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78
Algorithms for Identifying Boolean Networks and Related Biological Networks Based on Matrix Multiplication and Fingerprint Function
 J. Comp. Biol
"... Due to the recent progress of the DNA microarray technology, a large number of gene expression pro � le data are being produced. How to analyze gene expression data is an important topic in computational molecular biology. Several studies have been done using the Boolean network as a model of a gene ..."
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Cited by 69 (6 self)
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Due to the recent progress of the DNA microarray technology, a large number of gene expression pro � le data are being produced. How to analyze gene expression data is an important topic in computational molecular biology. Several studies have been done using the Boolean network as a model of a genetic network. This paper proposes ef � cient algorithms for identifying Boolean networks of bounded indegree and related biological networks, where identi� cation of a Boolean network can be formalized as a problem of identifying many Boolean functions simultaneously. For the identi � cation of a Boolean network, an 1 time naive algorithm and a simple time algorithm are known, where denotes the number of nodes, denotes the number of examples, and denotes the maximum indegree. This paper presents an improved 2 3 time MonteCarlo type randomized algorithm, where is the exponent of matrix multiplication (currently, 2 376). The algorithm is obtained by combining fast matrix multiplication with the randomized � ngerprint function for string matching. Although the algorithm and its analysis are simple, the result is nontrivial and the technique can be applied to several related problems.
Microarray data mining with visual programming
 Bioinformatics
, 2005
"... Summary: Visual programming offers an intuitive means of combining known analysis and visualization methods into powerful applications. The system presented here enables users who are not programmers to manage microarray and genomic data flow and to customize their analysis by combining common data ..."
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Cited by 39 (1 self)
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Summary: Visual programming offers an intuitive means of combining known analysis and visualization methods into powerful applications. The system presented here enables users who are not programmers to manage microarray and genomic data flow and to customize their analysis by combining common data analysis tools to fit their needs.
Optimal shrinkage estimation of variances with applications to microarray data analysis
 J. Am. Statist. Ass
, 2006
"... Microarray technology allows a scientist to study genomewide patterns of gene expression. Thousands of individual genes are measured with relatively small number of replications which poses challenges to traditional statistical methods. In particular, the genespecific estimators of variances are n ..."
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Cited by 20 (8 self)
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Microarray technology allows a scientist to study genomewide patterns of gene expression. Thousands of individual genes are measured with relatively small number of replications which poses challenges to traditional statistical methods. In particular, the genespecific estimators of variances are not reliable and genebygene tests have low power. In this paper we propose a family of shrinkage estimators for variances raised to a fixed power. We derive optimal shrinkage parameters under both Stein and the squared loss functions. Our results show that the standard sample variance is inadmissible under either loss functions. We propose several estimators for the optimal shrinkage parameters and investigate their asymptotic properties under two scenarios: large number of replications and large number of genes. We conduct simulations to evaluate the finite sample performance of the datadriven optimal shrinkage estimators and compare them with some existing methods. We construct Flike statistics using these shrinkage variance estimators and apply them to detect differentially expressed genes in a microarray experiment. We also conduct simulations to evaluate performance of these Flike statistics and compare them with some existing methods. Key words and phrases: Flike statistic, gene expression data, inadmissibility, JamesStein shrinkage estimator, loss function. 1.
Gene Expression Profile Classification: A Review
 Current Bioinformatics
, 2006
"... Abstract: In this review, we have discussed the classprediction and discovery methods that are applied to gene expression data, along with the implications of the findings. We attempted to present a unified approach that considers both classprediction and classdiscovery. We devoted a substantial ..."
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Cited by 16 (0 self)
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Abstract: In this review, we have discussed the classprediction and discovery methods that are applied to gene expression data, along with the implications of the findings. We attempted to present a unified approach that considers both classprediction and classdiscovery. We devoted a substantial part of this review to an overview of pattern classification/recognition methods and discussed important issues such as preprocessing of gene expression data, curse of dimensionality, feature extraction/selection, and measuring or estimating classifier performance. We discussed and summarized important properties such as generalizability (sensitivity to overtraining), builtin feature selection, ability to report prediction strength, and transparency (ease of understanding of the operation) of different classpredictor design approaches to provide a quick and concise reference. We have also covered the topic of biclustering, which is an emerging clustering method that processes the entries of the gene expression data matrix in both gene and sample directions simultaneously, in detail. 1.
