An efficient kernel normalized least mean square algorithm with compactly supported kernel

Abstract

We investigate the use of compactly supported kernels (CSKs) for the kernel normalized least mean square (KNLMS) algorithm proposed initially by Richard et al. in 2009. The use of CSKs yields sparse kernelized input vectors, offering an opportunity for complexity reduction. We propose a simple two-step method to compute the kernelized input vectors efficiently. In the first step, it computes an over-estimation of the support of the kernelized input vector based on a certain ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -ball. In the second step, it identifies the exact support by detailed examinations based on an ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -ball. Also, we employ the identified support given by the second step for coherence construction. The proposed method reduces the amount of ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -distance evaluations, leading to the complexity reduction. The numerical examples show that the proposed algorithm achieves significant complexity reduction.