Partial recovery bounds for clustering with the relaxed Kmeans
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We investigate the clustering performances of the relaxed Kmeans in the setting of sub-Gaussian Mixture Model (sGMM) and Stochastic Block Model (SBM). After identifying the appropriate signal-to-noise ratio (SNR), we prove that the misclassification error decay exponentially fast with respect to this SNR. These partial recovery bounds for the relaxed Kmeans improve upon results currently known in the sGMM setting. In the SBM setting, applying the relaxed Kmeans SDP allows to handle general connection probabilities whereas other SDPs investigated in the literature are restricted to the assortative case (where within group probabilities are larger than between group probabilities). Again, this partial recovery bound complements the state-of-the-art results. All together, these results put forward the versatility of the relaxed Kmeans.
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