The $($cross$-$entropy$)$ error function for binary classification problems for a network having a logistic$-$

sigmoid output activation function, so that $0y(x,w)1,$ and data having target values tin$\{0,1\},$

can be shown to be of the form:

$E(w)=-{\displaystyle \underset{n=1}{\overset{N}{}}}\{t_{n}ln{y}_n+(1-t_n)ln(1-y_n)\}$

Derive the corresponding error function if we consider a network having an output $-1y(x,w)1$

and target values $t=1$ for class $C_1$ and $t=-1$ for class $C_2.$ What would be the appropriate choice

of output unit activation function?