  The contaminated Gaussian distribution represents a simple heavy-tailed
elliptical generalization of the Gaussian distribution; unlike the
often-considered t-distribution, it also allows for automatic detection of mild
outlying or "bad" points in the same way that observations are typically
assigned to the groups in the finite mixture model context. Starting from this
distribution, we propose the contaminated factor analysis model as a method for
dimensionality reduction and detection of bad points in higher dimensions. A
mixture of contaminated Gaussian factor analyzers (MCGFA) model follows
therefrom, and extends the recently proposed mixture of contaminated Gaussian
distributions to high-dimensional data. We introduce a family of 32
parsimonious models formed by introducing constraints on the covariance and
contamination structures of the general MCGFA model. We outline a variant of
the expectation-maximization algorithm for parameter estimation. Various
implementation issues are discussed, and the novel family of models is compared
to well-established approaches on both simulated and real data.
