Mixtures of Contaminated Shifted Asymmetric Laplace Factor Analyzers

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Cluster analysis can be defined as the search for interesting groups within data. When a finite mixture model is used for cluster analysis, it is called model-based clustering. Typically, the development of novel model-based clustering approaches has focused on the Gaussian mixture model. Unfortunately, the assumption that the subpopulations of the observed data are Gaussian distributed is ofttimes unrealistic. The research proposed herein will extend the current literature on model-based clustering via development of finite mixtures of non-Gaussian distributions. Specifically, a mixture of contaminated shifted asymmetric Laplace factor analyzers (MCSALFA) will be developed. This model will be well suited for the analysis of high-dimensional and big data that contain spurious, outlying, or noisy observations. Of special interest are data sets whose number of variables exceeds the number of observations, like those arising from microarray gene expression analysis.