Missing data are common in real-world data sets and are a problem for many estimation techniques. We have developed a variational Bayesian method to perform independent component analysis (ICA) on high-dimensional data containing missing entries. Missing data are handled naturally in the Bayesian framework by integrating the generative density model. Modeling the distributions of the independent sources with mixture of gaussians allows sources to be estimated with different kurtosis and skewness. Unlike the maximum likelihood approach, the variational Bayesian method automatically determines the dimensionality of the data and yields an accurate density model for the observed data without overfitting problems. The technique is also extended to the clusters of ICA and supervised classification framework.