Robust clustering via mixtures of t factor analyzers with incomplete data

Mixtures of t factor analyzers (MtFA) are powerful and widely used tools for robust clustering of high-dimensional data in the presence of outliers. However, the occurrence of missing values may cause analytical intractability and computational complexity when fitting the MtFA model. We explicitly derive the score vector and Hessian matrix of the MtFA model with incomplete data to approximate the information matrix. In this regard, some asymptotic properties can be established under certain regularity conditions. Three expectation-maximization-based algorithms are developed for maximum likelihood estimation of the MtFA model with possibly missing values at random. Practical issues related to the recovery of missing values and clustering of partially observed samples are also investigated. The relevant utility of our methodology is exemplified through the analysis of simulated and real data sets.