Singular Value Decomposition and Principal Component Analysis

by: Michael E Wall, Andreas Rechtsteiner, Luis M Rocha

(3 Mar 2003)

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arXiv (abstract), arXiv (PDF), NASA ADS

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Abstract

This chapter describes gene expression analysis by Singular Value Decomposition (SVD), emphasizing initial characterization of the data. We describe SVD methods for visualization of gene expression data, representation of the data using a smaller number of variables, and detection of patterns in noisy gene expression data. In addition, we describe the precise relation between SVD analysis and Principal Component Analysis (PCA) when PCA is calculated using the covariance matrix, enabling our descriptions to apply equally well to either method. Our aim is to provide definitions, interpretations, examples, and references that will serve as resources for understanding and extending the application of SVD and PCA to gene expression analysis.

@misc{citeulike:352522, abstract = {This chapter describes gene expression analysis by Singular Value Decomposition (SVD), emphasizing initial characterization of the data. We describe SVD methods for visualization of gene expression data, representation of the data using a smaller number of variables, and detection of patterns in noisy gene expression data. In addition, we describe the precise relation between SVD analysis and Principal Component Analysis (PCA) when PCA is calculated using the covariance matrix, enabling our descriptions to apply equally well to either method. Our aim is to provide definitions, interpretations, examples, and references that will serve as resources for understanding and extending the application of SVD and PCA to gene expression analysis.}, author = {Wall, Michael E. and Rechtsteiner, Andreas and Rocha, Luis M. }, citeulike-article-id = {352522}, eprint = {physics/0208101}, keywords = {algebra, algorithms, kdd}, month = {Mar}, posted-at = {2008-05-13 05:16:47}, priority = {2}, title = {Singular Value Decomposition and Principal Component Analysis}, url = {http://arxiv.org/abs/physics/0208101}, year = {2003} }

RIS record

TY - ELEC ID - citeulike:352522 L3 - citeulike-article-id:352522 TI - Singular Value Decomposition and Principal Component Analysis N2 - This chapter describes gene expression analysis by Singular Value Decomposition (SVD), emphasizing initial characterization of the data. We describe SVD methods for visualization of gene expression data, representation of the data using a smaller number of variables, and detection of patterns in noisy gene expression data. In addition, we describe the precise relation between SVD analysis and Principal Component Analysis (PCA) when PCA is calculated using the covariance matrix, enabling our descriptions to apply equally well to either method. Our aim is to provide definitions, interpretations, examples, and references that will serve as resources for understanding and extending the application of SVD and PCA to gene expression analysis. KW - algebra KW - algorithms KW - kdd AU - Wall, Michael AU - Rechtsteiner, Andreas AU - Rocha, Luis PY - 2003/Mar/03/ UR - http://arxiv.org/abs/physics/0208101 ER -

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