Exercise $17\mathrm{.}1$ Fitting an SVM classifier by hand $*]$

$($Source: Jaakkola.$)$ Consider a dataset with $2$ points in Id: $($X$1=0,31=-1)$ and $(22=$ V$2,42=1).$

Consider mapping each point to $3$d using the feature vector $($x$)=[1,$ V$2$x$,$ x$217.($This is equivalent to using

a second order polynomial kernel.$)$ The max margin classifier has the form

min $|$w$|?$ s$.$t$.$

$1($wo $($X$1)+$ wO$)>=1$

$2($W$$d $($X$2)+$ wo$)>1$

$(17\mathrm{.}119)$

$(17\mathrm{.}120)$

$(17\mathrm{.}121)$