Directed Network Community Detection: A Popularity and Productivity Link Model

Abstract

In this paper, we consider the problem of community detection in directed networks by using probabilistic models. Most existing probabilistic models for community detection are either symmetric in which incoming links and outgoing links are treated equally or conditional in which only one type (i.e., either incoming or outgoing) of links is modeled. We present a probabilistic model for directed network community detection that aims to model both incoming links and outgoing links simultaneously and differentially. In particular, we introduce latent variables node productivity and node popularity to explicitly capture outgoing links and incoming links, respectively. We demonstrate the generality of the proposed framework by showing that both symmetric models and conditional models for community detection can be derived from the proposed framework as special cases, leading to better understanding of the existing models. We derive efficient EM algorithms for computing the maximum likelihood solutions to the proposed models. Extensive empirical studies verify the effectiveness of the new models as well as the insights obtained from the unified framework.