Semi-Supervised Community Detection via Quasi-Stationary Distributions

TL;DR

This paper introduces a semi-supervised community detection method using quasi-stationary distributions of random walks, achieving optimal error rates and improved empirical performance in networks with partial labels.

Contribution

It develops a novel quasi-stationary distribution-based classifier for semi-supervised community detection, providing theoretical bounds and demonstrating empirical improvements.

Findings

Achieves optimal error rates in the connected regime.

Improves community detection performance on real-world datasets.

Provides theoretical bounds for quasi-stationary algorithms.

Abstract

Spectral clustering is a widely used method for community detection in networks. We focus on a semi-supervised community detection scenario in the Partially Labeled Stochastic Block Model (PL-SBM) with two balanced communities, where a fixed portion of labels is known. Our approach leverages random walks in which the revealed nodes in each community act as absorbing states. By analyzing the quasi-stationary distributions associated with these random walks, we construct a classifier that distinguishes the two communities by examining differences in the associated eigenvectors. We establish upper and lower bounds on the error rate for a broad class of quasi-stationary algorithms, encompassing both spectral and voting-based approaches. In particular, we prove that this class of algorithms can achieve the optimal error rate in the connected regime. We further demonstrate empirically that our quasi-stationary approach improves performance on both real-world and simulated datasets.