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.

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

Further reading

• Leurgans, S.E.; Moyeed, R.A.; Silverman, B.W. (1993). "Canonical correlation analysis when the data are curves". Journal of the Royal Statistical Society. Series B (Methodological). 55 (3): 725–740. doi:10.1111/j.2517-6161.1993.tb01936.x. JSTOR 2345883.
• Elena Tuzhilina; Leonardo Tozzi; Trevor Hastie (3 October 2021). "Canonical correlation analysis in high dimensions with structured regularization". Statistical Modelling. 23 (3): 203–227. doi:10.1177/1471082X211041033. ISSN 1471-082X. Wikidata Q132973388.