RBF (Radial Basis Function) Kernel

知道了 Radial basis function 和 kernel function 之后，Radial basis function kernel 就好理解了：它是一个 kernel function，然后属于 radial basis function 大类。

Wikipedia: Radial basis function kernel: The RBF kernel on two samples $\mathbf{x}$ and ${\mathbf{x}}^{\prime }$, represented as feature vectors in some input space, is defined as

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

Since the value of the RBF kernel decreases with distance and ranges between 0 (in the limit) and 1 (when $\mathbf{x}={\mathbf{x}}^{\prime }$), it has a ready interpretation as a similarity measure.