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 [math]\displaystyle{ \operatorname{cov}(X, X) }[/math] and [math]\displaystyle{ \operatorname{cov}(Y, Y) }[/math] into [math]\displaystyle{ \operatorname{cov}(X, X) + \lambda I_X }[/math] and [math]\displaystyle{ \operatorname{cov}(Y, Y) + \lambda I_Y }[/math], 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. Multivariate Analysis.
- ↑ Finn Årup 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. http://www2.imm.dtu.dk/pubdb/views/edoc_download.php/4981/pdf/imm4981.pdf.
- ↑ 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.
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