Consider a hard-margin SVM classifier with 1D inputs, using the kernel

function K(u,v)=(uv+2).

(a) What function p(x) from input space to feature space does this

induce? What is the dimensionality of feature space? (Recall that

K(u,v)=p(u)p(v).)

(b) Draw a diagram of the maximum margin linear classifier in feature

space for 2 input points of opposite classes of your choice. Show the

points in input space and in feature space. Show the classification

surface as it appears in feature space and as it appears mapped back

to input space.

(c) Exhibit a set of input points with classes whose images are not

linearly separable in feature space, with a diagram as in part (b).

Explain what this implies about the support vector machine trained on

that data.