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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 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". 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.

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. 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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