3.1 ( ) www Show that the tanh function and the logistic sigmoid function (3.6) are related by tanh (a) = 2(2a) 1. (3.100)

3.1 () www Show that the ‘tanh’ function and the logistic sigmoid function (3.6)

are related by tanh

(a) = 2σ(2a) − 1. (3.100)

Hence show that a general linear combination of logistic sigmoid functions of the form y(x,w) = w0 +

M

j=1 wjσ

x − μj s



(3.101)

is equivalent to a linear combination of ‘tanh’ functions of the form y(x, u) = u0 +

M

j=1 uj tanh

x − μj s



(3.102)

and find expressions to relate the new parameters {u1, . . . , uM} to the original parameters

{w1, . . . , wM}.