## Clustering gene expression time course data using mixtures of multivariate $$t$$-distributions.(English)Zbl 1236.62068

Summary: Clustering gene expression time course data is an important problem in bioinformatics because understanding which genes behave similarly can lead to the discovery of important biological information. Statistically, the problem of clustering time course data is a special case of the more general problem of clustering longitudinal data. In this paper, a very general and flexible model-based technique is used to cluster longitudinal data. Mixtures of multivariate t-distributions are utilized, with a linear model for the mean and a modified Cholesky-decomposed covariance structure. Constraints are placed upon the covariance structure, leading to a novel family of mixture models, including parsimonious models. In addition to model-based clustering, these models are also used for model-based classification, i.e., semi-supervised clustering. Parameters, including the component degrees of freedom, are estimated using an expectation-maximization algorithm and two different approaches to model selection are considered. The models are applied to simulated data to illustrate their efficacy; this includes a comparison with their Gaussian analogues, the use of these Gaussian analogues with a linear model for the mean is novel in itself. Our family of multivariate t mixture models is then applied to two real gene expression time course data sets and the results are discussed. We conclude with a summary, suggestions for future work, and a discussion about constraining the degrees of freedom parameter.

### MSC:

 62H30 Classification and discrimination; cluster analysis (statistical aspects) 92C40 Biochemistry, molecular biology 62H10 Multivariate distribution of statistics 62H12 Estimation in multivariate analysis 65C60 Computational problems in statistics (MSC2010) 62P10 Applications of statistics to biology and medical sciences; meta analysis

### Keywords:

Cholesky decomposition; model-based clustering

PGMM
Full Text:

### References:

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