Radial basis function kernel: Difference between revisions

Revision as of 17:12, 4 May 2018

Revision as of 21:44, 4 September 2018

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:<math>K(\mathbf{x}, \mathbf{x'}) = \exp\left(-\frac{\|\mathbf{x} - \mathbf{x'}\|^2}{2\sigma^2}\right)</math>

<math>\textstyle\|\mathbf{x} - \mathbf{x'}\|^2</math> may be recognized as the [[Euclidean distance#Squared Euclidean distance|squared Euclidean distance]] between the two feature vectors. <math>\sigma</math> is a free parameter. An equivalent, but simpler, definition involves a parameter <math>\textstyle\gamma = \tfrac{1}{2\sigma^2}</math>:

:<math>K(\mathbf{x}, \mathbf{x'}) = \exp(-\gamma\|\mathbf{x} - \mathbf{x'}\|^2)</math>