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 $\operatorname{cov}(X, X)$ and $\operatorname{cov}(Y, Y)$ into $\operatorname{cov}(X, X) + \lambda I_X$ and $\operatorname{cov}(Y, Y) + \lambda I_Y$ , 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]

References

↑ Hrishikesh D. Vinod (May 1976). "Canonical ridge and econometrics of joint production". Journal of Econometrics 4 (2): 147–166. doi:10.1016/0304-4076(76)90010-5.
↑ Kanti Mardia et al. Multivariate Analysis.
↑ Finn Årup Nielsen, Lars Kai Hansen, Stephen C. Strother (May 1998). "Canonical ridge analysis with ridge parameter optimization". NeuroImage 7: S758.
↑ Finn Årup Nielsen (2001). Neuroinformatics in Functional Neuroimaging (Thesis). Technical University of Denmark. Section 3.18.5

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. JSTOR 2345883.