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.

The mixture of factor analyzers (MFA) model is a famous mixture model-based approach for unsupervised learning with high-dimensional data. It can be useful, inter alia, in situations where the data dimensionality far exceeds the number of observations. In recent years, the MFA model has been extended to non-Gaussian mixtures to account for clusters with heavier tail weight and/or asymmetry. The generalized hyperbolic factor analyzers (MGHFA) model is one such extension, which leads to a flexible modelling paradigm that accounts for both heavier tail weight and cluster asymmetry. In many practical applications, the occurrence of missing values often complicates data analyses. A generalization of the MGHFA is presented to accommodate missing values. Under a missing-at-random mechanism, we develop a computationally efficient alternating expectation conditional maximization algorithm for parameter estimation of the MGHFA model with different patterns of missing values. The imputation of missing values under an incomplete-data structure of MGHFA is also investigated. The performance of our proposed methodology is illustrated through the analysis of simulated and real data.

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 .

BACKGROUND: A family of parsimonious Gaussian mixture models for the biclustering of gene expression data is introduced. Biclustering is accommodated by adopting a mixture of factor analyzers model with a binary, row-stochastic factor loadings matrix. This particular form of factor loadings matrix results in a block-diagonal covariance matrix, which is a useful property in gene expression analyses, specifically in biomarker discovery scenarios where blood can potentially act as a surrogate tissue for other less accessible tissues. Prior knowledge of the factor loadings matrix is useful in this application and is reflected in the one-way supervised nature of the algorithm. Additionally, the factor loadings matrix can be assumed to be constant across all components because of the relationship desired between the various types of tissue samples. Parameter estimates are obtained through a variant of the expectation-maximization algorithm and the best-fitting model is selected using the Bayesian information criterion. The family of models is demonstrated using simulated data and two real microarray data sets. The first real data set is from a rat study that investigated the influence of diabetes on gene expression in different tissues. The second real data set is from a human transcriptomics study that focused on blood and immune tissues. The microarray data sets illustrate the biclustering family's performance in biomarker discovery involving peripheral blood as surrogate biopsy material. RESULTS: The simulation studies indicate that the algorithm identifies the correct biclusters, most optimally when the number of observation clusters is known. Moreover, the biclustering algorithm identified biclusters comprised of biologically meaningful data related to insulin resistance and immune function in the rat and human real data sets, respectively. CONCLUSIONS: Initial results using real data show that this biclustering technique provides a novel approach for biomarker discovery by enabling blood to be used as a surrogate for hard-to-obtain tissues.

A mixture of shifted asymmetric Laplace distributions is introduced and used for clustering and classification. A variant of the EM algorithm is developed for parameter estimation by exploiting the relationship with the generalized inverse Gaussian distribution. This approach is mathematically elegant and relatively computationally straightforward. Our novel mixture modelling approach is demonstrated on both simulated and real data to illustrate clustering and classification applications. In these analyses, our mixture of shifted asymmetric Laplace distributions performs favourably when compared to the popular Gaussian approach. This work, which marks an important step in the non-Gaussian model-based clustering and classification direction, concludes with discussion as well as suggestions for future work.

We introduce a mixture model whereby each mixture component is itself a mixture of a multivariate Gaussian distribution and a multivariate uniform distribution. Although this model could be used for model-based clustering (model-based unsupervised learning) or model-based classification (model-based semi-supervised learning), we focus on the more general model-based classification framework. In this setting, we fit our mixture models to data where some of the observations have known group memberships and the goal is to predict the memberships of observations with unknown labels. We also present a density estimation example. A generalized expectation-maximization algorithm is used to estimate the parameters and thereby give classifications in this mixture of mixtures model. To simplify the model and the associated parameter estimation, we suggest holding some parameters fixed-this leads to the introduction of more parsimonious models. A simulation study is performed to illustrate how the model allows for bursts of probability and locally higher tails. Two further simulation studies illustrate how the model performs on data simulated from multivariate Gaussian distributions and on data from multivariate t-distributions. This novel approach is also applied to real data and the performance of our approach under the various restrictions is discussed.

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.

The genetic code that maps triples of DNA onto amino acids, is a central part of the biochemistry of life. In this study we incorporate an analogous code, called a translation table, into the self-avoiding walk test problem. Use of a translation table permits evolution of both the distribution of commands and the behavior of the mutation operator. It thus can evolve to encode two types of domain knowledge about the test problem. The translation tables are shown to specialize to specific cases of the test problem but yield no significant improvement in performance. The emergence of encoded problem-specific knowledge in the translation tables is demonstrated. A translation table constructed from extrapolation of the evolutionary trend yields a performance improvement, suggesting that the current algorithm would require more time than that allocated in the experiments to locate translation tables that would enhance performance. A tentative technique for overcoming this limitation is outlined.

MOTIVATION: In recent years, work has been carried out on clustering gene expression microarray data. Some approaches are developed from an algorithmic viewpoint whereas others are developed via the application of mixture models. In this article, a family of eight mixture models which utilizes the factor analysis covariance structure is extended to 12 models and applied to gene expression microarray data. This modelling approach builds on previous work by introducing a modified factor analysis covariance structure, leading to a family of 12 mixture models, including parsimonious models. This family of models allows for the modelling of the correlation between gene expression levels even when the number of samples is small. Parameter estimation is carried out using a variant of the expectation-maximization algorithm and model selection is achieved using the Bayesian information criterion. This expanded family of Gaussian mixture models, known as the expanded parsimonious Gaussian mixture model (EPGMM) family, is then applied to two well-known gene expression data sets. RESULTS: The performance of the EPGMM family of models is quantified using the adjusted Rand index. This family of models gives very good performance, relative to existing popular clustering techniques, when applied to real gene expression microarray data. AVAILABILITY: The reduced, preprocessed data that were analysed are available at www.paulmcnicholas.info