## f1-score in knn

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The F1-score is a metric used to evaluate the performance of a classification model. It is the harmonic mean of the precision and recall of the model. Precision is the fraction of positive predictions that are actually correct, while recall is the fraction of actual positives that are correctly predicted.

The F1-score is a good measure of the overall performance of a classification model, because it takes into account both precision and recall. It is particularly useful for evaluating models that are used to classify imbalanced datasets, where there are many more negative examples than positive examples.

To calculate the F1-score for a KNN model, we first need to calculate the precision and recall of the model. We can do this by counting the number of true positives, false positives, true negatives, and false negatives. The following table shows how to calculate these metrics:

Once we have calculated the precision and recall, we can calculate the F1-score using the following formula:

F1-score = 2 * (precision * recall) / (precision + recall)

The F1-score is a value between 0 and 1, with a higher score indicating better performance. A perfect score of 1 indicates that the model has perfect precision and recall.

Here is an example of how to calculate the F1-score for a KNN model in Python:

import numpy as np
from sklearn.metrics import f1_score

knn = KNeighborsClassifier(n_neighbors=5)

# Predict the labels for the test data
y_pred = knn.predict(X_test)

# Calculate the F1-score
f1_score = f1_score(y_test, y_pred)

# Print the F1-score
print(f1_score)

This code will print the F1-score for the KNN model on the test data.

The F1-score is a useful metric for evaluating the performance of KNN models, and it can be used to compare the performance of different KNN models or to compare the performance of KNN models to other classification models.