Fast Network Community Detection with Profile-Pseudo Likelihood Methods
This work addresses the problem of scalable and reliable community detection in networks for researchers and practitioners, offering an incremental improvement over prior methods by enhancing performance across network scales.
The authors tackled the computational inefficiency and lack of convergence guarantees in existing stochastic block model methods for community detection by proposing a novel likelihood-based approach that decouples row and column labels, enabling fast alternating maximization. The method outperforms the pseudo-likelihood approach in estimation accuracy and computational efficiency, especially for large sparse networks, with provable convergence and strong consistency.
The stochastic block model is one of the most studied network models for community detection. It is well-known that most algorithms proposed for fitting the stochastic block model likelihood function cannot scale to large-scale networks. One prominent work that overcomes this computational challenge is Amini et al.(2013), which proposed a fast pseudo-likelihood approach for fitting stochastic block models to large sparse networks. However, this approach does not have convergence guarantee, and is not well suited for small- or medium- scale networks. In this article, we propose a novel likelihood based approach that decouples row and column labels in the likelihood function, which enables a fast alternating maximization; the new method is computationally efficient, performs well for both small and large scale networks, and has provable convergence guarantee. We show that our method provides strongly consistent estimates of the communities in a stochastic block model. As demonstrated in simulation studies, the proposed method outperforms the pseudo-likelihood approach in terms of both estimation accuracy and computation efficiency, especially for large sparse networks. We further consider extensions of our proposed method to handle networks with degree heterogeneity and bipartite properties.