Radial basis function kernel: Difference between revisions

Revision as of 01:55, 27 February 2013

Revision as of 13:11, 27 February 2013

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:<math>K(\mathbf{x}, \mathbf{x'}) = \exp(-\frac{||\mathbf{x} - \mathbf{x'}||_2^2}{2\sigma^2})</math>

<math>\textstyle||\mathbf{x} - \mathbf{x'}||_2^2</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 = -\fractfrac{-1}{2\sigma^2}</math>:

:<math>K(\mathbf{x}, \mathbf{x'}) = \exp(\gamma||\mathbf{x} - \mathbf{x'}||_2^2)</math>