Singular Value Decomposition and Principal Component Analysis

TL;DR

This chapter explains how Singular Value Decomposition (SVD) and Principal Component Analysis (PCA) can be used to analyze gene expression data, focusing on data visualization, pattern detection, and data reduction.

Contribution

It clarifies the relationship between SVD and PCA in gene expression analysis and provides practical guidance and examples for their application.

Findings

SVD effectively visualizes gene expression data.

SVD and PCA are mathematically related when PCA uses the covariance matrix.

The methods help detect patterns in noisy gene expression data.

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.