Selecting a small subset of genes out of the thousands of genes in microarray data is important for accurate classification of phenotypes. Widely used methods typically rank genes according to their differential expressions among phenotypes and pick the top-ranked genes. We observe that feature sets so obtained have certain redundancy and study methods to minimize it. Feature sets obtained through the minimum redundancy -maximum relevance framework represent broader spectrum of characteristics of phenotypes than those obtained through standard ranking methods; they are more robust, generalize well to unseen data, and lead to significantly improved classifications in extensive experiments on 5 gene expressions data sets.

BackgroundLiquid chromatography-mass spectrometry (LC-MS) is one of the major techniques for the quantification of metabolites in complex biological samples. Peak modeling is one of the key components in LC-MS data pre-processing.ResultsTo quantify asymmetric peaks with high noise level, we developed an estimation procedure using the bi-Gaussian function. In addition, to accurately quantify partially overlapping peaks, we developed a deconvolution method using the bi-Gaussian mixture model combined with statistical model selection.ConclusionsUsing extensive simulations and real data, we demonstrated the advantage of the bi-Gaussian mixture model over the Gaussian mixture model and the method of kernel smoothing combined with signal summation in peak quantification and deconvolution. The method is implemented in the R package apLCMS: http://www.sph.emory.edu/apLCMS/.

High-throughput expression technologies, including gene expression array and liquid chromatography – mass spectrometry (LC-MS) etc., measure thousands of features, i.e. genes or metabolites, on a continuous scale. In such data, both linear and nonlinear relations exist between features. Nonlinear relations can reflect critical regulation patterns in the biological system. However they are not identified and utilized by traditional clustering methods based on linear associations. Clustering based on general dependencies, i.e. both linear and nonlinear relations, is hampered by the high dimensionality and high noise level of the data. We developed a sensitive nonparametric measure of general dependency between (groups of) random variables in high-dimensions. Based on this dependency measure, we developed a hierarchical clustering method. In simulation studies, the method outperformed correlation- and mutual information (MI) – based hierarchical clustering methods in clustering features with nonlinear dependencies. We applied the method to a microarray dataset measuring the gene expression in cell-cycle time series to show it generates biologically relevant results. The R code is available at http://userwww.service.emory.edu/~tyu8/GDHC.

Microarray gene expression data often contain missing values. Accurate estimation of the missing values is important for down-stream data analyses that require complete data. Nonlinear relationships between gene expression levels have not been well-utilized in missing value imputation. We propose an imputation scheme based on nonlinear dependencies between genes. By simulations based on real microarray data, we show that incorporating non-linear relationships could improve the accuracy of missing value imputation, both in terms of normalized root mean squared error and in terms of the preservation of the list of significant genes in statistical testing. In addition, we studied the impact of artificial dependencies introduced by data normalization on the simulation results. Our results suggest that methods relying on global correlation structures may yield overly optimistic simulation results when the data has been subjected to row (gene) – wise mean removal.

Probabilistic association discovery aims at identifying the association between random vectors, regardless of number of variables involved or linear/nonlinear functional forms. Recently, applications in high-dimensional data have generated rising interest in probabilistic association discovery. We developed a framework based on functions on the observation graph, named MeDiA (Mean Distance Association). We generalize its property to a group of functions on the observation graph. The group of functions encapsulates major existing methods in association discovery, e.g. mutual information and Brownian Covariance, and can be expanded to more complicated forms. We conducted numerical comparison of the statistical power of related methods under multiple scenarios. We further demonstrated the application of MeDiA as a method of gene set analysis that captures a broader range of responses than traditional gene set analysis methods.