$3.$ Email spam filtering models often use a bag$-$of$-$words representation for emails. In a bag$-$of$-$words representation, the descriptive features that describe a document $($in this case, an email$)$ each represent how many times a particular word occurs in the document. One descriptive feature is included for each word in a predefined dictionary. The dictionary is typically defined as the complete set of words that occur in the training dataset.

Table $2$ lists the bag$-$of$-$words representation for the following five emails and a target feature, SPAM, whether they are spam emails or genuine emails.

$-$ "money, money, money"

$-$ "free money for free gambling fun"

$-$ "gambling for fun"

$-$ "machine learning for fun, fun, fun"

$-$ "free machine learning"

Table $2$

$3\mathrm{.}1$ What target level would a nearest neighbour model using Manhattan distance return for the following email: "machine learning for free"? Show calculation for the first instance only and thereafter, show only the calculated Euclidean distances without showing the calculations.

$3\mathrm{.}2$ What target level would a k$-$NN model with $\backslash (\backslash$mathrm$\{$k$\}=3\backslash )$ and using Manhattan distance return for the same query?

$3\mathrm{.}3$ What target level would a weighted $\backslash (\backslash$mathrm$\{$K$\}-\backslash$mathrm$\{$NN$\}\backslash )$ model with $\backslash (\backslash$mathrm$\{$k$\}=3\backslash )$ and using a weighting scheme of the reciprocal of the squared Manhattan distance between the neighbour and the query, return for the query? Show only the calculated weights without showing the calculations.