  Gaussian Mixture models (GMMs) are a powerful tool for clustering,
classification and density estimation when clustering structures are embedded
in the data. The presence of missing values can largely impact the GMMs
estimation process, thus handling missing data turns out to be a crucial point
in clustering, classification and density estimation. Several techniques have
been developed to impute the missing values before model estimation. Among
these, multiple imputation is a simple and useful general approach to handle
missing data. In this paper we propose two different methods to fit Gaussian
mixtures in the presence of missing data. Both methods use a variant of the
Monte Carlo Expectation-Maximisation (MCEM) algorithm for data augmentation.
Thus, multiple imputations are performed during the E-step, followed by the
standard M-step for a given eigen-decomposed component-covariance matrix. We
show that the proposed methods outperform the multiple imputation approach,
both in terms of clusters identification and density estimation.
