Adaptive Learning in Cartesian Product of Reproducing Kernel Hilbert Spaces

We propose a novel adaptive learning algorithm based on iterative orthogonal projections in the Cartesian product of multiple reproducing kernel Hilbert spaces (RKHSs). The objective is to estimate or track nonlinear functions that are supposed to contain multiple components such as i) linear and nonlinear components and ii) high- and low- frequency components. 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 particular case, the “sum” space of the RKHSs is isomorphic, under a straightforward correspondence, 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.