setups. The simulation studies and real data applications confirm the superior performance of the proposed approaches in comparison to independent modeling of the layers or majority voting.