EMMIXmfa-package {EMMIXmfa}

Mixture Models with Component-Wise Factor Analyzers

Description

This package provides functions for fitting mixtures of factor analyzers (MFA) and mixtures of common factor analyzers (MCFA) models.

MFA and MCFA models belong to the class of finite mixture models, that adopt factor models for the component-covariance matrices. More specifically, under the factor model, the correlations between feature variables can be explained by the linear dependance of these variables on a smaller small number q of (unobservable) latent factors. The component distributions can be either from the family of multivariate normals or from the family of multivariate t-distributions. Maximum likelihood estimation of the model parameters is implemented using the Expectation–Maximization algorithm.

The joint distribution of the factors and errors can be taken to be either the multivariate normal or t-distribution. The factor analytic representation of the component-covariance matrices is a way of dimension reduction in that it enables the mixture distributions to be fitted to data with dimension p relatively large compared to the sample size n.

Unlike MFA, MCFA models can be used to display the observed data points in the q-dimensional factor space. The MCFA would also provide a greater reduction in the number of parameters in the model.

Author(s)

Suren Rathnayake, Geoffrey McLachlan, David Peel, Jangsun Baek

References

Baek J, and McLachlan GJ (2008). Mixtures of factor analyzers with common factor loadings for the clustering and visualisation of high-dimensional data. Technical Report NI08018-SCH, Preprint Series of the Isaac Newton Institute for Mathematical Sciences, Cambridge.

Baek J, McLachlan GJ, and Flack LK (2010). Mixtures of factor analyzers with common factor loadings: applications to the clustering and visualisation of high-dimensional data. IEEE Transactions on Pattern Analysis and Machine Intelligence 32, 2089–2097.

Baek J, and McLachlan GJ (2011). Mixtures of common t-factor analyzers for clustering highdimensional microarray data. Bioinformatics 27, 1269–1276.

McLachlan GJ, Baek J, and Rathnayake SI (2011). Mixtures of factor analyzers for the analysis of high-dimensional data. In Mixture Estimation and Applications, KL Mengersen, CP Robert, and DM Titterington (Eds). Hoboken, New Jersey: Wiley, pp. 171–191.

McLachlan GJ and Peel D (2000). Finite Mixture Models. New York: Wiley.

McLachlan GJ, and Peel D (2000). Mixtures of factor analyzers. In Proceedings of the Seventeenth International Conference on Machine Learning, P. Langley (Ed.). San Francisco: Morgan Kaufmann, pp. 599–606.

McLachlan GJ, Bean RW, Ben-Tovim Jones L (2007). Extension of the mixture of factor analyzers model to incorporate the multivariate t distribution. Computational Statistics & Data Analysis, 51, 5327–5338.

McLachlan GJ, Peel D, and Bean RW (2003). Modelling high-dimensional data by mixtures of factor analyzers. Computational Statistics & Data Analysis 41, 379–388.

Examples

set.seed(1)
Y <- iris[, -5]
mfa_model <- mfa(Y, g = 3, q = 3)
mtfa_model <- mtfa(Y, g = 3, q = 3)
mcfa_model <- mcfa(Y, g = 3, q = 3)
mctfa_model <- mctfa(Y, g = 3, q = 3)