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. ISSN 0304-4076. Wikidata Q130748684.
^ Kantilal Mardia; J. T. Kent; J. M. Bibby (1979). Multivariate Analysis. Academic Press. ISBN 978-0-12-471252-2. OL 4425343M. Wikidata Q28842820.
^ F.Å. Nielsen; Lars Kai Hansen; Stephen C. Strother (May 1998). "Canonical Ridge Analysis with Ridge Parameter Optimization". NeuroImage. 7 (4): S758. doi:10.1016/S1053-8119(18)31591-X. ISSN 1053-8119. Wikidata Q129222383.
^ 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. doi:10.1111/j.2517-6161.1993.tb01936.x. JSTOR 2345883.

[1] 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. ISSN 0304-4076. Wikidata Q130748684.

[2] Kantilal Mardia; J. T. Kent; J. M. Bibby (1979). Multivariate Analysis. Academic Press. ISBN 978-0-12-471252-2. OL 4425343M. Wikidata Q28842820.

[3] F.Å. Nielsen; Lars Kai Hansen; Stephen C. Strother (May 1998). "Canonical Ridge Analysis with Ridge Parameter Optimization". NeuroImage. 7 (4): S758. doi:10.1016/S1053-8119(18)31591-X. ISSN 1053-8119. Wikidata Q129222383.

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

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