Radial basis function kernel: Difference between revisions

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Fourier random features: the Fourier transform of the kernel has the inverse variance
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:<math>K(\mathbf{x}, \mathbf{x'}) = \exp(-\gamma\|\mathbf{x} - \mathbf{x'}\|^2)</math>
 
Since the value of the RBF kernel decreases with distance and ranges between zero (in the infinite-distance limit) and one (when {{math|'''x''' {{=}} '''x''''}}), it has a ready interpretation as a [[similarity measure]].<ref name="primer"/>
The [[feature space]] of the kernel has an infinite number of dimensions; for <math>\sigma = 1</math>, its expansion using the [[multinomial theorem]] is:<ref>{{cite arXiv
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