RBF (Radial Basis Function) Kernel

Yao Yao on May 15, 2018

知道了 Radial basis functionkernel 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 $\mathbf{x’}$, represented as feature vectors in some input space, is defined as

$\|\mathbf{x} -\mathbf{x’} \|^{2}$ 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 $\gamma ={\tfrac{1}{2\sigma^{2}}}$:

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



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