Extending mixtures of factor models using the restricted multivariate skew-normal distribution

• Published in: Journal of multivariate analysis Vol. 143; pp. 398 - 413
• Main Authors: Lin, Tsung-I, McLachlan, Geoffrey J., Lee, Sharon X.
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01.01.2016; Taylor & Francis LLC
• Subjects: Algorithms; Clustering; Data reduction; Discriminant analysis; ECM algorithm; Factor analyzer; Mathematical models; Maximum likelihood method; Multivariate analysis; Normal distribution; rMSN distribution; Skewness; Studies; Skewness; 62H30; ECM algorithm; Factor analyzer; rMSN distribution; 65C60; Clustering; Data reduction; 62H25
• ISSN: 0047-259X; 1095-7243
• DOI: 10.1016/j.jmva.2015.09.025

The mixture of factor analyzers (MFA) model provides a powerful tool for analyzing high-dimensional data as it can reduce the number of free parameters through its factor-analytic representation of the component covariance matrices. This paper extends the MFA model to incorporate a restricted version of the multivariate skew-normal distribution for the latent component factors, called mixtures of skew-normal factor analyzers (MSNFA). The proposed MSNFA model allows us to relax the need of the normality assumption for the latent factors in order to accommodate skewness in the observed data. The MSNFA model thus provides an approach to model-based density estimation and clustering of high-dimensional data exhibiting asymmetric characteristics. A computationally feasible Expectation Conditional Maximization (ECM) algorithm is developed for computing the maximum likelihood estimates of model parameters. The potential of the proposed methodology is exemplified using both real and simulated data.