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Mixtures of common factor analyzers (MCFA), thought of as a parsimonious extension of mixture factor analyzers (MFA), have recently been developed as a novel approach to analyzing high-dimensional data, where the number of observations is not very large relative to their dimension. The key idea behind MCFA is to reduce further the number of parameters in the specification of the component-covariance matrices. The occurrence of missing data persists in many scientific investigations and often complicates data analysis. In this work, I present a computationally flexible expectation conditional maximization (ECM) algorithm for maximum likelihood estimation of the MCFA model with partially observed data. To facilitate the implementation, two auxiliary permutation matrices are incorporated into the estimating procedure for exactly extracting the location of observed and missing components of each observation. Practical techniques for the model-based clustering and discriminant analysis are also provided. The proposed methodology is illustrated with the analysis of ozone data and an experimental study on image reconstruction.