Which metric compares an observation's distance to its own cluster (cohesion) with its distance to the nearest neighboring cluster (separation)?

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Multiple Choice

Which metric compares an observation's distance to its own cluster (cohesion) with its distance to the nearest neighboring cluster (separation)?

Silhouette analysis measures how well a data point fits its assigned cluster by weighing two ideas: cohesion and separation. For a given point, cohesion is how close it is to other points in the same cluster, while separation is how far it is from points in the nearest neighboring cluster. The silhouette score combines these two aspects for that point, roughly by comparing the distance to its own cluster with the distance to the nearest other cluster and then normalizing. This yields a value between -1 and 1: close to 1 means the point is well inside its cluster and far from others, around 0 means it’s near a boundary, and negative values indicate it would be better assigned to a different cluster. Because it directly expresses the trade-off between staying in the current cluster (cohesion) and being closer to another cluster (separation) on a per-point basis, silhouette scores best capture the described metric. Dendrograms show hierarchical relationships and are visualizations rather than a per-point cohesion/separation ratio. BCSS and WCSS are aggregate dispersion measures—between-cluster and within-cluster sums of squares—not the per-point cohesion-versus-separation comparison that silhouette provides.

Silhouette analysis measures how well a data point fits its assigned cluster by weighing two ideas: cohesion and separation. For a given point, cohesion is how close it is to other points in the same cluster, while separation is how far it is from points in the nearest neighboring cluster. The silhouette score combines these two aspects for that point, roughly by comparing the distance to its own cluster with the distance to the nearest other cluster and then normalizing. This yields a value between -1 and 1: close to 1 means the point is well inside its cluster and far from others, around 0 means it’s near a boundary, and negative values indicate it would be better assigned to a different cluster. Because it directly expresses the trade-off between staying in the current cluster (cohesion) and being closer to another cluster (separation) on a per-point basis, silhouette scores best capture the described metric. Dendrograms show hierarchical relationships and are visualizations rather than a per-point cohesion/separation ratio. BCSS and WCSS are aggregate dispersion measures—between-cluster and within-cluster sums of squares—not the per-point cohesion-versus-separation comparison that silhouette provides.

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