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. "Canonical ridge and econometrics of joint production". Journal of Econometrics. 4 (2): 147–166. doi:10.1016/0304-4076(76)90010-5. {{cite journal}}: Unknown parameter |month= ignored (help)
^ Kanti Mardia; et al. Multivariate Analysis. {{cite book}}: Explicit use of et al. in: |author= (help)
^ Finn Årup Nielsen, Lars Kai Hansen, Stephen C. Strother (1998). "Canonical ridge analysis with ridge parameter optimization" (PDF). NeuroImage. 7: S758. {{cite journal}}: Unknown parameter |month= ignored (help)CS1 maint: multiple names: authors list (link)
^ Finn Årup Nielsen (2001). Neuroinformatics in Functional Neuroimaging (PDF) (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.

[1] Hrishikesh D. Vinod. "Canonical ridge and econometrics of joint production". Journal of Econometrics. 4 (2): 147–166. doi:10.1016/0304-4076(76)90010-5. {{cite journal}}: Unknown parameter |month= ignored (help)

[2] Kanti Mardia; et al. Multivariate Analysis. {{cite book}}: Explicit use of et al. in: |author= (help)

[3] Finn Årup Nielsen, Lars Kai Hansen, Stephen C. Strother (1998). "Canonical ridge analysis with ridge parameter optimization" (PDF). NeuroImage. 7: S758. {{cite journal}}: Unknown parameter |month= ignored (help)CS1 maint: multiple names: authors list (link)

[4] Finn Årup Nielsen (2001). Neuroinformatics in Functional Neuroimaging (PDF) (Thesis). Technical University of Denmark. Section 3.18.5

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