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

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Sofiane Kharbech
Sofiane Kharbech 2018-5-4
编辑： Leon 2025-4-7
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 ?

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Ayush Anand
Ayush Anand 2024-1-12
编辑：Ayush Anand 2024-1-12
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!
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Leon
Leon 2025-4-7
编辑：Leon 2025-4-7
KernelScale is not quite the same as sigma: KernelScale = sqrt(2) * sigma, see my answer below.

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Leon
Leon 2025-4-7
编辑：Leon 2025-4-7
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

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