Question $5$

$($a$)$ What is the basic computational unit of an ANN? Show its complete structure and

operations when the input is a feature vector $v=(x_1,x_2,x_3,x_4,x_5)$

$($b$)$ Which of the following activation functions is better and why?

i$)$ Sigmoid

ii$)$ Tanh

iii$)$ ReLU

$($c$)$ Show the structure of an ANN with one hidden layer containing $4$ neurons for a mass

classification problem $($normal vs mass$)$ on mammogram images; assume that a

mammogram is represented using three features.

$($d$)$ Consider a three$-$class problem and an instance $x$ belonging to class $3.$

i$)$ Represent the label y of $x$ in one$-$hot encoding.

ii$)$ If the vector of the predicted posterior probabilities of $x$ is $p={\left[\begin{array}{ccc}0\mathrm{.}2& 0\mathrm{.}4& 0\mathrm{.}4\end{array}\right]}^T,$

compute the cross$-$entropy loss made by the algorithm.