Adaptive Learning in Cartesian Product of Reproducing Kernel Hilbert Spaces

TL;DR

This paper introduces an adaptive learning algorithm that utilizes iterative orthogonal projections in the Cartesian product of multiple RKHSs to effectively estimate complex multicomponent nonlinear functions.

Contribution

It combines multikernel adaptive filtering with hyperplane projection methods to handle multicomponent functions in a novel way.

Findings

Demonstrates effectiveness through numerical examples

Handles multicomponent functions with linear and nonlinear parts

Applicable to high- and low-frequency components

Abstract

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.