Gaussian Mixture Models for Stochastic Block Models with Non-Vanishing Noise

TL;DR

This paper introduces a new GMM-based community detection method for stochastic block models that accounts for non-vanishing noise, supported by theoretical insights and validated on simulated and real data.

Contribution

It proposes a tractable GMM-based community detection approach tailored for networks with persistent noise, extending previous models to more realistic scenarios.

Findings

Effective community detection in noisy networks

Theoretical support for GMM modeling in non-vanishing noise regimes

Validated approach on real-world data

Abstract

Community detection tasks have received a lot of attention across statistics, machine learning, and information theory with a large body of work concentrating on theoretical guarantees for the stochastic block model. One line of recent work has focused on modeling the spectral embedding of a network using Gaussian mixture models (GMMs) in scaling regimes where the ability to detect community memberships improves with the size of the network. However, these regimes are not very realistic. This paper provides tractable methodology motivated by new theoretical results for networks with non-vanishing noise. We present a procedure for community detection using GMMs that incorporates certain truncation and shrinkage effects that arise in the non-vanishing noise regime. We provide empirical validation of this new representation using both simulated and real-world data.