scAI: an unsupervised approach for the integrative analysis of parallel single-cell transcriptomic and epigenomic profiles.

Simultaneous measurements of transcriptomic and epigenomic profiles in the same individual cells provide an unprecedented opportunity to understand cell fates. However, effective approaches for the integrative analysis of such data are lacking. Here, we present a single-cell aggregation and integration (scAI) method to deconvolute cellular heterogeneity from parallel transcriptomic and epigenomic profiles. Through iterative learning, scAI aggregates sparse epigenomic signals in similar cells learned in an unsupervised manner, allowing coherent fusion with transcriptomic measurements. Simulation studies and applications to three real datasets demonstrate its capability of dissecting cellular heterogeneity within both transcriptomic and epigenomic layers and understanding transcriptional regulatory mechanisms

A k-mean-directions Algorithm for Fast Clustering of Data on the Sphere

A k-means-type algorithm is proposed for efficiently clustering data constrained to lie on the surface of a p-dimensional unit sphere, or data that are mean-zero-unit-variance standardized observations such as those that occur when using Euclidean distance to cluster time series gene expression data using a correlation metric. We also provide methodology to initialize the algorithm and to estimate the number of clusters in the dataset. Results from a detailed series of experiments show excellent performance, even with very large datasets. The methodology is applied to the analysis of the mitotic cell division cycle of budding yeast dataset of Cho et al. [Molecular Cell (1998), 2, 65–73]. The entire dataset has not been analyzed previously, so our analysis provides an understanding for the complete set of genes acting in concert and differentially. We also use our methodology on the submitted abstracts of oral presentations made at the 2008 Joint Statistical Meetings (JSM) to identify similar topics. Our identified groups are both interpretable and distinct and the methodology provides a possible automated tool for efficient parallel scheduling of presentations at professional meetings

Sparse integrative clustering of multiple omics data sets

High resolution microarrays and second-generation sequencing platforms are powerful tools to investigate genome-wide alterations in DNA copy number, methylation and gene expression associated with a disease. An integrated genomic profiling approach measures multiple omics data types simultaneously in the same set of biological samples. Such approach renders an integrated data resolution that would not be available with any single data type. In this study, we use penalized latent variable regression methods for joint modeling of multiple omics data types to identify common latent variables that can be used to cluster patient samples into biologically and clinically relevant disease subtypes. We consider lasso [J. Roy. Statist. Soc. Ser. B 58 (1996) 267-288], elastic net [J. R. Stat. Soc. Ser. B Stat. Methodol. 67 (2005) 301-320] and fused lasso [J. R. Stat. Soc. Ser. B Stat. Methodol. 67 (2005) 91-108] methods to induce sparsity in the coefficient vectors, revealing important genomic features that have significant contributions to the latent variables. An iterative ridge regression is used to compute the sparse coefficient vectors. In model selection, a uniform design [Monographs on Statistics and Applied Probability (1994) Chapman & Hall] is used to seek "experimental" points that scattered uniformly across the search domain for efficient sampling of tuning parameter combinations. We compared our method to sparse singular value decomposition (SVD) and penalized Gaussian mixture model (GMM) using both real and simulated data sets. The proposed method is applied to integrate genomic, epigenomic and transcriptomic data for subtype analysis in breast and lung cancer data sets.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS578 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Microarray data mining: A novel optimization-based approach to uncover biologically coherent structures

<p>Abstract</p> <p>Background</p> <p>DNA microarray technology allows for the measurement of genome-wide expression patterns. Within the resultant mass of data lies the problem of analyzing and presenting information on this genomic scale, and a first step towards the rapid and comprehensive interpretation of this data is gene clustering with respect to the expression patterns. Classifying genes into clusters can lead to interesting biological insights. In this study, we describe an iterative clustering approach to uncover biologically coherent structures from DNA microarray data based on a novel clustering algorithm EP_GOS_Clust.</p> <p>Results</p> <p>We apply our proposed iterative algorithm to three sets of experimental DNA microarray data from experiments with the yeast <it>Saccharomyces cerevisiae </it>and show that the proposed iterative approach improves biological coherence. Comparison with other clustering techniques suggests that our iterative algorithm provides superior performance with regard to biological coherence. An important consequence of our approach is that an increasing proportion of genes find membership in clusters of high biological coherence and that the average cluster specificity improves.</p> <p>Conclusion</p> <p>The results from these clustering experiments provide a robust basis for extracting motifs and trans-acting factors that determine particular patterns of expression. In addition, the biological coherence of the clusters is iteratively assessed independently of the clustering. Thus, this method will not be severely impacted by functional annotations that are missing, inaccurate, or sparse.</p

