High-dimensional Microarray Data Research Articles

Gene Association Networks from Microarray Data Using a Regularized Estimation of Partial Correlation Based on PLS Regression

Reconstruction of gene-gene interactions from large-scale data such as microarrays is a first step toward better understanding the mechanisms at work in the cell. Two main issues have to be managed in such a context: 1) choosing which measures have to be used to distinguish between direct and indirect interactions from high-dimensional microarray data and 2) constructing networks with a low proportion of false-positive edges. We present an efficient methodology for the reconstruction of gene interaction networks in a small-sample-size setting. The strength of independence of any two genes is measured, in such "high-dimensional network," by a regularized estimation of partial correlation based on Partial Least Squares Regression. We finally emphasize specific properties of the proposed method. To assess the sensitivity and specificity of the method, we carried out the reconstruction of networks from simulated data. We also tested PLS-based partial correlation network on static and dynamic real microarray data. An R implementation of the proposed algorithm is available from http://biodev.extra.cea.fr/plspcnetwork/.

A two-stage gene selection scheme utilizing MRMR filter and GA wrapper

Gene expression data usually contain a large number of genes, but a small number of samples. Feature selection for gene expression data aims at finding a set of genes that best discriminates biological samples of different types. In this paper, we propose a two-stage selection algorithm for genomic data by combining MRMR (Minimum Redundancy–Maximum Relevance) and GA (Genetic Algorithm). In the first stage, MRMR is used to filter noisy and redundant genes in high-dimensional microarray data. In the second stage, the GA uses the classifier accuracy as a fitness function to select the highly discriminating genes. The proposed method is tested for tumor classification on five open datasets: NCI, Lymphoma, Lung, Leukemia and Colon using Support Vector Machine (SVM) and Naive Bayes (NB) classifiers. The comparison of the MRMR-GA with MRMR filter and GA wrapper shows that our method is able to find the smallest gene subset that gives the most classification accuracy in leave-one-out cross-validation (LOOCV).

On the prognostic value of survival models with application to gene expression signatures

As part of the validation of any statistical model, it is a good statistical practice to quantify the prediction accuracy and the amount of prognostic information represented by the model; this includes gene expression signatures derived from high-dimensional microarray data. Several approaches exist for right-censored survival data measuring the gain in prognostic information compared with established clinical parameters or biomarkers in terms of explained variation or explained randomness. They are either model-based or use estimates of prediction accuracy.As these measures differ in their underlying mechanisms, they vary in their interpretation, assumptions and properties, in particular in how they deal with the presence of censoring. It remains unclear, under what conditions and to what extent they are comparable. We present a comparison of several common measures and illustrate their behaviour in high-dimensional situations in simulation examples as well as in applications to real gene expression microarray data sets. An overview of available software implementations in R is given.

AutoSOME: a clustering method for identifying gene expression modules without prior knowledge of cluster number

BackgroundClustering the information content of large high-dimensional gene expression datasets has widespread application in "omics" biology. Unfortunately, the underlying structure of these natural datasets is often fuzzy, and the computational identification of data clusters generally requires knowledge about cluster number and geometry.ResultsWe integrated strategies from machine learning, cartography, and graph theory into a new informatics method for automatically clustering self-organizing map ensembles of high-dimensional data. Our new method, called AutoSOME, readily identifies discrete and fuzzy data clusters without prior knowledge of cluster number or structure in diverse datasets including whole genome microarray data. Visualization of AutoSOME output using network diagrams and differential heat maps reveals unexpected variation among well-characterized cancer cell lines. Co-expression analysis of data from human embryonic and induced pluripotent stem cells using AutoSOME identifies >3400 up-regulated genes associated with pluripotency, and indicates that a recently identified protein-protein interaction network characterizing pluripotency was underestimated by a factor of four.ConclusionsBy effectively extracting important information from high-dimensional microarray data without prior knowledge or the need for data filtration, AutoSOME can yield systems-level insights from whole genome microarray expression studies. Due to its generality, this new method should also have practical utility for a variety of data-intensive applications, including the results of deep sequencing experiments. AutoSOME is available for download at http://jimcooperlab.mcdb.ucsb.edu/autosome.

