6.16 ( ) Consider a parametric model governed by the parameter vector w together with a data set of input values x1, . . . , xN and a nonlinear feature mapping φ(x).

Suppose that the dependence of the error function on w takes the form J(w) = f(wTφ(x1), . . . ,wTφ(xN)) + g(wTw) (6.97)

where g(·) is a monotonically increasing function. By writing w in the form w =

N n=1

αnφ(xn) + w⊥ (6.98)

show that the value of w that minimizes J(w) takes the form of a linear combination of the basis functions φ(xn) for n = 1, . . . , N.