Which of the following metrics would you use to evaluate the compactness of clusters in K-means?Silhouette ScoreMean Squared ErrorR-squaredPrecision and Recall
Question
Which of the following metrics would you use to evaluate the compactness of clusters in K-means?Silhouette ScoreMean Squared ErrorR-squaredPrecision and Recall
Solution
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:
- For each point, calculate the average distance to all other points in the same cluster (a).
- For the same point, calculate the average distance to all points in the nearest cluster (b).
- The silhouette score for that point is (b - a) / max(a, b).
- 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.
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How is the final set of clusters determined in the k-means algorithm?Select one:a.By selecting the set of clusters that minimize the sum of squared errorsb.By selecting the set of clusters that maximize the within-cluster variancec.By selecting the set of clusters that maximize the sum of squared errorsd.By selecting the set of clusters that minimize the within-cluster variance
The metric is commonly used to evaluate the performance of clustering algorithms.
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