Radial basis function kernel

In machine learning, the (Gaussian) 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 x and x', represented as feature vectors in some input space, is defined as

${\displaystyle \textstyle \|\mathbf {x} -\mathbf {x'} \|^{2}}$ may be recognized as the squared Euclidean distance between the two feature vectors. ${\displaystyle \sigma }$ is a free parameter. An equivalent, but simpler, definition involves a parameter ${\displaystyle \textstyle \gamma ={\tfrac {1}{2\sigma ^{2}}}}$:

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