Node Clustering in Binary Asymmetric Stochastic Block Model with Noisy Label Attributes via SDP

Abstract

This paper calculates sufficient conditions for semidefinite programming (SDP) to achieve exact recovery under the binary asymmetric stochastic block model with a noisy-label attribute for each node. We show that in regimes where semidefinite programming fails and cannot achieve the exact recovery on a graph realization, the presence of a noisy label attribute for each node permits exact recovery. We also calculate necessary conditions that are tight, showing that semidefinite programming is asymptotically optimal. Finally, numerical results on synthetic data are provided, indicating that the asymptotic results of this paper can also be useful for analyzing a graph realization with a finite number of nodes.