  We analyze the clustering problem through a flexible probabilistic model that
aims to identify an optimal partition on the sample X 1 , ..., X n. We perform
exact clustering with high probability using a convex semidefinite estimator
that interprets as a corrected, relaxed version of K-means. The estimator is
analyzed through a non-asymptotic framework and showed to be optimal or
near-optimal in recovering the partition. Furthermore, its performances are
shown to be adaptive to the problem's effective dimension, as well as to K the
unknown number of groups in this partition. We illustrate the method's
performances in comparison to other classical clustering algorithms with
numerical experiments on simulated data.
