Regularized canonical correlation analysis is a way of using
ridge regression
Ridge regression is a method of estimating the coefficients of multiple-regression models in scenarios where the independent variables are highly correlated. It has been used in many fields including econometrics, chemistry, and engineering. Also ...
to solve the
singularity problem in the
cross-covariance matrices of
canonical correlation analysis
In statistics, canonical-correlation analysis (CCA), also called canonical variates analysis, is a way of inferring information from cross-covariance matrices. If we have two vectors ''X'' = (''X''1, ..., ''X'n'') and ''Y' ...
. 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
Functional neuroimaging is the use of neuroimaging technology to measure an aspect of brain function, often with a view to understanding the relationship between activity in certain brain areas and specific mental functions. It is primarily used a ...
data as such data are often singular.
It is possible to compute the regularized canonical vectors in the lower-dimensional space.
[ Section 3.18.5]
References
* {{cite journal, last1=Leurgans, first1=S.E., author1-link=Sue Leurgans, last2=Moyeed, first2=R.A., last3=Silverman, first3=B.W., title=Canonical correlation analysis when the data are curves, journal=
Journal of the Royal Statistical Society
The ''Journal of the Royal Statistical Society'' is a peer-reviewed scientific journal of statistics. It comprises three series and is published by Wiley for the Royal Statistical Society.
History
The Statistical Society of London was founded ...
, series=Series B (Methodological), year=1993, volume=55, number=3, pages=725–740, jstor=2345883
Mathematical analysis
Calculus of variations