Question $4$

$($a$)$ Which classification approach an SVM is based on$?$

$($b$)$ SVM uses the function

$f(x|W,w_0)=W^{T}x+w_0$

to define a boundary between the regions corresponding to two classes and predict the label

of an unknown instance $x.$ Which idea is used to learn the parameters $W$ and $w_0$ and why?

Illustrate it with a diagram.

$($c$)$ Formulate the problem of learning the parameters $W$ and $w_0$ as an optimization problem.$[2]$

$($d$)$ In the case of soft$-$margin SVM$,$ the constraints are as follows:

$y_i(w^T{x}_i+b)1-{}_i$

${}_{i}0,i=1,2,$dots,$n$

Interpret these constraints with the help of a diagram.

$-$can you please interpret those constraints with the help of a diagram as asked?