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Community detection is a fundamental unsupervised learning problem forunlabeled networks which has a broad range of applications. Many communitydetection algorithms assume that the number of clusters $r$ is known apriori.In this paper, we propose an approach based on semi-definite relaxations, whichdoes not require prior knowledge of model parameters like many existing convexrelaxation methods and recovers the number of clusters and the clusteringmatrix exactly under a broad parameter regime, with probability tending to one.On a variety of simulated and real data experiments, we show that the proposedmethod often outperforms state-of-the-art techniques for estimating the numberof clusters.

Provable Estimation of the Number of Blocks in Block Models