Variational approximation for mixtures of linear mixed models

Mixtures of linear mixed models (MLMMs) are useful for clustering grouped data and can be estimated by likelihood maximization through the EM algorithm. The conventional approach to determining a suitable number of components is to compare different mixture models using penalized log-likelihood criteria such as BIC.We propose fitting MLMMs with variational methods which can perform parameter estimation and model selection simultaneously. A variational approximation is described where the variational lower bound and parameter updates are in closed form, allowing fast evaluation. A new variational greedy algorithm is developed for model selection and learning of the mixture components. This approach allows an automatic initialization of the algorithm and returns a plausible number of mixture components automatically. In cases of weak identifiability of certain model parameters, we use hierarchical centering to reparametrize the model and show empirically that there is a gain in efficiency by variational algorithms similar to that in MCMC algorithms. Related to this, we prove that the approximate rate of convergence of variational algorithms by Gaussian approximation is equal to that of the corresponding Gibbs sampler which suggests that reparametrizations can lead to improved convergence in variational algorithms as well.Comment: 36 pages, 5 figures, 2 tables, submitted to JCG

Algorithmic Techniques in Gene Expression Processing. From Imputation to Visualization

The amount of biological data has grown exponentially in recent decades. Modern biotechnologies, such as microarrays and next-generation sequencing, are capable to produce massive amounts of biomedical data in a single experiment. As the amount of the data is rapidly growing there is an urgent need for reliable computational methods for analyzing and visualizing it. This thesis addresses this need by studying how to efficiently and reliably analyze and visualize high-dimensional data, especially that obtained from gene expression microarray experiments. First, we will study the ways to improve the quality of microarray data by replacing (imputing) the missing data entries with the estimated values for these entries. Missing value imputation is a method which is commonly used to make the original incomplete data complete, thus making it easier to be analyzed with statistical and computational methods. Our novel approach was to use curated external biological information as a guide for the missing value imputation. Secondly, we studied the effect of missing value imputation on the downstream data analysis methods like clustering. We compared multiple recent imputation algorithms against 8 publicly available microarray data sets. It was observed that the missing value imputation indeed is a rational way to improve the quality of biological data. The research revealed differences between the clustering results obtained with different imputation methods. On most data sets, the simple and fast k-NN imputation was good enough, but there were also needs for more advanced imputation methods, such as Bayesian Principal Component Algorithm (BPCA). Finally, we studied the visualization of biological network data. Biological interaction networks are examples of the outcome of multiple biological experiments such as using the gene microarray techniques. Such networks are typically very large and highly connected, thus there is a need for fast algorithms for producing visually pleasant layouts. A computationally efficient way to produce layouts of large biological interaction networks was developed. The algorithm uses multilevel optimization within the regular force directed graph layout algorithm.Siirretty Doriast

Conditional clustering of temporal expression profiles

<p>Abstract</p> <p>Background</p> <p>Many microarray experiments produce temporal profiles in different biological conditions but common cluster techniques are not able to analyze the data conditional on the biological conditions.</p> <p>Results</p> <p>This article presents a novel technique to cluster data from time course microarray experiments performed across several experimental conditions. Our algorithm uses polynomial models to describe the gene expression patterns over time, a full Bayesian approach with proper conjugate priors to make the algorithm invariant to linear transformations, and an iterative procedure to identify genes that have a common temporal expression profile across two or more experimental conditions, and genes that have a unique temporal profile in a specific condition.</p> <p>Conclusion</p> <p>We use simulated data to evaluate the effectiveness of this new algorithm in finding the correct number of clusters and in identifying genes with common and unique profiles. We also use the algorithm to characterize the response of human T cells to stimulations of antigen-receptor signaling gene expression temporal profiles measured in six different biological conditions and we identify common and unique genes. These studies suggest that the methodology proposed here is useful in identifying and distinguishing uniquely stimulated genes from commonly stimulated genes in response to variable stimuli. Software for using this clustering method is available from the project home page.</p