The nature of statistical learning theory
The nature of statistical learning theory
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Kernel Principal Component Analysis
ICANN '97 Proceedings of the 7th International Conference on Artificial Neural Networks
Model Selection for Regularized Least-Squares Algorithm in Learning Theory
Foundations of Computational Mathematics
Radial kernels and their reproducing kernel Hilbert spaces
Journal of Complexity
Mercer’s theorem, feature maps, and smoothing
COLT'06 Proceedings of the 19th annual conference on Learning Theory
An Explicit Description of the Reproducing Kernel Hilbert Spaces of Gaussian RBF Kernels
IEEE Transactions on Information Theory
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Kernel methods play an important role in machine learning, pattern recognition and data mining. Although the kernel functions are the central part of the kernel methods, little is known about the structure of its reproducing kernel Hilbert spaces (RKHS) and the eigenvalues of the integral operator. In this paper, we first give the definition of the extended Gaussian kernel which includes the Gaussian kernel as its special case. Then, through a generalization form of the Weyl inner product, we present an explicit description of the RKHS of the extended Gaussian kernel. Furthermore, using the Funk-Hecke formula, we get the eigenvalues and eigenfunctions of the integral operator on the unit sphere.