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 cov ( X , X ) {\displaystyle \operatorname {cov} (X,X)} and cov ( Y , Y ) {\displaystyle \operatorname {cov} (Y,Y)} into cov ( X , X ) + λ I X {\displaystyle \operatorname {cov} (X,X)+\lambda I_{X}} and cov ( Y , Y ) + λ I Y {\displaystyle \operatorname {cov} (Y,Y)+\lambda I_{Y}} , it ensures that the above matrices will have reliable inverses.
