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".[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]


  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. 
  2. ^ Kanti Mardia; et al. Multivariate Analysis. 
  3. ^ Finn Årup Nielsen; Lars Kai Hansen; Stephen C. Strother (May 1998). "Canonical ridge analysis with ridge parameter optimization" (PDF). NeuroImage. 7: S758. 
  4. ^ Finn Årup Nielsen (2001). Neuroinformatics in Functional Neuroimaging (PDF) (Thesis). Technical University of Denmark.  Section 3.18.5