Regularized canonical correlation analysis

Regularized canonical correlation analysis is a way of using ridge regression to solve the singularity problem in the cross-covariance matrices of canonical correlation analysis. By converting ${\displaystyle \operatorname {cov} (X,X)}$ and ${\displaystyle \operatorname {cov} (Y,Y)}$ into ${\displaystyle \operatorname {cov} (X,X)+\lambda I_{X}}$ and ${\displaystyle \operatorname {cov} (Y,Y)+\lambda I_{Y}}$, it ensures that the above matrices will have reliable inverses.

The idea probably dates back to Hrishikesh D. Vinod's publication in 1976 where he called it "Canonical ridge".^[1][2] It has been suggested for use in the analysis of functional neuroimaging data as such data are often singular.^[3] It is possible to compute the regularized canonical vectors in the lower-dimensional space.^[4]