A reproducing-kernel Hilbert space is a Hilbert space of functions in which point evaluation is continuous and satisfies .
The representer theorem reduces regularized optimization over a reproducing-kernel Hilbert space to the span of kernel sections at the observed points.
Every positive-semidefinite kernel has a Hilbert-space feature map satisfying , and determines a unique reproducing-kernel Hilbert space.
The kernel trick evaluates feature-space inner products through without explicitly constructing the feature vectors.
Kernel principal component analysis diagonalizes a centered kernel matrix to perform principal component analysis in an implicit feature space.
If a stationary Gaussian process has covariance spectral density , its reproducing-kernel Hilbert space has normon the functions for which this integral is finite.
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A Reproducing Kernel Hilbert Space (RKHS) is a fundamental concept in functional analysis and machine learning, particularly in the context of kernel methods. It is a Hilbert space of functions in which point evaluations are continuous linear functionals. The main feature of an RKHS is the presence of a reproducing kernel, which allows for an elegant and powerful way to characterize functions in the space.