Which quality metric assesses how close a data point is to its own cluster relative to its distance to the nearest other cluster?

Which quality metric assesses how close a data point is to its own cluster relative to its distance to the nearest other cluster?

• A. WCSS
• B. BCSS
• C. Silhouette Score
• D. Dendrogram

Answer: (C)

This item tests how a clustering quality metric evaluates, for each data point, whether it fits best in its own group compared to the nearest other group. The silhouette score does this directly by comparing intra-cluster similarity to inter-cluster separation for each point. For a given point, you measure a(i) as the average distance to all other points in the same cluster, and b(i) as the average distance to points in the nearest neighboring cluster. The silhouette for that point is s(i) = (b(i) - a(i)) / max(a(i), b(i)). If the point is much closer to its own cluster than to any other cluster, s(i) will be near 1; if it sits near the boundary, s(i) is near 0; if it would rather belong to a different cluster, s(i) can be negative. Averaging s(i) across all points gives an overall score of how well the clustering separates and assigns points. Why the other metrics don’t fit this specific idea: WCSS (within-cluster sum of squares) measures how tightly points are grouped inside each cluster but only looks at within-cluster distances to the cluster center, not how far the point is from the nearest other cluster. BCSS (between-cluster sum of squares) captures how far cluster centers are from each other, focusing on global separation rather than the per-point comparison to the nearest alternate cluster. A Dendrogram visualizes hierarchical relationships and linkages between clusters, not a per-point measure of closeness to its own cluster versus the nearest other cluster.

This item tests how a clustering quality metric evaluates, for each data point, whether it fits best in its own group compared to the nearest other group. The silhouette score does this directly by comparing intra-cluster similarity to inter-cluster separation for each point.

For a given point, you measure a(i) as the average distance to all other points in the same cluster, and b(i) as the average distance to points in the nearest neighboring cluster. The silhouette for that point is s(i) = (b(i) - a(i)) / max(a(i), b(i)). If the point is much closer to its own cluster than to any other cluster, s(i) will be near 1; if it sits near the boundary, s(i) is near 0; if it would rather belong to a different cluster, s(i) can be negative. Averaging s(i) across all points gives an overall score of how well the clustering separates and assigns points.

Why the other metrics don’t fit this specific idea: WCSS (within-cluster sum of squares) measures how tightly points are grouped inside each cluster but only looks at within-cluster distances to the cluster center, not how far the point is from the nearest other cluster. BCSS (between-cluster sum of squares) captures how far cluster centers are from each other, focusing on global separation rather than the per-point comparison to the nearest alternate cluster. A Dendrogram visualizes hierarchical relationships and linkages between clusters, not a per-point measure of closeness to its own cluster versus the nearest other cluster.