Modelling high-dimensional data by mixtures of factor analyzers

Authors:
G. J. McLachlan;D. Peel;R. W. Bean
Affiliations:
Department of Mathematics, University of Queensland, St. Lucia, Brisbane 4072, Australia;Department of Mathematics, University of Queensland, St. Lucia, Brisbane 4072, Australia;Department of Mathematics, University of Queensland, St. Lucia, Brisbane 4072, Australia
Venue:
Computational Statistics & Data Analysis
Year:
2003

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Abstract

We focus on mixtures of factor analyzers from the perspective of a method for model-based density estimation from high-dimensional data, and hence for the clustering of such data. This approach enables a normal mixture model to be fitted to a sample of n data points of dimension p, where p is large relative to n. The number of free parameters is controlled through the dimension of the latent factor space. By working in this reduced space, it allows a model for each component-covariance matrix with complexity lying between that of the isotropic and full covariance structure models. We shall illustrate the use of mixtures of factor analyzers in a practical example that considers the clustering of cell lines on the basis of gene expressions from microarray experiments.