Margin-Maximizing Feature Elimination Methods for Linear and Nonlinear Kernel-Based Discriminant Functions

Feature selection for classification in high-dimensional spaces can improve generalization, reduce classifier complexity, and identify important, discriminating feature "markers." For support vector machine (SVM) classification, a widely used technique is recursive feature elimination (RFE). We demonstrate that RFE is not consistent with margin maximization, central to the SVM learning approach. We thus propose explicit margin-based feature elimination (MFE) for SVMs and demonstrate both improved margin and improved generalization, compared with RFE. Moreover, for the case of a nonlinear kernel, we show that RFE assumes that the squared weight vector 2-norm is strictly decreasing as features are eliminated. We demonstrate this is not true for the Gaussian kernel and, consequently, RFE may give poor results in this case. MFE for nonlinear kernels gives better margin and generalization. We also present an extension which achieves further margin gains, by optimizing only two degrees of freedom--the hyperplane's intercept and its squared 2-norm--with the weight vector orientation fixed. We finally introduce an extension that allows margin slackness. We compare against several alternatives, including RFE and a linear programming method that embeds feature selection within the classifier design. On high-dimensional gene microarray data sets, University of California at Irvine (UCI) repository data sets, and Alzheimer's disease brain image data, MFE methods give promising results.

ConsensusCluster: A Software Tool for Unsupervised Cluster Discovery in Numerical Data

We have created a stand-alone software tool, ConsensusCluster, for the analysis of high-dimensional single nucleotide polymorphism (SNP) and gene expression microarray data. Our software implements the consensus clustering algorithm and principal component analysis to stratify the data into a given number of robust clusters. The robustness is achieved by combining clustering results from data and sample resampling as well as by averaging over various algorithms and parameter settings to achieve accurate, stable clustering results. We have implemented several different clustering algorithms in the software, including K-Means, Partition Around Medoids, Self-Organizing Map, and Hierarchical clustering methods. After clustering the data, ConsensusCluster generates a consensus matrix heatmap to give a useful visual representation of cluster membership, and automatically generates a log of selected features that distinguish each pair of clusters. ConsensusCluster gives more robust and more reliable clusters than common software packages and, therefore, is a powerful unsupervised learning tool that finds hidden patterns in data that might shed light on its biological interpretation. This software is free and available from http://code.google.com/p/consensus-cluster .

Rasch-based high-dimensionality data reduction and class prediction with applications to microarray gene expression data

Class prediction is an important application of microarray gene expression data analysis. The high-dimensionality of microarray data, where number of genes (variables) is very large compared to the number of samples (observations), makes the application of many prediction techniques (e.g., logistic regression, discriminant analysis) difficult. An efficient way to solve this problem is by using dimension reduction statistical techniques. Increasingly used in psychology-related applications, Rasch model (RM) provides an appealing framework for handling high-dimensional microarray data. In this paper, we study the potential of RM-based modeling in dimensionality reduction with binarized microarray gene expression data and investigate its prediction accuracy in the context of class prediction using linear discriminant analysis. Two different publicly available microarray data sets are used to illustrate a general framework of the approach. Performance of the proposed method is assessed by re-randomization scheme using principal component analysis (PCA) as a benchmark method. Our results show that RM-based dimension reduction is as effective as PCA-based dimension reduction. The method is general and can be applied to the other high-dimensional data problems.

Ridge penalized logistical and ordinal partial least squares regression for predicting stroke deficit from infarct topography

Improving the ability to assess potential stroke deficit may aid the selection of patients most likely to benefit from acute stroke therapies. Methods based only on ‘at risk’ volumes or initial neurological condition do predict eventual outcome but not perfectly. Given the close relationship between anatomy and function in the brain, we propose the use of a modified version of partial least squares (PLS) regression to examine how well stroke outcome covary with infarct location. The modified version of PLS incorporates penalized regression and can handle either binary or ordinal data. This version is known as partial least squares with penalized logistic regression (PLS-PLR) and has been adapted from its original use for high-dimensional microarray data. We have adapted this algorithm for use in imaging data and demonstrate the use of this algorithm in a set of patients with aphasia (high level language disorder) following stroke.

