  We propose a novel adaptive learning algorithm based on iterative orthogonal
projections in the Cartesian product of multiple reproducing kernel Hilbert
spaces (RKHSs). The task is estimating/tracking nonlinear functions which are
supposed to contain multiple components such as (i) linear and nonlinear
components, (ii) high- and low- frequency components etc. In this case, the use
of multiple RKHSs permits a compact representation of multicomponent functions.
The proposed algorithm is where two different methods of the author meet:
multikernel adaptive filtering and the algorithm of hyperplane projection along
affine subspace (HYPASS). In a certain particular case, the sum space of the
RKHSs is isomorphic to the product space and hence the proposed algorithm can
also be regarded as an iterative projection method in the sum space. The
efficacy of the proposed algorithm is shown by numerical examples.
