$2$

$((($ Do it in python $)))$

$1\mathrm{.}2$ Finding the Optimal Value of $K$ for $KNN$

The choice of $\text{'}$K$\text{'}$ in K$-$Nearest Neighbors $($KNN$)$ significantly affects the model's ability to

generalize well from the training data to unseen data. This task focuses on identifying the

optimal $\text{'}K\text{'}$ that achieves a balance between overfitting and underfitting.

Objective:

Implement a function to find and return the optimal $\text{'}K\text{'}$ for a $KNN$ model, evaluated on given

training and testing$/$validation data.

Requirements:

The function should be named find$\_$best$\_$k $.$

Parameters:

x$\_$train : A $2$D array of the training features.

y$\_$train : A $1$D array of the training labels.

X$\_$test : A $2$D array of the testing$/$validation features.

y$\_$test : A $1$D array of the testing$/$validation labels.

$k_{\text{m}\text{a}\text{x}\text{:}}$ : An integer representing the maximum value of $\text{'}K\text{'}$ to be considered in the

search for the optimal $\text{'}K\text{'}.$

Return:

The function should return two values:

best$\_$k : An integer representing the optimal number of neighbors based on the

evaluation.

best$\_$error$\_$rate : A float representing the lowest error rate achieved with the

optimal $\text{'}$K$\text{'}.$

In $[]$: def find$\_$best$\_$k

X$\_$train: Training data features.

y$\_$train: Training data labels.

X$\_$test: Testing$/$validation data features.

y$\_$test: Testing$/$validation data labels.

k$\_$max: The maximum value of $K$ to consider.

Returns:

best$\_$k: The optimal value of $K$ that results in the lowest error rate.

best$\_$error$\_$rate: The lowest error rate corresponding to the best $K.$

$"""$

return best$\_$k$,$ best$\_$error$\_$rate

# Usage example:

# best$\_$k$,$ best$\_$error$\_$rate $=$ find$\_$best$\_$k$($X$\_$train, y$\_$train, X$\_$test, $y_{-}$test, $10)$

# print $(f^{\text{'}\text{'}}$ Best $K$ : $\{$best$\_$k$\}$ with error rate: $\{$best$\_$error$\_$rate$\}")$