atus

$,$ counterfeit

$,$ genuine

Replace $A$

$B$

$C$

$D$ and $E$ in the code below to create this plot.

ggplot $($banknote$,,$ colour $=[D]$

$[$E$]()$

$6.$ Now, let's perform k$-$means clustering. We will ignore the fact that the banknotes are classified as genuine or counterfeit, and work only with the variables Top and Diagonal to see if the k$-$means algorithm with $k=2$ will cluster the genuine notes into a group and the counterfeit notes into a group. Firstly, we will create a new dataset that contains only the Top and Diagonal from the banknote dataset. Then we will run the kmeans algorithm with $2$ clusters on this data. Replace $A$

$B$ and $C$ in the code such that this objective can be achieved.

banknote banknote $\%>\%$

$[$A$]($Top$,$ Diagonal$)$

kmean$\_$res B$]($banknote$2,$ centers $=[$C$])$

$2$

$7.$ Next we want to visualise the results in the following way:

library $($factoextra$)$

$,$ data $=$ banknote$2,[$C$]=$ "point"$)$

$8.$ Based on comparing the plot in $3$ with the plot in $1,$ did the $k-$means algorithm cluster all the genuine notes into the same cluster? Give a reason for your answer.