Topic summary
Kernel function
Extracted from the Wikipedia article Positive-definite kernel.
Kernels in machine learning
Positive-definite kernels, through their equivalence with reproducing kernel Hilbert spaces (RKHS), are particularly important in the field of statistical learning theory because of the celebrated representer theorem which states that every minimizer function in an RKHS can be written as a linear combination of the kernel function evaluated at the training points. This is a practically useful result as it effectively simplifies the empirical risk minimization problem from an infinite dimensional to a finite dimensional optimization problem.