Radial basis function kernel

In machine learning, the (Gaussian) radial basis function kernel, or RBF kernel, is a popular kernel function. It is the most popular kernel function used in support vector machine classification.^[1]

${\displaystyle \exp \left(-{\frac {1}{2}}||\mathbf {x} -\mathbf {x'} ||_{2}^{2}\right)=\sum _{j=0}^{\infty }{\frac {(\mathbf {x} ^{\top }\mathbf {x'} )^{j}}{j!}}\exp \left(-{\frac {1}{2}}||\mathbf {x} ||_{2}^{2}\right)\exp \left(-{\frac {1}{2}}||\mathbf {x'} ||_{2}^{2}\right)}$

Approximations

Because support vector machines and other models employing the kernel trick do not scale well to large numbers of training samples or large numbers of features in the input space, several approximations to the RBF kernel (and similar kernels) have been devised.Cite error: A <ref> tag is missing the closing </ref> (see the help page). Another approach uses the Nyström method to approximate the eigendecomposition of the Gram matrix K, using only a random sample of the training set.^[2]

External links

• Kernels Part 1: What is an RBF Kernel? Really?

See also

• Polynomial kernel
• Radial basis function network

References

1. Yin-Wen Chang, Cho-Jui Hsieh, K |class=cs.LG |year=2009 |version=1 |accessdate=26 March 2013 }}
2. "Using the Nyström method to speed up kernel machines". Advances in Neural Information Processing Systems. 2001. {{cite journal}}: Unknown parameter |authors= ignored (help)