Positive definite kernels and reproducing kernel Hilbertspaces

In this paper, we give aspects of positive definite functions with their respectivereproducing kernel Hilbert spaces and applications. The following topics helps tounderstand reproducing kernel Hilbert spaces and their boundary spaces. We providea characterization of kernel functions and reproducing kernel, derive their properties,and discuss methods for designing them. Given a kernel and a training set, we canform the matrix known as the kernel, or Gram matrix: the matrix containing theevaluation of the kernel function on all pairs of data points.

کلیدواژه ها:

Positive definite matrices ، Gram matrix ، Positive definite kernel ، Reproducingkernel Hilbert space ، Reproducing property.