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 cov ⁡ ( X , X ) {\displaystyle \operatorname {cov} (X,X)} and cov ⁡ ( Y , Y ) {\displaystyle \operatorname {cov} (Y,Y)} into cov ⁡ ( X , X ) + λ I X {\displaystyle \operatorname {cov} (X,X)+\lambda I_{X}} and cov ⁡ ( Y , Y ) + λ I Y {\displaystyle \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

  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 (4): S758. doi:10.1016/S1053-8119(18)31591-X. S2CID 54414890.
  4. ^ 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.