Modelling high-dimensional data by mixtures of factor analyzers

• Published in: Computational statistics & data analysis Vol. 41; no. 3; pp. 379 - 388
• Main Authors: McLachlan, G.J., Peel, D., Bean, R.W.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Amsterdam Elsevier B.V 28.01.2003; Elsevier Science; Elsevier
• Series: Computational Statistics & Data Analysis
• Subjects: EM algorithm; Exact sciences and technology; Factor analyzers; Mathematics; Mixture modelling; Multivariate analysis; Nonparametric inference; Probability and statistics; Sciences and techniques of general use; Statistics; Mixture modelling; EM algorithm; Factor analyzers; Mixed distribution; Density estimation; Discriminant analysis; Factor analysis; Cluster analysis (statistics); Eigenvector; Gaussian distribution; Non parametric estimation; Multivariate distribution; Statistical estimation; Covariance matrix; Multivariate analysis; Modeling; Mixture; Model matching; Covariance
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/S0167-9473(02)00183-4

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.