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Modelling high-dimensional data by mixtures of factor analyzers. (English) Zbl 1256.62036

Summary: 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 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.

MSC:

62H25 Factor analysis and principal components; correspondence analysis
62G07 Density estimation
62H30 Classification and discrimination; cluster analysis (statistical aspects)
62P10 Applications of statistics to biology and medical sciences; meta analysis
92C40 Biochemistry, molecular biology
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