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Since the value of the RBF kernel decreases with distance and ranges between zero (in the limit) and one (when '''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 is:<ref>{{cite arXiv
|last=Shashua
|first=Amnon
|eprint=0904.3664
|title=Introduction to Machine Learning: Class Notes 67577
|class=cs.LG
|year=2009
|version=1
|accessdate=26 March 2013
}}</ref>
:<math>\exp(-\frac{1}{2}||\mathbf{x} - \mathbf{x'}||_2^2) = \sum_{j=0}^\infty \frac{(\mathbf{x'}^\top \mathbf{x'})^j}{j!} \exp(-\frac{1}{2}||\mathbf{x}||_2^2) \exp(-\frac{1}{2}||\mathbf{x'}||_2^2)</math>
==Approximations==
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