Geometric interpretation of SVD, rank, mean centering and scaling in applying multivariate statistical analysis methods

摘要

A geometric interpretation of the singular value decomposition (SVD) of a matrix, its rank determination. along with the preprocessing steps of mean centering and scaling in applying multivariate statistical analysis methods is presented. The SVD of a matrix is viewed from the perspective of sphere to ellipsoid transformation. The effect of mean centering and scaling to the SVD of the resultant matrix, and thus the tank determination is discussed. Examples of 2-dimensional data matrices are used to illustrate the visualization.