Semi-Supervised Clustering of Sparse Graphs: Crossing the Information-Theoretic Threshold
This provides a solution for network analysis and community detection in semi-supervised settings, representing a significant advancement beyond previous theoretical limits.
The paper tackles the problem of clustering sparse graphs in the stochastic block model, showing that with any fraction of revealed labels, detection becomes feasible across all parameters, overcoming the Kesten-Stigum threshold limitation.
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.