Handling missing data in model-based clustering

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.