Results 1  10
of
470
Applications of Resampling Methods to Estimate the Number of Clusters and to Improve the Accuracy of a Clustering Method
, 2001
"... The burgeoning field of genomics, and in particular microarray experiments, have revived interest in both discriminant and cluster analysis, by raising new methodological and computational challenges. The present paper discusses applications of resampling methods to problems in cluster analysis. A r ..."
Abstract

Cited by 233 (0 self)
 Add to MetaCart
The burgeoning field of genomics, and in particular microarray experiments, have revived interest in both discriminant and cluster analysis, by raising new methodological and computational challenges. The present paper discusses applications of resampling methods to problems in cluster analysis. A resampling method, known as bagging in discriminant analysis, is applied to increase clustering accuracy and to assess the confidence of cluster assignments for individual observations. A novel predictionbased resampling method is also proposed to estimate the number of clusters, if any, in a dataset. The performance of the proposed and existing methods are compared using simulated data and gene expression data from four recently published cancer microarray studies.
Fast Monte Carlo Algorithms for Matrices II: Computing a LowRank Approximation to a Matrix
 SIAM JOURNAL ON COMPUTING
, 2004
"... ... matrix A. It is often of interest to find a lowrank approximation to A, i.e., an approximation D to the matrix A of rank not greater than a specified rank k, where k is much smaller than m and n. Methods such as the Singular Value Decomposition (SVD) may be used to find an approximation to A ..."
Abstract

Cited by 216 (21 self)
 Add to MetaCart
... matrix A. It is often of interest to find a lowrank approximation to A, i.e., an approximation D to the matrix A of rank not greater than a specified rank k, where k is much smaller than m and n. Methods such as the Singular Value Decomposition (SVD) may be used to find an approximation to A which is the best in a well defined sense. These methods require memory and time which are superlinear in m and n; for many applications in which the data sets are very large this is prohibitive. Two simple and intuitive algorithms are presented which, when given an m n matrix A, compute a description of a lowrank approximation D to A, and which are qualitatively faster than the SVD. Both algorithms have provable bounds for the error matrix A D . For any matrix X , let kXk and kXk 2 denote its Frobenius norm and its spectral norm, respectively. In the rst algorithm, c = O(1) columns of A are randomly chosen. If the m c matrix C consists of those c columns of A (after appropriate rescaling) then it is shown that from C C approximations to the top singular values and corresponding singular vectors may be computed. From the computed singular vectors a description D of the matrix A may be computed such that rank(D ) k and such that holds with high probability for both = 2; F . This algorithm may be implemented without storing the matrix A in Random Access Memory (RAM), provided it can make two passes over the matrix stored in external memory and use O(m + n) additional RAM memory. The second algorithm is similar except that it further approximates the matrix C by randomly sampling r = O(1) rows of C to form a r c matrix W . Thus, it has additional error, but it can be implemented in three passes over the matrix using only constant ...
Incremental Singular Value Decomposition Of Uncertain Data With Missing Values
 IN ECCV
, 2002
"... We introduce an incremental singular value decomposition (SVD) of incomplete data. The SVD is developed as data arrives, and can handle arbitrary missing/untrusted values, correlated uncertainty across rows or columns of the measurement matrix, and user priors. Since incomplete data does not uniq ..."
Abstract

Cited by 178 (5 self)
 Add to MetaCart
(Show Context)
We introduce an incremental singular value decomposition (SVD) of incomplete data. The SVD is developed as data arrives, and can handle arbitrary missing/untrusted values, correlated uncertainty across rows or columns of the measurement matrix, and user priors. Since incomplete data does not uniquely specify an SVD, the procedure selects one having minimal rank. For a dense p q matrix of low rank r, the incremental method has time complexity O(pqr) and space complexity O((p + q)r)better than highly optimized batch algorithms such as MATLAB 's svd(). In cases of missing data, it produces factorings of lower rank and residual than batch SVD algorithms applied to standard missingdata imputations. We show applications in computer vision and audio feature extraction. In computer vision, we use the incremental SVD to develop an efficient and unusually robust subspaceestimating flowbased tracker, and to handle occlusions/missing points in structurefrommotion factorizations.
Cluster Analysis for Gene Expression Data: A Survey
 IEEE Transactions on Knowledge and Data Engineering
, 2004
"... Abstract—DNA microarray technology has now made it possible to simultaneously monitor the expression levels of thousands of genes during important biological processes and across collections of related samples. Elucidating the patterns hidden in gene expression data offers a tremendous opportunity f ..."
Abstract

Cited by 142 (5 self)
 Add to MetaCart
(Show Context)
Abstract—DNA microarray technology has now made it possible to simultaneously monitor the expression levels of thousands of genes during important biological processes and across collections of related samples. Elucidating the patterns hidden in gene expression data offers a tremendous opportunity for an enhanced understanding of functional genomics. However, the large number of genes and the complexity of biological networks greatly increases the challenges of comprehending and interpreting the resulting mass of data, which often consists of millions of measurements. A first step toward addressing this challenge is the use of clustering techniques, which is essential in the data mining process to reveal natural structures and identify interesting patterns in the underlying data. Cluster analysis seeks to partition a given data set into groups based on specified features so that the data points within a group are more similar to each other than the points in different groups. A very rich literature on cluster analysis has developed over the past three decades. Many conventional clustering algorithms have been adapted or directly applied to gene expression data, and also new algorithms have recently been proposed specifically aiming at gene expression data. These clustering algorithms have been proven useful for identifying biologically relevant groups of genes and samples. In this paper, we first briefly introduce the concepts of microarray technology and discuss the basic elements of clustering on gene expression data. In particular, we divide cluster analysis for gene expression data into three categories. Then, we present specific challenges pertinent to each clustering category and introduce several representative approaches. We also discuss the problem of cluster validation in three aspects and review various methods to assess the quality and reliability of clustering results. Finally, we conclude this paper and suggest the promising trends in this field. Index Terms—Microarray technology, gene expression data, clustering.
Analyzing time series gene expression data
 Bioinformatics
, 2004
"... doi:10.1093/bioinformatics/bth283 ..."
(Show Context)
A Bayesian missing value estimation method for gene expression profile data
 Bioinformatics
, 2003
"... Motivation: Gene expression profile analyses have been used in numerous studies covering a broad range of areas in biology. When unreliable measurements are excluded, missing values are introduced in gene expression profiles. Although existing multivariate analysis methods have difficulty with the t ..."
Abstract

