$1$ K$-$Nearest Neighbors $($KNN$)$ Classifier

$1\mathrm{.}1$ Create and Train K$-$NN Model#

You are tasked with creating and training a K$-$Nearest Neighbors $($KNN$)$ model. Your goal is to understand how to implement a KNN classifier and train your model on a given dataset.

Objective:

Create and train a KNN model using the input training set.

Return the trained model.

Requirements:

The function should be named create$\_$and$\_$train$\_$knn$\_$model.

Parameters:

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

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

k: An integer representing the number of neighbors to consider. The default value should be $1.$

Return:

The function should return the trained KNN model, which is trained onn the input training data and with the input value of k$.$

om

from sklearn.neighbors import KNeighborsClassifier

$$

def create$\_$and$\_$train$\_$knn$\_$model$($X$\_$train, y$\_$train, k$=1)$:

$"""$

Creates and trains a K$-$Nearest Neighbors $($KNN$)$ model.

$$

Parameters:

$-$ X$\_$train: $2$D array of training features.

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

$-$ k: Integer, number of neighbors $($default: $1).$

$$

Returns:

$-$ Trained KNN model.

$"""$

$$

# Initialize the KNN model with k neighbors

$$

# Train the model with X$\_$train and y$\_$train

$$

# Return the trained model

return model

# Example usage:

# model $=$ create$\_$and$\_$train$\_$knn$\_$model$($X$\_$train, y$\_$train, k$=5)$

$$

$1\mathrm{.}2$ 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$\_$max: 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$\text{'}.$

def find$\_$best$\_$k$($X$\_$train, y$\_$train, X$\_$test, y$\_$test, k$\_$max$)$:

$"""$

Finds the best value of K for KNN based on the given training and testing$/$validation data.

$$

Parameters:

$-$ 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$"$Best K: $\{$best$\_$k$\}$ with error rate: $\{$best$\_$error$\_$rate$\}")$

$1\mathrm{.}3$ Using the KNN Classifier for Classification

The K$-$Nearest Neighbors $($KNN$)$ classifier offers a straightforward approach to classification tasks by leveraging the properties of nearby data points. This task involves using the KNN classifier to predict the class of new instances based on the $\text{'}$K$\text{'}$ nearest neighbors and evaluating its performance on a test set.

Objective:

Use the KNN classifier to make predictions on a test dataset.

Evaluate the classifier's performance using metrics such as accuracy, precision, recall, true positives, and true negatives.

Requirements:

Implement a function named evaluate$\_$knn$\_$classifier.

Parameters:

X$\_$train: Training data features as a numpy array.

y$\_$train: Training data labels as a numpy array.

X$\_$test: Test data features as a numpy array.

y$\_$test: Test data labels as a numpy array.

best$\_$k: The optimal number of neighbors as an integer. This should be taken from the output of last function.

Return:

The function should return the evaluation metrics for the test set: accuracy, precision, recall, true positives, and true negatives.

def evaluate$\_$knn$\_$classifier$($X$\_$train, y$\_$train, X$\_$test, y$\_$test, best$\_$k$)$:

$"""$

Evaluates the KNN classifier on the test set with the given best $\text{'}$K$\text{'}$ value.

$$

Parameters:

$-$ X$\_$train: Training data features.

$-$ y$\_$train: Training data labels.

$-$ X$\_$test: Test data features.

$-$ y$\_$test: Test data labels.

$-$ best$\_$k: The optimal$/$best number of neighbors.

$$

Returns:

$-$ accuracy, precision, recall, true$\_$positives, true$\_$negatives: Evaluation metrics.

$"""$

$$

return accuracy, precision, recall, true$\_$positives, true$\_$negatives

# Usage example :

# accuracy, precision, recall, true$\_$positives, true$\_$negativ