30 research outputs found
Mixtures of Skew-t Factor Analyzers
In this paper, we introduce a mixture of skew-t factor analyzers as well as a
family of mixture models based thereon. The mixture of skew-t distributions
model that we use arises as a limiting case of the mixture of generalized
hyperbolic distributions. Like their Gaussian and t-distribution analogues, our
mixture of skew-t factor analyzers are very well-suited to the model-based
clustering of high-dimensional data. Imposing constraints on components of the
decomposed covariance parameter results in the development of eight flexible
models. The alternating expectation-conditional maximization algorithm is used
for model parameter estimation and the Bayesian information criterion is used
for model selection. The models are applied to both real and simulated data,
giving superior clustering results compared to a well-established family of
Gaussian mixture models
Mixtures of Common Skew-t Factor Analyzers
A mixture of common skew-t factor analyzers model is introduced for
model-based clustering of high-dimensional data. By assuming common component
factor loadings, this model allows clustering to be performed in the presence
of a large number of mixture components or when the number of dimensions is too
large to be well-modelled by the mixtures of factor analyzers model or a
variant thereof. Furthermore, assuming that the component densities follow a
skew-t distribution allows robust clustering of skewed data. The alternating
expectation-conditional maximization algorithm is employed for parameter
estimation. We demonstrate excellent clustering performance when our model is
applied to real and simulated data.This paper marks the first time that skewed
common factors have been used
Parsimonious Shifted Asymmetric Laplace Mixtures
A family of parsimonious shifted asymmetric Laplace mixture models is
introduced. We extend the mixture of factor analyzers model to the shifted
asymmetric Laplace distribution. Imposing constraints on the constitute parts
of the resulting decomposed component scale matrices leads to a family of
parsimonious models. An explicit two-stage parameter estimation procedure is
described, and the Bayesian information criterion and the integrated completed
likelihood are compared for model selection. This novel family of models is
applied to real data, where it is compared to its Gaussian analogue within
clustering and classification paradigms