Learning from incomplete data via parameterized t mixture models through eigenvalue decomposition

A framework of using t mixture models with fourteen eigen-decomposed covariance structures for the unsupervised learning of heterogeneous multivariate data with possible missing values is designed and implemented. Computationally flexible EM-type algorithms are developed for parameter estimation of these models under a missing at random (MAR) mechanism. For ease of computation and theoretical developments, two auxiliary indicator matrices are incorporated into the estimating procedure for exactly extracting the location of observed and missing components of each observation. Computational aspects related to the specification of starting values, convergence assessment and model choice are also discussed. The practical usefulness of the proposed methodology is illustrated with real data examples and a simulation study with varying proportions of missing values.