Active learning in the geometric block model

TL;DR

This paper introduces active learning algorithms for the geometric block model, demonstrating that querying a small fraction of nodes can enable exact community recovery where unsupervised methods fail.

Contribution

It presents novel active learning algorithms that combine motif-counting with label query policies, achieving exact recovery with sub-linear label queries in challenging regimes.

Findings

Sub-linear label queries suffice for exact recovery.

Active algorithms outperform unsupervised methods in certain regimes.

Validated on real and synthetic datasets.

Abstract

The geometric block model is a recently proposed generative model for random graphs that is able to capture the inherent geometric properties of many community detection problems, providing more accurate characterizations of practical community structures compared with the popular stochastic block model. Galhotra et al. recently proposed a motif-counting algorithm for unsupervised community detection in the geometric block model that is proved to be near-optimal. They also characterized the regimes of the model parameters for which the proposed algorithm can achieve exact recovery. In this work, we initiate the study of active learning in the geometric block model. That is, we are interested in the problem of exactly recovering the community structure of random graphs following the geometric block model under arbitrary model parameters, by possibly querying the labels of a limited number of chosen nodes. We propose two active learning algorithms that combine the idea of motif-counting with two different label query policies. Our main contribution is to show that sampling the labels of a vanishingly small fraction of nodes (sub-linear in the total number of nodes) is sufficient to achieve exact recovery in the regimes under which the state-of-the-art unsupervised method fails. We validate the superior performance of our algorithms via numerical simulations on both real and synthetic datasets.