Support Vector Machine: Linear or Non-linear

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Tiago Dias
Tiago Dias 2020-7-11
回答： Thiago Henrique Gomes Lobato 2020-7-12
Hi,
I have a doubt on SVM.
SVM is a linear or non-linear method, or it depend on the type of kernel i am using.
If i am using a polynomial or rbf kernel, i think that the SVM-poly or SVM-rbf is non-linear.
But if i am using a linear kernel, does that make the SVM non-linear or sill linear?
Thanks for any upcoming help

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Thiago Henrique Gomes Lobato
SVM is always linear in the parameters, but using non-linear kernels allows it to consider non-linear relations between the data by transforming then to another feature space (ex: both f(x,y) = a*x+b*y and f(x,y) = a*x*y+b*log(y)/x are linear in the parameters, but the second example is a non-linear function in x and y), especially with kernels like rbf that can have an infinite equivalent in the parameter space. You can check own matlab documentation page about the method for some more insights. One of the main advantages of SVM is to replace this feature space transformation by a kernel function, since then only the dot product is needed and, depending of your kernel, can produce an enourmous computational and description gain.

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