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De Vito, E., Umanità, V. and Villa, S. (2011) An Extension of Mercer Theorem to Vector-Valued Measurable Kernels. arXiv:1110.4017v1.

has been cited by the following article:

• TITLE: Legendre Polynomial Kernel: Application in SVM

  AUTHORS: Habib Rebei, Nouf S. H. Alharbi

  KEYWORDS: SVM, Polynomial Legendre Kernel, Classification Problem, Mercer Theorem

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.10 No.5, May 30, 2022

  ABSTRACT: In machines learning problems, Support Vector Machine is a method of classification. For non-linearly separable data, kernel functions are a basic ingredient in the SVM technic. In this paper, we briefly recall some useful results on decomposition of RKHS. Based on orthogonal polynomial theory and Mercer theorem, we construct the high power Legendre polynomial kernel on the cube [-1,1]d. Following presentation of the theoretical background of SVM, we evaluate the performance of this kernel on some illustrative examples in comparison with Rbf, linear and polynomial kernels.