Gaussian Mixture Models for Stochastic Block Models with Non-Vanishing Noise
Community detection tasks have received a lot of attention across statistics, machine learning, and information theory with work concentrating on providing theoretical guarantees for different methodological approaches to the stochastic block model. Recent work on community detection 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 novel GMMs that incorporate truncation and shrinkage effects. We provide empirical validation of this new representation as well as experimental results using a large email dataset.
