Statistical Convergence of Kernel CCA

While kernel canonical correlation analysis (kernel CCA) has been applied in many problems, the asymptotic convergence of the functions estimated from a finite sample to the true functions has not yet been established. This paper gives a rigorous proof of the statistical convergence of kernel CCA and a related method (NOCCO), which provides a theoretical justification for these methods. The result also gives a sufficient condition on the decay of the regularization coefficient in the methods to ensure convergence.