MOTIVATION: 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 of discovering gene co-expression networks. RESULTS: 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. We propose three different frameworks for parameter estimation: a Markov chain Monte Carlo-based approach, a variational Gaussian approximation-based approach, and a hybrid approach. Various information criteria are used for model selection. The models are applied to both real and simulated data, and we demonstrate that the proposed approaches can recover the underlying cluster structure in both cases. In simulation studies where the true model parameters are known, our proposed approach shows good parameter recovery. AVAILABILITY AND IMPLEMENTATION: The GitHub R package for this work is available at https://github.com/anjalisilva/mixMVPLN and is released under the open source MIT license.

BACKGROUND: High-dimensional data of discrete and skewed nature is commonly encountered in high-throughput sequencing studies. Analyzing the network itself or the interplay between genes in this type of data continues to present many challenges. As data visualization techniques become cumbersome for higher dimensions and unconvincing when there is no clear separation between homogeneous subgroups within the data, cluster analysis provides an intuitive alternative. The aim of applying mixture model-based clustering in this context is to discover groups of co-expressed genes, which can shed light on biological functions and pathways of gene products. RESULTS: A mixture of multivariate Poisson-log normal (MPLN) model is developed for clustering of high-throughput transcriptome sequencing data. Parameter estimation is carried out using a Markov chain Monte Carlo expectation-maximization (MCMC-EM) algorithm, and information criteria are used for model selection. CONCLUSIONS: The mixture of MPLN model is able to fit a wide range of correlation and overdispersion situations, and is suited for modeling multivariate count data from RNA sequencing studies. All scripts used for implementing the method can be found at https://github.com/anjalisilva/MPLNClust .

Recent work concerning quantitative traits of interest has focused on selecting a small subset of single nucleotide polymorphisms (SNPs) from amongst the SNPs responsible for the phenotypic variation of the trait. When considered as covariates, the large number of variables (SNPs) and their association with those in close proximity pose challenges for variable selection. The features of sparsity and shrinkage of regression coefficients of the least absolute shrinkage and selection operator (LASSO) method appear attractive for SNP selection. Sparse partial least squares (SPLS) is also appealing as it combines the features of sparsity in subset selection and dimension reduction to handle correlations amongst SNPs. In this paper we investigate application of the LASSO and SPLS methods for selecting SNPs that predict quantitative traits. We evaluate the performance of both methods with different criteria and under different scenarios using simulation studies. Results indicate that these methods can be effective in selecting SNPs that predict quantitative traits but are limited by some conditions. Both methods perform similarly overall but each exhibit advantages over the other in given situations. Both methods are applied to Canadian Holstein cattle data to compare their performance.