# Types of Kernel

The ANOVA Radial Basis Kernel The ANOVA radial basis kernel is closely related from ENG 101 at Westlake High

Gaussian Kernel

in front of the one-dimensional Gaussian kernel is the normalization constant. It comes from the fact that the integral over the exponential function is not unity: ¾- e- x2 2 s 2 Ç x = !!!!! !!! 2 p s . With the normalization constant this Gaussian kernel is a normalized kernel, i.e. its integral over its full domain is unity for every s .

source: stat.wisc.edu

The RBF kernel on two samples x and x', represented as feature vectors in some input space, is defined as (, ′) = ⁡ (− ‖ − ′ ‖) ‖ − ′ ‖ may be recognized as the squared Euclidean distance between the two feature vectors.

Hyperbolic Tangent Kernel

Hyperbolic Tangent kernels are sometimes also called Sigmoid Kernels or tanh kernels and are defined as $$k(x,x^\prime)=\tanh\left(\nu+ x\cdot x^\prime\right)$$ This website provides some discussion.

Laplace RBF Kernel

An intriguing article. To look at an RBF kernel as a low pass filter is something novel. It also basically shows why RBF kernels work brilliantly on high dimensional images.

The linear kernel is what you would expect, a linear model. I believe that the polynomial kernel is similar, but the boundary is of some defined but arbitrary order (e.g. order 3: $a= b_1 + b_2 \cdot X + b_3 \cdot X^2 + b_4 \cdot X^3$).