Cited by 125 (2 self)
 Add to MetaCart
(Show Context)
Motivation: Gene expression profile analyses have been used in numerous studies covering a broad range of areas in biology. When unreliable measurements are excluded, missing values are introduced in gene expression profiles. Although existing multivariate analysis methods have difficulty with the treatment of missing values, this problem has received little attention. There are many options for dealing with missing values, each of which reaches drastically different results. Ignoring missing values is the simplest method and is frequently applied. This approach, however, has its flaws. In this article, we propose an estimation method for missing values, which is based on Bayesian principal component analysis (BPCA). Although the methodology that a probabilistic model and latent variables are estimated simultaneously within the framework of Bayes
Spectral Regularization Algorithms for Learning Large Incomplete Matrices
, 2009
"... We use convex relaxation techniques to provide a sequence of regularized lowrank solutions for largescale matrix completion problems. Using the nuclear norm as a regularizer, we provide a simple and very efficient convex algorithm for minimizing the reconstruction error subject to a bound on the n ..."
Abstract

Cited by 104 (5 self)
 Add to MetaCart
We use convex relaxation techniques to provide a sequence of regularized lowrank solutions for largescale matrix completion problems. Using the nuclear norm as a regularizer, we provide a simple and very efficient convex algorithm for minimizing the reconstruction error subject to a bound on the nuclear norm. Our algorithm SoftImpute iteratively replaces the missing elements with those obtained from a softthresholded SVD. With warm starts this allows us to efficiently compute an entire regularization path of solutions on a grid of values of the regularization parameter. The computationally intensive part of our algorithm is in computing a lowrank SVD of a dense matrix. Exploiting the problem structure, we show that the task can be performed with a complexity linear in the matrix dimensions. Our semidefiniteprogramming algorithm is readily scalable to large matrices: for example it can obtain a rank80 approximation of a 10 6 × 10 6 incomplete matrix with 10 5 observed entries in 2.5 hours, and can fit a rank 40 approximation to the full Netflix training set in 6.6 hours. Our methods show very good performance both in training and test error when compared to other competitive stateofthe art techniques. 1.
Missing value estimation for DNA microarray gene expression data: local least squares imputation
 BIOINFORMATICS
, 2005
"... ..."
(Show Context)
I.: Continuous representations of timeseries gene expression data
 J Comput Biol
"... We present algorithms for timeseries gene expression analysis that permit the principled estimation of unobserved time points, clustering, and dataset alignment. Each expression pro � le is modeled as a cubic spline (piecewise polynomial) that is estimated from the observed data and every time poin ..."
Abstract

Cited by 95 (12 self)
 Add to MetaCart
We present algorithms for timeseries gene expression analysis that permit the principled estimation of unobserved time points, clustering, and dataset alignment. Each expression pro � le is modeled as a cubic spline (piecewise polynomial) that is estimated from the observed data and every time point in � uences the overall smooth expression curve. We constrain the spline coef � cients of genes in the same class to have similar expression patterns, while also allowing for gene speci � c parameters. We show that unobserved time points can be reconstructed using our method with 10–15 % less error when compared to previous best methods. Our clustering algorithm operates directly on the continuous representations of gene expression pro � les, and we demonstrate that this is particularly effective when applied to nonuniformly sampled data. Our continuous alignment algorithm also avoids dif � culties encountered by discrete approaches. In particular, our method allows for control of the number of degrees of freedom of the warp through the speci � cation of parameterized functions, which helps to avoid over � tting. We demonstrate that our algorithm produces stable lowerror alignments on real expression data and further show a speci � c application to yeast knockout data that produces biologically meaningful results. Key words: time series expression data, missing value estimation, clustering, alignment. 1.
A new approach to analyzing gene expression time series data
, 2002
"... 1 Introduction Principled methods for estimating unobserved timepoints,clustering, and aligning microarray gene expression timeseries are needed to make such data useful for detailed analysis. Datasets measuring temporal behavior of thousands of genes offer rich opportunities for computational bio ..."
Abstract

Cited by 90 (5 self)
 Add to MetaCart
1 Introduction Principled methods for estimating unobserved timepoints,clustering, and aligning microarray gene expression timeseries are needed to make such data useful for detailed analysis. Datasets measuring temporal behavior of thousands of genes offer rich opportunities for computational biologists. For example, Dynamic Bayesian Networks may be usedto build models and try to understand how genetic responses unfold. However, such modeling frameworks need a sufficient quantity of data in the appropriate format. Current gene expression timeseries data often do not meet these requirements, since they may be missing data points, sampled nonuniformly, and measure biological processes that exhibittemporal variation.