#normalized-kernel

Question 1: Single choice

An SVM with an offset uses the normalized linear kernel $K(x, x') = \dfrac{x^\top x'}{\lVert x \rVert\,\lVert x' \rVert}$ on points $x \in \mathbb{R}^2$ (none at the origin). What shape can its decision regions have in the original input plane?

Half-planes, because the kernel is still a linear kernel up to scaling1
Discs centred at the origin, since the feature map keeps only $\lVert x \rVert$ 2
Arbitrary curved regions, as with a radial basis kernel3
Wedges bounded by rays from the origin, since $f(sx) = f(x)$ for every $s > 0$ 4

Timed test