Weighted Message Passing and Minimum Energy Flow for Heterogeneous Stochastic Block Models with Side Information
This addresses community detection in networks with unequal communities and noisy labels, but it is incremental as it builds on existing message passing methods with optimization.
The paper tackles community detection in heterogeneous stochastic block models with side information by connecting misclassification error to minimum energy flow and developing an optimally weighted message passing algorithm to reconstruct labels, achieving improved misclassification rates.
We study the misclassification error for community detection in general heterogeneous stochastic block models (SBM) with noisy or partial label information. We establish a connection between the misclassification rate and the notion of minimum energy on the local neighborhood of the SBM. We develop an optimally weighted message passing algorithm to reconstruct labels for SBM based on the minimum energy flow and the eigenvectors of a certain Markov transition matrix. The general SBM considered in this paper allows for unequal-size communities, degree heterogeneity, and different connection probabilities among blocks. We focus on how to optimally weigh the message passing to improve misclassification.