Kernel-based canonical coordinate decomposition of two-channel nonlinear maps

A kernel-based formulation for decomposing nonlinear maps of two data channels into their canonical coordinates is derived. Each data channel is implicitly mapped to a high dimensional feature space defined by a nonlinear kernel. The canonical coordinates of the nonlinear maps are then found by transforming the kernel maps with the eigenvector matrices of a coupled asymmetric generalized eigenvalue problem. This generalized eigenvalue problem is constructed in the explicit space of kernel maps. The measures of linear dependence and coherence between the nonlinear maps of the channels are also presented. These measures may be determined in the kernel domain, without explicit computation of the nonlinear mappings. A numerical example is also presented.