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Reproducing Kernel Function Based on Walsh Series

Che Hao Chang

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Abstract

A new reproducing kernel function of least square support vector machines based on Walsh series is presented in this paper.The reproducing kernel is constructed in reproducing kernel Hilbert space(RKHS).Because the Hilbert space and the square integrable space are isomorphic,according to the wavelet multi-resolution analysis,Walsh consequence can be seen a set of orthogonal basis to construct the reproducing kernel.The simulation results are discussed to illustrate the proposed method.

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What this paper is about

A new reproducing kernel function of least square support vector machines based on Walsh series is presented in this paper.The reproducing kernel is constructed in reproducing kernel Hilbert space(RKHS).Because the Hilbert space and the square integrable space are isomorphic,according to the wavelet multi-resolution analysis,Walsh consequence can be seen a set of orthogonal basis to construct the reproducing kernel.The simulation results are discussed to illustrate the proposed method.

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Available abstract

A new reproducing kernel function of least square support vector machines based on Walsh series is presented in this paper.The reproducing kernel is constructed in reproducing kernel Hilbert space(RKHS).Because the Hilbert space and the square integrable space are isomorphic,according to the wavelet multi-resolution analysis,Walsh consequence can be seen a set of orthogonal basis to construct the reproducing kernel.The simulation results are discussed to illustrate the proposed method.

Key concepts: Reproducing kernel Hilbert space, Representer theorem, Kernel (algebra), Square-integrable function, Walsh function, Mathematics, Kernel embedding of distributions, Series (stratigraphy)

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