Finite mixtures of matrix-variate Poisson-log normal distributions for three-way count data

Three-way data structures, characterized by three entities, the units, the variables and the occasions, are frequent in biological studies. In RNA sequencing, three-way data structures are obtained when high-throughput transcriptome sequencing data are collected for n genes across p conditions at r occasions. Matrix-variate distributions offer a natural way to model three-way data and mixtures of matrix-variate distributions can be used to cluster three-way data. Clustering of gene expression data is carried out as means to discovering gene co-expression networks. In this work, a mixture of matrix-variate Poisson-log normal distributions is proposed for clustering read counts from RNA sequencing. By considering the matrix-variate structure, full information on the conditions and occasions of the RNA sequencing dataset is simultaneously considered, and the number of covariance parameters to be estimated is reduced. A Markov chain Monte Carlo expectation-maximization algorithm is used for parameter estimation and information criteria are used for model selection. The models are applied to both real and simulated data, giving favourable clustering results

Unsupervised Learning via Mixtures of Skewed Distributions with Hypercube Contours

Mixture models whose components have skewed hypercube contours are developed via a generalization of the multivariate shifted asymmetric Laplace density. Specifically, we develop mixtures of multiple scaled shifted asymmetric Laplace distributions. The component densities have two unique features: they include a multivariate weight function, and the marginal distributions are also asymmetric Laplace. We use these mixtures of multiple scaled shifted asymmetric Laplace distributions for clustering applications, but they could equally well be used in the supervised or semi-supervised paradigms. The expectation-maximization algorithm is used for parameter estimation and the Bayesian information criterion is used for model selection. Simulated and real data sets are used to illustrate the approach and, in some cases, to visualize the skewed hypercube structure of the components

EMMIX-uskew: An R Package for Fitting Mixtures of Multivariate Skew t-distributions via the EM Algorithm

This paper describes an algorithm for fitting finite mixtures of unrestricted Multivariate Skew t (FM-uMST) distributions. The package EMMIX-uskew implements a closed-form expectation-maximization (EM) algorithm for computing the maximum likelihood (ML) estimates of the parameters for the (unrestricted) FM-MST model in R. EMMIX-uskew also supports visualization of fitted contours in two and three dimensions, and random sample generation from a specified FM-uMST distribution. Finite mixtures of skew t-distributions have proven to be useful in modelling heterogeneous data with asymmetric and heavy tail behaviour, for example, datasets from flow cytometry. In recent years, various versions of mixtures with multivariate skew t (MST) distributions have been proposed. However, these models adopted some restricted characterizations of the component MST distributions so that the E-step of the EM algorithm can be evaluated in closed form. This paper focuses on mixtures with unrestricted MST components, and describes an iterative algorithm for the computation of the ML estimates of its model parameters. The usefulness of the proposed algorithm is demonstrated in three applications to real data sets. The first example illustrates the use of the main function fmmst in the package by fitting a MST distribution to a bivariate unimodal flow cytometric sample. The second example fits a mixture of MST distributions to the Australian Institute of Sport (AIS) data, and demonstrate that EMMIX-uskew can provide better clustering results than mixtures with restricted MST components. In the third example, EMMIX-uskew is applied to classify cells in a trivariate flow cytometric dataset. Comparisons with other available methods suggests that the EMMIX-uskew result achieved a lower misclassification rate with respect to the labels given by benchmark gating analysis