For a binary classification problem, there is a data set with $2$ feature variables. The data are

presented in a scatter plot, see Figure $2.$ The following R codes are used to train two candidate

models.

model$1<-$ ksvm $($ Species ~$.,$ data $=$ data $,$ kernel $=$rbfdot $,$ kpar $=$ list $($ sigma $=\mathrm{.}1))$

model$2<-$ ksvm $($ Species ~$.,$ data $=$ data $,$ kernel $=$rbfdot $,$ kpar $=$ list $($ sigma $=10))$

The resulting models are visualized in Figure $3.$

$($i$)$ Which model do you prefer? Given the meaning of the parameter of RBF kernel, explain

why the two resulting models have dramatically different behaviors. Note: $$sigma$$ in $$ksvm$$

function is the inverse kernel width for the Radial Basis kernel function, i$.$e$.\backslash$sigma $1.$ RBF kernel is

$\backslash$kappa $($x$,$ y$)=$ exp$(\backslash |$ x $$ y$\backslash |2/2\backslash$sigma $2),$ where $\backslash |\backslash |$ is the $2$ norm.