# Kernel selection intuition

Which problems are best solved using which kernels and why?

Can you give a simple toy problem that isn't linearly separable in input space but is linearly separable in feature space, using an RBF kernel? A polynomial kernel?

• maybe the most simple example is the case where you have a circle on the plane. You want to segment that circle by considering the points within that circle to belong to one class, and the points outside that circle to another one. This is not linearly separable, but mapping it in polar coordinates becomes linearly separable. Commented May 14, 2013 at 11:56
• what is the kernel that corresponds to mapping in polar coordinates? Commented May 14, 2013 at 19:57
• The polar transformation corresponds to $(x,y) \rightarrow \left(\sqrt{x^{2}+y^{2}}, \arctan(x,y)\right)$. The closest related polynomial kernel might be $(x,y) \rightarrow \left( x^{2},y^{2},\sqrt{2}xy\right)$. In any case, this will work for that toy case. Commented May 14, 2013 at 21:09