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FAST MONTECARLO LOW RANK APPROXIMATIONS FOR MATRICES
"... In many applications, it is of interest to approximate data, given by m × n matrix A, by a matrix B of at most rank k, which is much smaller than m and n. The best approximation is given by singular value decomposition, which is too time consuming for very large m and n. We present here a Monte Carl ..."
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In many applications, it is of interest to approximate data, given by m × n matrix A, by a matrix B of at most rank k, which is much smaller than m and n. The best approximation is given by singular value decomposition, which is too time consuming for very large m and n. We present here a Monte Carlo algorithm for iteratively computing a krank approximation to the data consisting of m × n matrix A. Each iteration involves the reading of O(k) of columns or rows of A. The complexity of our algorithm is O(kmn). Our algorithm, distinguished from other known algorithms, guarantees that each iteration is a better krank approximation than the previous iteration. We believe that this algorithm will have many applications in data mining, data storage and data analysis.
ORIGINAL RESEARCH Use of biclustering for missing value imputation in gene expression data
"... 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 ..."
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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. Key words Missing value imputation, Biclustering, Gene expression data analysis, Biclusters detection
EXPLOITING BICLUSTERING FOR MISSING VALUE ESTIMATION IN DNA MICROARRAY DATA
"... The missing values in gene expression data harden subsequent analysis such as biclustering which aims to find a set of coexpressed genes across a number of experimental conditions. Missing values are thus required to be estimated before biclusters detection. Existing estimation algorithms rely on fi ..."
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The missing values in gene expression data harden subsequent analysis such as biclustering which aims to find a set of coexpressed genes across a number of experimental conditions. Missing values are thus required to be estimated before biclusters detection. Existing estimation algorithms rely on finding coherence among expression values throughout the entire genes and/or across all the conditions. In view that both missing values estimation and biclusters detection aim at exploiting coherence inside the expression data, we propose to integrate them into a single framework. The benefits are twofold, the missing value estimation can improve bicluster analysis and the coherence in detected biclusters can be exploited for better missing value estimation. Experimental results show that the integrated framework outperforms existing missing values estimation algorithms. It reduces error in missing value estimation and facilitates the detection of biologically meaningful biclusters. Index Terms — Gene expression, missing value
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"... ent pr oit rela e b imi esti Ext ll a mis & 2011 Elsevier Ltd. All rights reserved. [1] allo s of ge is usef lysis, owev e val s on ent an f missi covariance structure in all genes [9,10] while the local approaches similarity is critical for finding the coherence structure. Often, the m is ell a ..."
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ent pr oit rela e b imi esti Ext ll a mis & 2011 Elsevier Ltd. All rights reserved. [1] allo s of ge is usef lysis, owev e val s on ent an f missi covariance structure in all genes [9,10] while the local approaches similarity is critical for finding the coherence structure. Often, the m is ell as ence nclusion is drawn in Section 5. 2. Review—local least square imputation Contents lists available at SciVerse ScienceDirect w. Pattern Rec Pattern Recognition 45 (2012) 1281–1289that the data can contain 10 % missing values and in
2 Singular Value Decomposition
, 2006
"... the inverse eigenvalue problems techniques, and their applications to DNA microarrays and image processing. 2. A joint SVD decomposition of two or more matrices to compare several biological processes. Most of the results can be found in the following recent papers, which are available at ..."
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the inverse eigenvalue problems techniques, and their applications to DNA microarrays and image processing. 2. A joint SVD decomposition of two or more matrices to compare several biological processes. Most of the results can be found in the following recent papers, which are available at