Sharp optimal recovery in the two component Gaussian mixture model

In this paper, we study the problem of clustering in Two component Gaussian mixture model when centers are separated by some Δ>0. We present a nonasymptotic lower bound for corresponding minimax Hamming risk improving on existing results. also propose an optimal, efficient and adaptive procedure that is rate optimal. The optimality moreover sharp asymptotics sample size goes to infinity. Our based variant Lloyd’s iterations initialized spectral method. As consequence results, find phase transition exact recovery model. prove occurs around critical threshold Δ¯ given Δ¯2=σ2(1+ 1+2p nlogn)logn.