Sensitivity coefficients for the subspaces spanned by principal components

Abstract

In the context of sensitivity analysis in principal component analysis, Tanaka (1988) tackles the problem of the stability of the subspace spanned by dominant principal components. He derives the influence functions related to the projection operator on this subspace and to the spectral decomposition of the covariance or correlation matrix as sensitivity indicators. We suggest here a different approach based on some measures of closeness between the subspaces spanned by the initial eigenvectors and their corresponding version derived from an infinitesimal perturbation of the data distribution.