Singular Value Decomposition and Principal Component Analysis

Details Singular Value Decomposition and Principal Component Analysis Singular Value Decomposition and Principal Component Analysis

2002-08-29

arxiv.org/abs/physics/0208101v4

Wall ME, Rechtsteiner A, Rocha LM. In: A Practical Approach to Microarray Data Analysis. (Berrar DP, Dubitzky W, Granzow M, ed

Physics

Biological Physics

18 pages. (9/12/2002) Replaced title. (9/16/2002) Replaced book title. Fixed typos. (3/3/2003) Published. P. 10: "unit varianc

Scientific paper

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.

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