Penalized mixtures of factor analyzers with application to clustering high-dimensional microarray data

Model-based clustering has been widely used, e.g. in microarray data analysis. Since for high-dimensional data variable selection is necessary, several penalized model-based clustering methods have been proposed tørealize simultaneous variable selection and clustering. However, the existing methods all assume that the variables are independent with the use of diagonal covariance matrices. To model non-independence of variables (e.g. correlated gene expressions) while alleviating the problem with the large number of unknown parameters associated with a general non-diagonal covariance matrix, we generalize the mixture of factor analyzers to that with penalization, which, among others, can effectively realize variable selection. We use simulated data and real microarray data to illustrate the utility and advantages of the proposed method over several existing ones.

Fuzzy–Rough Sets for Information Measures and Selection of Relevant Genes From Microarray Data

Several information measures such as entropy, mutual information, and f-information have been shown to be successful for selecting a set of relevant and nonredundant genes from a high-dimensional microarray data set. However, for continuous gene expression values, it is very difficult to find the true density functions and to perform the integrations required to compute different information measures. In this regard, the concept of the fuzzy equivalence partition matrix is presented to approximate the true marginal and joint distributions of continuous gene expression values. The fuzzy equivalence partition matrix is based on the theory of fuzzy-rough sets, where each row of the matrix represents a fuzzy equivalence partition that can automatically be derived from the given expression values. The performance of the proposed approach is compared with that of existing approaches using the class separability index and the predictive accuracy of the support vector machine. An important finding, however, is that the proposed approach is shown to be effective for selecting relevant and nonredundant continuous-valued genes from microarray data.

Variable selection using probability density function similarity for support vector machine classification of high-dimensional microarray data

One problem with discriminant analysis of microarray data is representation of each sample by a large number of genes that are possibly irrelevant, insignificant or redundant. Methods of variable selection are, therefore, of great significance in microarray data analysis. To circumvent the problem, a new gene mining approach is proposed based on the similarity between probability density functions on each gene for the class of interest with respect to the others. This method allows the ascertainment of significant genes that are informative for discriminating each individual class rather than maximizing the separability of all classes. Then one can select genes containing important information about the particular subtypes of diseases. Based on the mined significant genes for individual classes, a support vector machine with local kernel transform is constructed for the classification of different diseases. The combination of the gene mining approach with support vector machine is demonstrated for cancer classification using two public data sets. The results reveal that significant genes are identified for each cancer, and the classification model shows satisfactory performance in training and prediction for both data sets.

Iterative Bayesian Model Averaging: a method for the application of survival analysis to high-dimensional microarray data.

BackgroundMicroarray technology is increasingly used to identify potential biomarkers for cancer prognostics and diagnostics. Previously, we have developed the iterative Bayesian Model Averaging (BMA) algorithm for use in classification. Here, we extend the iterative BMA algorithm for application to survival analysis on high-dimensional microarray data. The main goal in applying survival analysis to microarray data is to determine a highly predictive model of patients' time to event (such as death, relapse, or metastasis) using a small number of selected genes. Our multivariate procedure combines the effectiveness of multiple contending models by calculating the weighted average of their posterior probability distributions. Our results demonstrate that our iterative BMA algorithm for survival analysis achieves high prediction accuracy while consistently selecting a small and cost-effective number of predictor genes.ResultsWe applied the iterative BMA algorithm to two cancer datasets: breast cancer and diffuse large B-cell lymphoma (DLBCL) data. On the breast cancer data, the algorithm selected a total of 15 predictor genes across 84 contending models from the training data. The maximum likelihood estimates of the selected genes and the posterior probabilities of the selected models from the training data were used to divide patients in the test (or validation) dataset into high- and low-risk categories. Using the genes and models determined from the training data, we assigned patients from the test data into highly distinct risk groups (as indicated by a p-value of 7.26e-05 from the log-rank test). Moreover, we achieved comparable results using only the 5 top selected genes with 100% posterior probabilities. On the DLBCL data, our iterative BMA procedure selected a total of 25 genes across 3 contending models from the training data. Once again, we assigned the patients in the validation set to significantly distinct risk groups (p-value = 0.00139).ConclusionThe strength of the iterative BMA algorithm for survival analysis lies in its ability to account for model uncertainty. The results from this study demonstrate that our procedure selects a small number of genes while eclipsing other methods in predictive performance, making it a highly accurate and cost-effective prognostic tool in the clinical setting.

