Efficient Dictionary-Refining Kernel Adaptive Filter with Fundamental Insights

Masa Aki Takizawa, Masahiro Yukawa

    Research output: Contribution to journalArticle

    17 Citations (Scopus)

    Abstract

    First, we study a basic kernel adaptive filtering algorithm based on stochastic restricted-gradient , which is a natural extension of the naive online regularized risk minimization algorithm (NORMA). Our error surface analysis shows that the algorithm has a decorrelation property due to its explicit use of kernel matrix. It turns out that its normalized version projects the current coefficient vector onto the same hyperplane, but with a different metric, as the kernel normalized least mean square (KNLMS) algorithm. This gives us a fundamental insight bridging two classes of kernel adaptive filtering algorithms. Second, we use this insight to derive an efficient forward-backward splitting algorithm. The same metric as used for the normalized algorithm is employed in the forward step, whereas the ordinary Euclidean metric is employed in the backward step, leading to efficient adaptive refinements of the filter dictionary. We show a monotone approximation property of the proposed algorithm with respect to some modified cost function under certain conditions. Numerical examples show the efficacy of the proposed algorithm.

    Original languageEnglish
    Article number7465845
    Pages (from-to)4337-4350
    Number of pages14
    JournalIEEE Transactions on Signal Processing
    Volume64
    Issue number16
    DOIs
    Publication statusPublished - 2016 Aug 15

    Keywords

    • adaptive proximal forward-backward splitting algorithm
    • Kernel adaptive filtering
    • reproducing kernel Hilbert space
    • {\ell }-{1} norm regularization

    ASJC Scopus subject areas

    • Signal Processing
    • Electrical and Electronic Engineering

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