# linear kernel SVM

The linear kernel is defined as: $K(x1,x2)=\langle x1,x2\rangle$. I can see that all that this kernel does is to calculate the dot product in the original space of the data. Why is this kernel then needed? Does it add anything to the plain (kernel-less) SVM?

I fail to understand this kernel; someone help clarify on why there is such a thing as a linear kernel. what does it add to the plain SVM implementation.

## 1 Answer

Linear kernel will not add anything to plain linear SVM, because linear SVM IS SVM with linear kernel. It's just a different mathematical way to look at the same problem.

• Why is it even called a kernel? I thought kernels compute a dot product in some high dimensional space. How does this plain computation of a dot product fit the definition of a kernel? Commented Jan 23, 2016 at 21:20
• form wiki: 'kernel methods require only a user-specified kernel, i.e., a similarity function over pairs of data points in raw representation.' which dot product definitely is. Commented Jan 23, 2016 at 21:32