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I read that the performance of some kernel functions in SVM can change if we change the number known as kernel option. For example, this article states that kernel option of value 2 was used, http://library.binus.ac.id/eColls/eThesisdoc/Bab5/TSA-2014-0084%205.pdf.

I searched a lot about the meaning of this parameter, but every time I either found results discussing the kernel function types (polynomial, Sigmoid,etc.), or I found research papers that use this parameter without stating what it is.

So, what is 'kernel option'? And what is it called in libsvm in Weka?

Thanks

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In LIBSVM, you can use different kernel types by changing the numerical value of the -t input. You can also set several parameter values depending on which kernel type is used. By "kernel option," the authors in your paper are likely referring to either the kernel type or one of these parameters.

  • If you input -t 0 it will use a linear function:$$K(x_i,x_j)=x_i^Tx_j$$
  • If you input -t 1 it will use a polynominal function: $$K(x_i,x_j)=(\gamma x_i^Tx_j+r)^d, \gamma>0$$
  • If you input -t 2 it will use a radial basis function: $$K(x_i,x_j)=\exp(-\gamma||x_i-x_j||^2), \gamma>0$$
  • If you input -t 3 it will use a sigmoid function: $$K(x_i,x_j)=\tanh(\gamma x_i^T x_j + r)$$

Here, $\gamma$, $r$, and $d$ are kernel parameters that can also be specified using input commands.

From context, I suspect that the authors were stating that they set $d=2$. However, their language is ambiguous and they should have explicitly stated which parameter they were referring to.

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