PRINCIPAL MANIFOLDS AND GRAPHS IN PRACTICE: FROM MOLECULAR BIOLOGY TO DYNAMICAL SYSTEMS
"... We present several applications of nonlinear data modeling, using principal manifolds and principal graphs constructed using the metaphor of elasticity (elastic principal graph approach). These approaches are generalizations of the Kohonen’s selforganizing maps, a class of artificial neural networ ..."
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Cited by 11 (1 self)
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We present several applications of nonlinear data modeling, using principal manifolds and principal graphs constructed using the metaphor of elasticity (elastic principal graph approach). These approaches are generalizations of the Kohonen’s selforganizing maps, a class of artificial neural networks. On several examples we show advantages of using nonlinear objects for data approximation in comparison to the linear ones. We propose four numerical criteria for comparing linear and nonlinear mappings of datasets into the spaces of lower dimension. The examples are taken from comparative political science, from analysis of highthroughput data in molecular biology, from analysis of dynamical systems.
The Centrality of
, 1992
"... This Article is brought to you for free and open access by the Biochemistry, Department of at DigitalCommons@University of Nebraska Lincoln. It ..."
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Cited by 10 (4 self)
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This Article is brought to you for free and open access by the Biochemistry, Department of at DigitalCommons@University of Nebraska Lincoln. It
BIOINFORMATICS ORIGINAL PAPER
"... doi:10.1093/bioinformatics/btl190 Independent component analysisbased penalized discriminant method for tumor classification using gene expression data ..."
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Cited by 8 (2 self)
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doi:10.1093/bioinformatics/btl190 Independent component analysisbased penalized discriminant method for tumor classification using gene expression data
Title: A Calibration Method for Estimating Absolute Expression Levels from Microarray Data Running head: A Calibration Method for Microarray Data
, 2006
"... Motivation: We describe an approach to normalizing spotted microarray data, based on a physically motivated calibration model. This model consists of two major components, describing the hybridization of target transcripts to their corresponding probes on the one hand, and the measurement of fluores ..."
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Cited by 5 (4 self)
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Motivation: We describe an approach to normalizing spotted microarray data, based on a physically motivated calibration model. This model consists of two major components, describing the hybridization of target transcripts to their corresponding probes on the one hand, and the measurement of fluorescence from the hybridized, labeled target on the other hand. The model parameters and error distributions are estimated from external control spikes. Results: Using a publicly available data set, we show that our procedure is capable of adequately removing the typical nonlinearities of the data, without making any assumptions on the distribution of differences in gene expression from one biological sample to the next. Since our model links target concentration to measured intensity, we show how absolute expression values of target transcripts in the hybridization solution can be estimated up to a certain degree. Contact:
Elastic maps and nets for approximating principal manifolds and their application to microarray data visualization
 In this book
"... Summary. Principal manifolds are defined as lines or surfaces passing through “the middle ” of data distribution. Linear principal manifolds (Principal Components Analysis) are routinely used for dimension reduction, noise filtering and data visualization. Recently, methods for constructing nonline ..."
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Cited by 5 (4 self)
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Summary. Principal manifolds are defined as lines or surfaces passing through “the middle ” of data distribution. Linear principal manifolds (Principal Components Analysis) are routinely used for dimension reduction, noise filtering and data visualization. Recently, methods for constructing nonlinear principal manifolds were proposed, including our elastic maps approach which is based on a physical analogy with elastic membranes. We have developed a general geometric framework for constructing “principal objects ” of various dimensions and topologies with the simplest quadratic form of the smoothness penalty which allows very effective parallel implementations. Our approach is implemented in three programming languages (C++, Java and Delphi) with two graphical user interfaces (VidaExpert and ViMiDa applications). In this paper we overview the method of elastic maps and present in detail one of its major applications: the visualization of microarray data in bioinformatics. We show that the method of elastic maps outperforms linear PCA in terms of data approximation, representation of betweenpoint distance structure, preservation of local point neighborhood and representing point classes in lowdimensional spaces. Key words: elastic maps, principal manifolds, elastic functional, data analysis, data visualization, surface modeling 1