Table 3 List of kernel functions and their mathematical expressions
Kernel type | Kernel function \(\left\{{\varvec{K}}\left({{\varvec{x}}}_{{\varvec{i}}}{,{\varvec{x}}}_{{\varvec{j}}}\right)\right\}\) |
|---|---|
Radial basis function (RBF) | \(exp(-\gamma {\| {x}_{i}-{x}_{j}\| }^{2})\) |
Polynomial | \((\gamma <{x}_{i}{,x}_{j}{>+r)}^{d}\) |
Linear | \(<{x}_{i}{,x}_{j}>\) |
Hyperbolic | \(tanh(\gamma <{x}_{i}{,x}_{j}>+r)\) |
Laplace | \(exp(-\gamma \| {x}_{i}-{x}_{\mathrm{j}}\| )\) |
Bessel | \(-{Bessel}_{order}^{d}\gamma {\| {x}_{i}-{x}_{\mathrm{j}}\| }^{2}\) |
Sigmoid | \({(<{x}_{i}{,x}_{j}>+r)}^{d}\) |