Influence Functions of Eigenvalues and Eigenvectors in Multidimensional Data Analysis

Influence functions [2] of the most important parameters in principal component analysis (PCA), e.g., eigenvalues, eigenvectors and projection operators, have been derived by a number of authors [1,3,7] using results from the perturbation theory of the ordinary eigenproblem. In the present paper we show that the perturbation theory of generalized eigenproblems [4] underlies and unifies the treatment of influence functions of eigenvalues and eigenvectors in multidimensional data analysis and we present new applications in canonical variate (CVA) and canonical correlation analysis (CCA).