The distance between feature subspaces of kernel canonical correlation analysis

Kernel canonical correlation analysis (CCA) is a nonlinear extension of CCA. It is widely used in information retrieval. However, relatively little research concerning the convergence rate and the distance between two feature spaces has been done so far. This paper gives the distance measure between two subspaces which was spanned by the eigenfunctions corresponding to the m largest eigenvalues of normalized cross-covariance operator (NOCCO) and its empirical version (empirical NOCCO) respectively. We established that the minimal distance between the above two spaces depends on two parameters, one is the decay rate of regularization parameter, the other is the decay rate of NOCCO compared with the eigenvalue and eigenfunctions of covariance operators.