Item response theory modeling for microarray gene expression data

The high dimensionality of global gene expression profiles, where number of variables (genes) is very large compared to the number of observations (samples), presents challenges that affect generalizability and applicability of microarray analysis. Latent variable modeling offers a promising approach to deal with high-dimensional microarray data. The latent variable model is based on a few latent variables that capture most of the gene expression information. Here, we describe how to accomplish a reduction in dimension by a latent variable methodology, which can greatly reduce the number of features used to characterize microarray data. We propose a general latent variable framework for prediction of predefined classes of samples using gene expression profiles from microarray experiments. The framework consists of (i) selection of smaller number of genes that are most differentially expressed between samples, (ii) dimension reduction using hierarchical clustering, where each cluster partition is identified as latent variable, (iii) discretization of gene expression matrix, (iv) fitting the Rasch item response model for genes in each cluster partition to estimate the expression of latent variable, and (v) construction of prediction model with latent variables as covariates to study the relationship between latent variables and phenotype. Two different microarray data sets are used to illustrate a general framework of the approach. We show that the predictive performance of our method is comparable to the current best approach based on an all-gene space. The method is general and can be applied to the other high-dimensional data problems.

Support Vector Machines with Disease-gene-centric Network Penalty for High Dimensional Microarray Data.

With the availability of genetic pathways or networks and accumulating knowledge on genes with variants predisposing to diseases (disease genes), we propose a disease-gene-centric support vector machine (DGC-SVM) that directly incorporates these two sources of prior information into building microarray-based classifiers for binary classification problems. DGC-SVM aims to detect the genes clustering together and around some key disease genes in a gene network. To achieve this goal, we propose a penalty over suitably defined groups of genes. A hierarchy is imposed on an undirected gene network to facilitate the definition of such gene groups. Our proposed DGC-SVM utilizes the hinge loss penalized by a sum of the L(infinity)-norm being applied to each group. The simulation studies show that DGC-SVM not only detects more disease genes along pathways than the existing standard SVM and SVM with an L(1)-penalty (L1-SVM), but also captures disease genes that potentially affect the outcome only weakly. Two real data applications demonstrate that DGC-SVM improves gene selection with predictive performance comparable to the standard-SVM and L1-SVM. The proposed method has the potential to be an effective classification tool that encourages gene selection along paths to or clustering around known disease genes for microarray data.

Regularized F‐Measure Maximization for Feature Selection and Classification

Receiver Operating Characteristic (ROC) analysis is a common tool for assessing the performance of various classifications. It gained much popularity in medical and other fields including biological markers and, diagnostic test. This is particularly due to the fact that in real-world problems misclassification costs are not known, and thus, ROC curve and related utility functions such as F-measure can be more meaningful performance measures. F-measure combines recall and precision into a global measure. In this paper, we propose a novel method through regularized F-measure maximization. The proposed method assigns different costs to positive and negative samples and does simultaneous feature selection and prediction with L1 penalty. This method is useful especially when data set is highly unbalanced, or the labels for negative (positive) samples are missing. Our experiments with the benchmark, methylation, and high dimensional microarray data show that the performance of proposed algorithm is better or equivalent compared with the other popular classifiers in limited experiments.

