(Solved): Q4. Consider the 2-dimensional data shown in Figure 4.1. There are three data points, two of them a ...

Q4. Consider the 2-dimensional data shown in Figure 4.1. There are three data points, two of them are classified as positive (red circles) and one is negative (blue square). Let the decision boundary of the linear classifier be $w^{?}x+b=0$ (shown as a red line in the diagram). The geometric margin of each data point is the perpendicular distance between each data point to the decision boundary (shown as $d_1,d_2$, and $d_3$, respectively). Derive an expression for the total geometric margin, $\mathrm{M}={\mathrm{d}}_1+{\mathrm{d}}_3$, as a function of $\mathrm{W},{\mathrm{c}}_1,{\mathrm{c}}_2$, and ${\mathrm{c}}_3$.