Modeling of DNA microarray data by using physical properties of hybridization.

DNA Microarray Technique Current Analytical Methods of DNA Microarray Data Advantages and Disadvantages Current Application of DNA Microarray Technique in Medicine A Novel Method for DNA Microarray Data Analysis Future Directions.

In a number of domains, such as DNA microarray data analysis, we need to cluster simultaneously rows (genes) and columns (conditions) of a data matrix to identify groups of constant rows with a group of columns. This kind of clustering is called biclustering. Biclustering algorithms are extensively used in DNA microarray data analysis. More effective biclustering algorithms are highly desirable and needed. We introduce a new algorithm called BestBinBicluster for biclustering of binary microarray data. Our biclustering algorithm BestBinBicluster extracts a group of biclusters from binary matrix Mb. This algorithm adopts the strategy of one bicluster at a time. It is a novel alternative to extract biclusters from binary data sets. Our algorithm is based on the use of a polynomial function to search Greatest Common Divisor (GCD) and the use of Galois Lattice. We propose to generate the Enumerative BinBicluster Lattice. The performance of the proposed algorithm is assessed using both synthetic and real DNA microarray data; our algorithm outperforms other biclustering algorithms for binary microarray data. We test the biological significance using a gene annotation web tool to show that our proposed method is able to produce biologically relevant biclusters.

Class prediction and feature selection is key in the context of diagnostic applications of DNA microarrays. Microarray data is noisy and typically composed of a low number of samples and a large number of genes. Perceptrons can constitute an efficient tool for accurate classification of microarray data. Nevertheless, the large input layers necessary for the direct application of perceptrons and the low samples available for the training process hamper its use. Two strategies can be taken for an optimal use of a perceptron with a favourable balance between samples for training and the size of the input layer: (a) reducing the dimensionality of the data set from thousands to no more than one hundred, highly informative average values, and using the weights of the perceptron for feature selection or (b) using a selection of only few genes that produce an optimal classification with the perceptron. In this case, feature selection is carried out first. Obviously, a combined approach is also possible. In this manuscript we explore and compare both alternatives. We study the informative contents of the data at different levels of compression with a very efficient clustering algorithm (Self Organizing Tree Algorithm). We show how a simple genetic algorithm selects a subset of gene expression values with 100% accuracy in the classification of samples with maximum efficiency. Finally, the importance of dimensionality reduction is discussed in light of its capacity for reducing noise and redundancies in microarray data.

The real-time system of the JT-60 has a cascade structure with the major and the minor control loops. The multi-variable feedback control is adopted in the major control loop in order to adjust non-linear effects which will appear in the high-/beta/region. By applying the concept of 'phase shift control' to the control program of the major control loop, a flexible tokamak discharge control is expected to be performed with taking account of machine protection.

DNA microarray data is a challenging issue for machine learning researchers due to the high number of gene expression contained and the small samples sizes. To deal with this problem, feature selection methods, such as filters and wrappers, are typically applied to reduce the dimensionality. In this work, we apply a filter method before the classification and include a discretization step. The results obtained over ten different microarray data sets confirm the adequacy of the proposed method, that achieves better performances than the classifier alone. Besides, the combination method is also compared with the approaches of other authors (using wrappers and filters), outperforming the prediction accuracy and maintaining or even decreasing the number of genes required.

Dimension reduction procedures have received increasing consideration over the past decades. Despite this attention, the effect of data contamination or outlying data points in dimension reduction is, however, not well understood, and is compounded by the issue that outliers can be difficult to classify in the presence of many variables. This paper formally investigates the influence of data contamination for sliced inverse regression (SIR), which is a prototypical dimension reduction procedure that targets a lower-dimensional subspace of a set of regressors needed to explain a response variable. We establish a general theory for how estimated reduction subspaces can be distorted through both the number and direction of outlying data points. The results depend critically on the regressor covariance structure and the most harmful types of data contamination are shown to differ in cases where this covariance structure is known or unknown. For example, if the covariance structure is estimated, data contamination is proven to produce an estimated subspace that is automatically orthogonal to the directions of outlying data points, constituting a potentially serious loss of information. Our main results demonstrate the degree to which data contamination indeed causes incorrect dimension reduction, depending on the amount, magnitude, and direction of contamination. Further, by metricizing distances between dimension reduction subspaces, worst case results for data contamination can be formulated to define a finite sample breakdown point for SIR as a measure of global robustness. Our theoretical findings are illustrated through simulation.

Clustering is an important approach to the analysis of DNA microarray data. In this paper, we develop a new algorithm that can cluster DNA microarray data with a graph cut based algorithm. The algorithm can generate a list of clustering results with statistically significant likelihood. It can thus resolve the issue where a gene product may participate in different subsets of co-expressed genes. Our testing results on two biological sets showed that this approach can achieve improved clustering accuracy, compared with other clustering methods.