Smoothly Clipped Absolute Deviation on High Dimensions

The smoothly clipped absolute deviation (SCAD) estimator, proposed by Fan and Li, has many desirable properties, including continuity, sparsity, and unbiasedness. The SCAD estimator also has the (asymptotically) oracle property when the dimension of covariates is fixed or diverges more slowly than the sample size. In this article we study the SCAD estimator in high-dimensional settings where the dimension of covariates can be much larger than the sample size. First, we develop an efficient optimization algorithm that is fast and always converges to a local minimum. Second, we prove that the SCAD estimator still has the oracle property on high-dimensional problems. We perform numerical studies to compare the SCAD estimator with the LASSO and SIS–SCAD estimators in terms of prediction accuracy and variable selectivity when the true model is sparse. Through the simulation, we show that the variance estimator of Fan and Li still works well for some limited high-dimensional cases where the true nonzero coefficients are not too small and the sample size is moderately large. We apply the proposed algorithm to analyze a high-dimensional microarray data set.

BATS: a Bayesian user-friendly software for Analyzing Time Series microarray experiments

BackgroundGene expression levels in a given cell can be influenced by different factors, namely pharmacological or medical treatments. The response to a given stimulus is usually different for different genes and may depend on time. One of the goals of modern molecular biology is the high-throughput identification of genes associated with a particular treatment or a biological process of interest. From methodological and computational point of view, analyzing high-dimensional time course microarray data requires very specific set of tools which are usually not included in standard software packages. Recently, the authors of this paper developed a fully Bayesian approach which allows one to identify differentially expressed genes in a 'one-sample' time-course microarray experiment, to rank them and to estimate their expression profiles. The method is based on explicit expressions for calculations and, hence, very computationally efficient.ResultsThe software package BATS (Bayesian Analysis of Time Series) presented here implements the methodology described above. It allows an user to automatically identify and rank differentially expressed genes and to estimate their expression profiles when at least 5–6 time points are available. The package has a user-friendly interface. BATS successfully manages various technical difficulties which arise in time-course microarray experiments, such as a small number of observations, non-uniform sampling intervals and replicated or missing data.ConclusionBATS is a free user-friendly software for the analysis of both simulated and real microarray time course experiments. The software, the user manual and a brief illustrative example are freely available online at the BATS website:

Closed Sets for Labeled Data

Closed sets have been proven successful in the context of compacted data representation for association rule learning. However, their use is mainly descriptive, dealing only with unlabeled data. This paper shows that when considering labeled data, closed sets can be adapted for classification and discrimination purposes by conveniently contrasting covering properties on positive and negative examples. We formally prove that these sets characterize the space of relevant combinations of features for discriminating the target class. In practice, identifying relevant/irrelevant combinations of features through closed sets is useful in many applications: to compact emerging patterns of typical descriptive mining applications, to reduce the number of essential rules in classification, and to efficiently learn subgroup descriptions, as demonstrated in real-life subgroup discovery experiments on a high dimensional microarray data set.

Wavelet feature extraction for high-dimensional microarray data

It is well known that the problem arising from high dimensionality of data should be considered in pattern recognition. Original microarray data are usually of high dimensionality, whereas, only limited training samples are available. Therefore, dimensionality reduction is an important strategy to greatly improve the classification performance of microarray data. A novel method of feature extraction and dimensionality reduction for high-dimensional microarray data is proposed in this study. A set of orthogonal wavelet detail coefficients based on wavelet decomposition at different levels is extracted to characterize the localized features of microarray data. Experiments are carried out on four datasets. A highly competitive accuracy is achieved in comparison with the performance of other models.

Mistakes in validating the accuracy of a prediction classifier in high-dimensional but small-sample microarray data

A major interest in gene expression microarray studies is to develop an accurate classifier which can be adopted in clinical practice. The usage of large numbers of genes with small data samples may lead to overfitting in classification, and generate promising, but often nonreproducible results. Therefore, assessing the reproducibility of a classifier is necessary. Appropriate methods for validating a developed classifier and estimating its predicting accuracy are discussed. In addition, some mistakes that can arise in the cross validation process are reviewed using published articles in prominent medical journals, to prevent the indefinite results of a classifier development from leading to inappropriate treatment.