Nonlinear measures of association with kernel canonical correlation analysis and applications

Measures of association between two sets of random variables have long been of interest to statisticians. The classical canonical correlation analysis (LCCA) can characterize, but also is limited to, linear association. This article introduces a nonlinear and nonparametric kernel method for association study and proposes a new independence test for two sets of variables. This nonlinear kernel canonical correlation analysis (KCCA) can also be applied to the nonlinear discriminant analysis. Implementation issues are discussed. We place the implementation of KCCA in the framework of classical LCCA via a sequence of independent systems in the kernel associated Hilbert spaces. Such a placement provides an easy way to carry out the KCCA. Numerical experiments and comparison with other nonparametric methods are presented.