Regularized canonical correlation analysis explained

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

\operatorname{cov}(X, X) and \operatorname{cov}(Y, Y) into \operatorname{cov}(X, X) + λ I _{X} and \operatorname{cov}(Y, Y) + λ 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]

References

• Leurgans. S.E.. Sue Leurgans. Moyeed. R.A.. Silverman. B.W.. Canonical correlation analysis when the data are curves. Journal of the Royal Statistical Society. Series B (Methodological). 1993. 55. 3. 725–740. 2345883.

Notes and References

1. Hrishikesh D. Vinod . Canonical ridge and econometrics of joint production . . 4 . 2. May 1976 . 147–166 . 10.1016/0304-4076(76)90010-5.
2. Book: Kanti Mardia . Kanti Mardia . Multivariate Analysis. etal.
3. Finn Årup Nielsen . Lars Kai Hansen . Stephen C. Strother . Canonical ridge analysis with ridge parameter optimization . May 1998 . . 7 . 4 . S758. 10.1016/S1053-8119(18)31591-X . 54414890 .
4. Finn Årup Nielsen . 2001 . Neuroinformatics in Functional Neuroimaging . Technical University of Denmark. Section 3.18.5