Which of the following metrics would you use to evaluate the compactness of clusters in K-means?Silhouette ScoreMean Squared ErrorR-squaredPrecision and Recall

The Silhouette Score is the metric you would use to evaluate the compactness of clusters in K-means. This score measures how close each point in one cluster is to the points in the neighboring clusters. It's a way to measure how much a point belongs to its assigned cluster compared to other clusters.

Here's a step-by-step explanation:

1. For each point, calculate the average distance to all other points in the same cluster (a).
2. For the same point, calculate the average distance to all points in the nearest cluster (b).
3. The silhouette score for that point is (b - a) / max(a, b).
4. The overall silhouette score is the average of all points' silhouette scores.

Mean Squared Error and R-squared are typically used for regression models, not clustering. Precision and Recall are used for classification models.