Support vector machine in the context of Radial basis function kernel

In machine learning, the radial basis function kernel, or RBF kernel, is a popular kernel function used in various kernelized learning algorithms. In particular, it is commonly used in support vector machine classification.

The RBF kernel on two samples ${\displaystyle \mathbf {x} ,\mathbf {x'} \in \mathbb {R} ^{k}}$, represented as feature vectors in some input space, is defined as