Table 1 The most typical kernel functions in the literature where γ , r , τ and d are kernel parameters

Linear

$x_i^T{x}_j$

Radial basis function

$exp(-\gamma {\parallel x_i-x_j\parallel }^2)$, γ>0

Polynomial

${(\gamma x_i^T{x}_j+r)}^d$, γ>0

Sigmoid

$tanh(\gamma x_i^T{x}_j+r)$, γ>0

Multi quadratic

${(\parallel x_i-x_j\parallel +\tau )}^{1/4}$

Inverse multi quadratic

${(\parallel x_i-x_j\parallel +\tau )}^{-1/4}$