RBF kernel mapping

Question

I was reading that the Gaussian/RBF kernel maps its input onto the surface of normalized hypersphere.

Our RBF kernel given by:

$k(x,z) = exp(\frac{- ||x-z||^2}{2\sigma^2})$

Can anyone explain why the RBF kernel maps the input space onto the surface of a unit hypersphere?

Answer 1

For easy to visualize, see below image. It says that from 2D dimension we want to map it to 3D dimension such that we'll have landmarks. The left image is 1 landmark, on the other side is n landmarks RBF Kernel