Penalized Clustering of Large Scale Functional Data with Multiple Covariates

In this article, we propose a penalized clustering method for large scale data with multiple covariates through a functional data approach. In the proposed method, responses and covariates are linked together through nonparametric multivariate functions (fixed effects), which have great flexibility in modeling a variety of function features, such as jump points, branching, and periodicity. Functional ANOVA is employed to further decompose multivariate functions in a reproducing kernel Hilbert space and provide associated notions of main effect and interaction. Parsimonious random effects are used to capture various correlation structures. The mixed-effect models are nested under a general mixture model, in which the heterogeneity of functional data is characterized. We propose a penalized Henderson's likelihood approach for model-fitting and design a rejection-controlled EM algorithm for the estimation. Our method selects smoothing parameters through generalized cross-validation. Furthermore, the Bayesian confidence intervals are used to measure the clustering uncertainty. Simulation studies and real-data examples are presented to investigate the empirical performance of the proposed method. Open-source code is available in the R package MFDA

Statistical Assessment of the Global Regulatory Role of Histone Acetylation in Saccharomyces cerevisiae

BACKGROUND: Histone acetylation plays important but incompletely understood roles in gene regulation. A comprehensive understanding of the regulatory role of histone acetylation is difficult because many different histone acetylation patterns exist and their effects are confounded by other factors, such as the transcription factor binding sequence motif information and nucleosome occupancy. RESULTS: We analyzed recent genomewide histone acetylation data using a few complementary statistical models and tested the validity of a cumulative model in approximating the global regulatory effect of histone acetylation. Confounding effects due to transcription factor binding sequence information were estimated by using two independent motif-based algorithms followed by a variable selection method. We found that the sequence information has a significant role in regulating transcription, and we also found a clear additional histone acetylation effect. Our model fits well with observed genome-wide data. Strikingly, including more complicated combinatorial effects does not improve the model's performance. Through a statistical analysis of conditional independence, we found that H4 acetylation may not have significant direct impact on global gene expression. CONCLUSION: Decoding the combinatorial complexity of histone modification requires not only new data but also new methods to analyze the data. Our statistical analysis confirms that histone acetylation has a significant effect on gene transcription rates in addition to that attributable to upstream sequence motifs. Our analysis also suggests that a cumulative effect model for global histone acetylation is justified, although a more complex histone code may be important at specific gene loci. We also found that the regulatory roles among different histone acetylation sites have important differences.Statistic

Bayesian Functional Data Clustering for Temporal Microarray Data

We propose a Bayesian procedure to cluster temporal gene expression microarray profiles, based on a mixed-effect smoothing-spline model, and design a Gibbs sampler to sample from the desired posterior distribution. Our method can determine the cluster number automatically based on the Bayesian information criterion, and handle missing data easily. When applied to a microarray dataset on the budding yeast, our clustering algorithm provides biologically meaningful gene clusters according to a functional enrichment analysis

A data-driven clustering method for time course gene expression data

Gene expression over time is, biologically, a continuous process and can thus be represented by a continuous function, i.e. a curve. Individual genes often share similar expression patterns (functional forms). However, the shape of each function, the number of such functions, and the genes that share similar functional forms are typically unknown. Here we introduce an approach that allows direct discovery of related patterns of gene expression and their underlying functions (curves) from data without a priori specification of either cluster number or functional form. Smoothing spline clustering (SSC) models natural properties of gene expression over time, taking into account natural differences in gene expression within a cluster of similarly expressed genes, the effects of experimental measurement error, and missing data. Furthermore, SSC provides a visual summary of each cluster's gene expression function and goodness-of-fit by way of a ‘mean curve’ construct and its associated confidence bands. We apply this method to gene expression data over the life-cycle of Drosophila melanogaster and Caenorhabditis elegans to discover 17 and 16 unique patterns of gene expression in each species, respectively. New and previously described expression patterns in both species are discovered, the majority of which are biologically meaningful and exhibit statistically significant gene function enrichment. Software and source code implementing the algorithm, SSClust, is freely available ()

Smoothing Spline ANOVA Models and their Applications in Complex and Massive Datasets

Complex and massive datasets can be easily accessed using the newly developed data acquisition technology. In spite of the fact that the smoothing spline ANOVA models have proven to be useful in a variety of fields, these datasets impose the challenges on the applications of the models. In this chapter, we present a selected review of the smoothing spline ANOVA models and highlight some challenges and opportunities in massive datasets. We review two approaches to significantly reduce the computational costs of fitting the model. One real case study is used to illustrate the performance of the reviewed methods