6.12 Explicit polynomial kernel mapping. Let K be a polynomial kernel of degree

d, i.e., K: RN  RN ! R, K(x; x0) = (x
x0 + c)d, with c > 0, Show that the dimension of the feature space associated to K is



N + d d



: (6.26)

Write K in terms of kernels ki : (x; x0) 7! (x
x0)i, i 2 f0; : : : ; dg. What is the weight assigned to each ki in that expression? How does it vary as a function of c?