Semi-Supervised Clustering of Sparse Graphs: Crossing the Information-Theoretic Threshold

TL;DR

This paper demonstrates that semi-supervised learning enables effective community detection in sparse graphs beyond the classical information-theoretic limits, introducing new algorithms and insights into network models.

Contribution

It shows that partial label information overcomes fundamental detection limits in sparse graphs and introduces two efficient algorithms for semi-supervised clustering.

Findings

Detection is feasible with any fraction of labels beyond the phase transition.

Two algorithms effectively integrate label info with graph structure.

The work extends stochastic block model analysis to semi-supervised settings.

Abstract

The stochastic block model is a canonical random graph model for clustering and community detection on network-structured data. Decades of extensive study on the problem have established many profound results, among which the phase transition at the Kesten-Stigum threshold is particularly interesting both from a mathematical and an applied standpoint. It states that no estimator based on the network topology can perform substantially better than chance on sparse graphs if the model parameter is below a certain threshold. Nevertheless, if we slightly extend the horizon to the ubiquitous semi-supervised setting, such a fundamental limitation will disappear completely. We prove that with an arbitrary fraction of the labels revealed, the detection problem is feasible throughout the parameter domain. Moreover, we introduce two efficient algorithms, one combinatorial and one based on optimization, to integrate label information with graph structures. Our work brings a new perspective to the stochastic model of networks and semidefinite program research.