A Multiscale Community Blockmodel for Network Exploration

Qirong Ho,Ankur P Parikh,Eric P Xing

doi:10.1080/01621459.2012.682530

Qirong Ho, Ankur P Parikh + Show 1 more

Open Access

https://doi.org/10.1080/01621459.2012.682530

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Abstract

Real-world networks exhibit a complex set of phenomena such as underlying hierarchical organization, multiscale interaction, and varying topologies of communities. Most existing methods do not adequately capture the intrinsic interplay among such phenomena. We propose a nonparametric multiscale community blockmodel (MSCB) to model the generation of hierarchies in social communities, selective membership of actors to subsets of these communities, and the resultant networks due to within- and cross-community interactions. By using the nested Chinese restaurant process, our model automatically infers the hierarchy structure from the data. We develop a collapsed Gibbs sampling algorithm for posterior inference, conduct extensive validation using synthetic networks, and demonstrate the utility of our model in real-world datasets, such as predator–prey networks and citation networks.

Highlights

How do complex networks and their self-organization arise from coordinated interactions and information sharing among the actors? One way to tap into this question is to understand the latent structures over actors, which lead to the formation and organization of these networks
We develop a Markov chain Monte Carlo (MCMC) algorithm for posterior inference and hyperparameter estimation, and study its performance on simulated and real datasets
The degree to which multiscale community blockmodel (MSCB) is nonidentifiable can be compared with two other models: the infinite relational model (IRM) (Kemp et al 2006) and the membership stochastic blockmodel (MMSB) (Airoldi et al 2008)

Summary

Introduction

How do complex networks and their self-organization arise from coordinated interactions and information sharing among the actors? One way to tap into this question is to understand the latent structures over actors, which lead to the formation and organization of these networks. We consider a community to be a group of actors that share a common theme, such as a clique of football fans in a social network, or an ecosystem of dependent organisms in a biological food web. (1) Hierarchy—not all communities are equal: a community can contain subcommunities, or be contained by supercommunities. This is a natural way to structure the latent space of actors

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