$[30$ marks$]($K$-$Nearest Neighbors Classification$)$ Please demonstrate a detailed process

of using the K$-$Nearest Neighbor $($KNN$)$ classifier to predict the qualification status of

the test instance vec$($x$)=($ Speed $=5\mathrm{.}20,$ Weight $=500).$

a$)$ Before employing the KNN classifier, apply Min$-$max normalization to preprocess

the attribute values. Refer to the instructions provided in the lecture note KNN$.$pdf

$($page $17)$ for the normalization process. This step ensures that the attributes are

standardized within a specified range. $(10$ points$)$

b$)$ Plot the preprocessed training dataset on a $2$D plane. Represent the attribute Speed

on the x $-$axis and Weight on the y $-$axis. Instances belonging to the class no should be

labeled with $"-",$ while instances belonging to the class yes should be labeled with $"+".$

$(10$ points$).$

c$)$ Use KNN to predict the qualification status of the test instance vec$($x$)=($ Speed $=5\mathrm{.}20,$

Weight $=500)$ by setting k to $1,3,$ and $5,$ respectively. Please show the detailed process

for each value of k$,$ including the calculation of distances, selection of nearest neighbors,

and determination of the predicted qualification status. $(10$ points$)$