6.12 ( ) www Consider the space of all possible subsets A of a given fixed set D.

Show that the kernel function (6.27) corresponds to an inner product in a feature space of dimensionality 2|D| defined by the mapping φ(A) where A is a subset of D and the element φU(A), indexed by the subset U, is given by

φU(A) =

1, if U ⊆ A;

0, otherwise. (6.95)

Here U ⊆ A denotes that U is either a subset of A or is equal to A.