Regularized canonical correlation analysis
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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 and into and , 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". It has been suggested for use in the analysis of functional neuroimaging data as such data are often singular. It is possible to compute the regularized canonical vectors in the lower-dimensional space.
- 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" (PDF). NeuroImage. 7: S758.
- Finn Årup Nielsen (2001). Neuroinformatics in Functional Neuroimaging (PDF) (Thesis). Technical University of Denmark. Section 3.18.5