Influence in canonical correlation analysis

Romanazzi (1992) — influence in canonical correlation analysis

Result

perturbation theory of the generalized eigenproblem yields the influence function of each squared canonical correlation and canonical vector pair; three sample versions; the squared multiple correlation and correspondence-analysis eigenvalues as special cases.

Use

second route to O7's influence function ($\log\eta_D=d^{-1}\sum_i\log\rho_i^2$); needs simple $\rho_i$, which the determinant route does not. Post-derivation check (6 Sep 2026): with the per-coefficient form $\operatorname{IF}(\rho_i^2)=-\rho_i^2u_i^2+2\rho_iu_iv_i-\rho_i^2v_i^2$ as restated by a citer (arXiv:1809.01625, secondary), O7's $\psi$ equals $(\eta_D/d)\sum_i\operatorname{IF}(\rho_i^2)/\rho_i^2$ exactly.

Verification

abstract read (primary text, Crossref), 5 Sep 2026; the formula only through a secondary restatement (6 Sep 2026).