Model-based clustering of large networks

TL;DR

This paper introduces a scalable, flexible model-based clustering framework for large discrete networks, utilizing advanced variational algorithms and bootstrap methods, demonstrated on networks with over 131,000 nodes and billions of edges.

Contribution

It presents a novel, more adaptable modeling approach with improved algorithms and standard error estimation, enabling analysis of much larger networks than previously possible.

Findings

Successfully clustered a network with 131,000+ nodes and 17 billion edges

Developed a scalable variational EM algorithm with MM enhancements

Provided bootstrap-based standard error estimates for network parameters

Abstract

We describe a network clustering framework, based on finite mixture models, that can be applied to discrete-valued networks with hundreds of thousands of nodes and billions of edge variables. Relative to other recent model-based clustering work for networks, we introduce a more flexible modeling framework, improve the variational-approximation estimation algorithm, discuss and implement standard error estimation via a parametric bootstrap approach, and apply these methods to much larger data sets than those seen elsewhere in the literature. The more flexible framework is achieved through introducing novel parameterizations of the model, giving varying degrees of parsimony, using exponential family models whose structure may be exploited in various theoretical and algorithmic ways. The algorithms are based on variational generalized EM algorithms, where the E-steps are augmented by a minorization-maximization (MM) idea. The bootstrapped standard error estimates are based on an efficient Monte Carlo network simulation idea. Last, we demonstrate the usefulness of the model-based clustering framework by applying it to a discrete-valued network with more than 131,000 nodes and 17 billion edge variables.