An efficient sparse kernel adaptive filtering algorithm based on isomorphism between functional subspace and Euclidean space

The existing kernel filtering algorithms are classified into two categories depending on what space the optimization is formulated in. This paper bridges the two different approaches by focusing on the isomorphism between the dictionary subspace and a Euclidean space with the inner product defined by the kernel matrix. Based on the isomorphism, we propose a novel kernel adaptive filtering algorithm which adaptively refines the dictionary and thereby achieves excellent performance with a small dictionary size. Numerical examples show the efficacy of the proposed algorithm.