  This paper proposes a variant of the method of Gu\'edon and Verhynin for
estimating the cluster matrix in the Mixture of Gaussians framework via
Semi-Definite Programming. A clustering oriented embedding is deduced from this
estimate. The procedure is suitable for very high dimensional data because it
is based on pairwise distances only. Theoretical garantees are provided and an
eigenvalue optimisation approach is proposed for computing the embedding. The
performance of the method is illustrated via Monte Carlo experiements and
comparisons with other embeddings from the literature.