Recent advances in DNA microarray hybridization technology make it possible to record the molecular biological signals, e.g., mRNA expression levels and proteins' DNA-binding occupancy levels, that guide the progression of cellular processes on genomic scales (1, 2). Biology and medicine today may be at a point similar to where physics was after the advent of the telescope (3). The rapidly growing number of DNA microarray data sets holds the key to the discovery of previously unknown molecular biological principles, just as the astronomical tables compiled by Galileo and Brahe (Fig. 1 A ) enabled accurate predictions of planetary motions and, later, the discovery of universal gravitation. Just as Kepler and Newton made these predictions and discoveries by using mathematical frameworks to describe trends in astronomical data (Fig. 1 B ), so future predictive power, discovery, and control in biology and medicine will come from the mathematical modeling of DNA microarray data, where the mathematical variables and operations represent biological reality: The variables, patterns uncovered in the data, might correlate with activities of cellular elements, such as regulators or transcription factors, that drive the measured signals. The operations, such as data classification and reconstruction in subspaces of selected patterns, might simulate experimental observation of the correlations and possibly also causal coordination of these activities. Such models were recently created from DNA microarray data by using singular value decomposition (SVD) (4) and generalized SVD (GSVD) (5), and their ability to predict previously unknown biological as well as physical principles was demonstrated (6, 7). Fig. 1. Kepler' discovery of his first law of planetary motion from mathematical modeling of Brahe's astronomical data. ( A ) Astronomical table of positions of the sun, Earth, and Mars at different times. ( B ) Geometrical reconstruction of the orbit of Mars from these data reveals an ellipse with the sun located … *E-mail: orlyal{at}mail.utexas.edu

DNA microarray data analysis has been used previously to identify marker genes which discriminate cancer from normal samples. However, due to the limited sample size of each study, there are few common markers among different studies of the same cancer. With the rapid accumulation of microarray data, it is of great interest to integrate inter-study microarray data to increase sample size, which could lead to the discovery of more reliable markers. We present a novel, simple method of integrating different microarray datasets to identify marker genes and apply the method to prostate cancer datasets. In this study, by applying a new statistical method, referred to as the top-scoring pair (TSP) classifier, we have identified a pair of robust marker genes (HPN and STAT6) by integrating microarray datasets from three different prostate cancer studies. Cross-platform validation shows that the TSP classifier built from the marker gene pair, which simply compares relative expression values, achieves high accuracy, sensitivity and specificity on independent datasets generated using various array platforms. Our findings suggest a new model for the discovery of marker genes from accumulated microarray data and demonstrate how the great wealth of microarray data can be exploited to increase the power of statistical analysis. leixu@jhu.edu.

We investigate discrete structures and combinatoric modeling of weighted prefix trees for managing and analyzing DNA microarray data. We describe the algorithms to construct the weighted trees for these data. Using these weighted trees with our algorithms, we propose methods to compute the appearance probability of a DNA microarray, to compare the informational distances in the expression of genes between the DNA microarrays, to search the characteristic microarrays and the group of candidate genes suggestive of a pathology.

SummaryTo review the current state of the art in computational methods for the analysis of DNA microarray data.The review considers methods of microarray data collection, transformation and representation, comparisons and predictions of gene expression from the data, their mechanistic analysis, related systems biology, and the application of clustering techniques.Functional genomics approaches have greatly increased the rate at which data on biological systems is generated, leading to corresponding challenges in analyzing the data through advanced computational techniques . The paper compares and contrasts the application of computational clustering for discovery, comparison, and prediction of gene expression classes, together with their evaluation and relation to mechanistic analyses of biological systems.Methods for assaying gene expression levels by DNA microarray experiments produce considerably more data than other techniques, and require a wide variety of computational techniques for identifying patterns of expression that may be biologically significant. These will have to be verified and validated by comparison to results from other methods, integrated with other systems data, and provide the feedback for further experimentation for testing mechanistic or other biological hypotheses.

DNA microarray data have provided us with the opportunity to assess the expression levels for thousands of genes simultaneously. One of the uses of this information is to classify cancer tumors. A noted challenge in using microarray information is analytical. Following the work of Zhang et al. (1), we further pursue the use of recursive partitioning in analyses of microarray data for cancer classification. Not only does the recursive partitioning technique create intuitive classification rules, but also it is most flexible as to the handling of a massive number of genes, missing expressions, and multi-class tissues. Using a published data set (2), we demonstrate that the recursive partitioning technique creates a more precise and simpler classification rule than other commonly used approaches. In particular, we introduce the concept of A-tree and propose a procedure to assess a large number of A-trees. One of the identified genes (ERBB2) is in the close region of BRCA1 (17q21.1) and has been shown by others to have altered expression levels in breast cancer. Nonetheless, our identified genes warrant further investigation as to whether they play a role in the etiology of breast cancer.

DNA microarray data always contains missing values. As subsequent analysis such as biclustering can only be applied on complete data, these missing values have to be imputed before any biclusters can be detected. Existing imputation methods exploit coherence among expression values in the microarray data. In view that biclustering attempts to find correlated expression values within the data, we propose to combine the missing value imputation and biclustering into a single framework in which the two processes are performed iteratively. In this way, the missing value imputation can improve bicluster analysis and the coherence in detected biclusters can be exploited for better missing value estimation. Experiments have been conducted on artificial datasets and real datasets to verify the effectiveness of the proposed algorithm in reducing estimation errors of missing values.

Analysis of covariance patterns in gene expression data and FT-IR spectra

The problem of fitting a straight line to a finite collection of points in the plane is an important problem in statistical estimation. Recently there has been a great deal of interest is robust estimators, because of their lack of sensitivity to outlying data points. The basic measure of the robustness of an estimator is its breakdown point, that is, the fraction (up to 50%) of outlying data points that can corrupt the estimator. One problem with robust estimators is that achieving high breakdown points (near 50%) has proved to be computationally demanding. In this paper we present the best known theoretical algorithm and a practical subquadratic algorithm for computing a 50% breakdown point line estimator, the Siegel or repeated median line estimator. We first present an O(n\log n) randomized expected-time algorithm, where n is the number of given points. This algorithm relies, however, on sophisticated data structures. We also present a very simple O(n log 2 n) randomized algorithm for this problem, which uses no complex data structures. We provide empirical evidence that, for many realistic input distributions, the running time of this second algorithm is actually O(n log n) expected time.