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A radial basis function (RBF) is a real-valued function whose value depends only on the distance from the origin. Gaussian function is one example.

A radial basis function (RBF) is a real-valued function whose value depends only on the distance from the origin, so that $\phi( x ) = \phi (\|x\|) $. Sums of radial basis functions are typically used to approximate given functions. Examples include Gaussian:

$$\phi( r ) =e^{-(\varepsilon r)^{2}}\;,$$

And others, and find application, for example, in simple neural networks, and for kernels in machine learning support vector machines.