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I am new to machine learning. Could anyone tell me the difference between linear kernel vs. polynomial kernel of degree 1 wrt SVM (if there is any difference)?
The reason I asked, I am getting different accuracy for both on the spam dataset from UCI.
Depending on your SVM implementation, there may be a difference. Compared to the linear kernel, the polynomial kernel has an additional parameter $c$ (and $d$ of course):
$K(x,y) = (x^\mathsf{T} y + c)^{d}$
However, if $c=0$ (and $d=1$), then:
(linear) $K(x,y) = x^\mathsf{T} y \equiv K(x,y) = (x^\mathsf{T} y + c)^{d}$ (polynomial)
Nonetheless, some SVM implementations may opt-out of calculating $c$ and assume homogeneity in order to reduce the number of hyper-parameters. So, it depends on how your SVM is implemented.
For example sklearn's polynomial kernel assumes by default $c=1$ if you do not specify the parameter, which would make it not exactly the same as a linear kernel.
There can be a difference, as the Polynomial kernel has an additional parameter. If you're including that as a hyper-parameter, it could explain the difference.
Otherwise, if it is fixed to 0, then they should be the same. How big a difference in accuracy are you talking? If it's fairly minor it could be due to numerical stability issues.
