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Table 3 List of kernel functions and their mathematical expressions

From: PredCRG: A computational method for recognition of plant circadian genes by employing support vector machine with Laplace kernel

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 \({(<{x}_{i}{,x}_{j}>+r)}^{d}\)
  1. \(\gamma\), \(d,\) \(r\) and \(order\) are kernel parameters and <  > denotes the inner product