A mixture of SDB skew- t factor analyzers

Abstract

Mixtures of skew-t distributions offer a flexible choice for model-based clustering. A mixture model of this sort can be implemented using a variety of formulations of the skew-t distribution. Herein we develop a mixture of skew-t factor analyzers model for clustering of high-dimensional data using a flexible formulation of the skew-t distribution. Methodological details of our approach, which represents an extension of the mixture of factor analyzers model to a flexible skew-t distribution, are outlined and details of parameter estimation are provided. Clustering results are illustrated and compared to an alternative formulation of the mixture of skew-t factor analyzers model as well as the mixture of factor analyzers model.

Model-Based Clustering

“…While this is obvious by inspection in two dimensions, it would be difficult to detect in higher dimensions. The unsuitability of Gaussian mixtures for capturing asymmetric clusters via a posteriori merging has been noted previously (e.g., Franczak et al 2014;Murray et al 2014a). This is one reason why it has been said that merging Gaussian components is not a "get out of jail free" card (McNicholas and Browne 2013).…”

“…Following this approach, Tortora, McNicholas, and Browne (2015) arrive at a mixture of generalized hyperbolic factor analyzers model. In doing so, they follow the same approach used by Murray et al (2014a), who develop a mixture of skew-t factor analyzers; the principal difference is the distribution of W , which is inverse gamma in the case of the skew-t distribution. Note that there is no skew-normal distribution nested within this formulation of the skew-t distribution because the skewness parameter goes to zero as the degrees of freedom parameter goes to infinity.…”

“…Note that there is no skew-normal distribution nested within this formulation of the skew-t distribution because the skewness parameter goes to zero as the degrees of freedom parameter goes to infinity. Interestingly, Murray et al (2014b) develop a mixture of common skew-t factor analyzers in a similar fashion.…”

Mixtures of commont-factor analyzers for modeling high-dimensional data with missing values

“…An interesting generalization is to consider how to impose multivariate skew distributions for factors and errors Murray et al, 2013Murray et al, , 2014a for flexible modeling of high-dimensional data involving missing values with strong asymmetry. Although the proposed EMtype algorithm is very convenient to implement, it does not provide any guidance on a joint determination of (g, q) for MCtFA within a single run of training procedure.…”

Big and Complex Data Analysis

“…For instance, from Fig. See, for instance, [1,2,4,6,9,17,29,47,49,55,59]. In cases when the normality and independence assumptions are invalid, it has been demonstrated in the literature that the performance of the related control charts is generally unreliable in the sense that their actual ATS 0 values could be substantially different from the assumed ATS 0 value (e.g., [3,39]).…”