Radial basis functions

A radial basis function (RBF) is a real-valued function whose value depends only on the distance from the origin, so that ${\displaystyle \phi (\mathbf {x} )=\phi (\|\mathbf {x} \|)}$; or alternatively on the distance from some other point c, called a center, so that ${\displaystyle \phi (\mathbf {x} ,\mathbf {c} )=\phi (\|\mathbf {x} -\mathbf {c} \|)}$. Any function ${\displaystyle \phi }$ that satisfies the property ${\displaystyle \phi (\mathbf {x} )=\phi (\|\mathbf {x} \|)}$ is a radial function. The norm is usually Euclidean distance, although other distance functions are also possible.

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