What is the right formula for the RBF 'KernelScale' of fitcsvm?

RBF kernel function is defined as exp(-1/(2*sigma^2) ....

The option 'KernelScale' of the Matlab function fitcsvm, does it refer to sigma, sigma^2, 2*sigma^2, or sqrt(2)*sigma ?

Answer 1

[Ayush Anand]

Hi,

The RBF kernel function is defined as :

The "KernelScale" option in the function "fitcsvm" refers to σ (sigma) in the above equation.

You can read more through the definition of parameters of the "fitcsvm" function here:

https://www.mathworks.in/help/stats/fitcsvm.html

Hope this helps!

[Leon]

KernelScale is not quite the same as sigma: KernelScale = sqrt(2) * sigma, see my answer below.

Answer 2

[Leon]

The RBF (Gaussian) kernel can be defined with either gamma or sigma:

or

where sigma is the standard deviation of the Gaussian distribution.

According to the fitcsvm documentation, instead of using sigma or gamma, the prediction data is simply divided by KernelScale before training, and

Therefore,

KernelScale = 1/sqrt(gamma)

as clarified by MathWorks staff here:

https://uk.mathworks.com/matlabcentral/answers/328796-gaussian-kernel-scale-for-rbf-svm#answer_257956

And:

KernelScale = sqrt(2) * sigma