Which measure reflects the separation between clusters in a dataset?

The separation between clusters in a dataset is effectively measured by the between-cluster sum of squares (BCSS). This statistic quantifies the variance among the centroids of the clusters, indicating how distinct the clusters are from one another. A higher BCSS value implies that the clusters are well separated, meaning that the variation among the clusters is greater compared to the variation within each cluster.

This is crucial for clustering analysis as one of the key objectives in clustering is to maximize the separation between different groups while minimizing variance within each group. In contrast, other metrics like within-cluster sum of squares focus on the compactness of individual clusters, which does not directly measure the distance between separate clusters. The silhouette score, while it provides insight into the quality of a clustering solution, combines the concepts of both within- and between-cluster distances to provide a single value indicating how well each point lies within its cluster compared to its nearest neighbor cluster—but it does not exclusively focus on separation. The variance ratio is also a broader measure and does not directly capture the notion of separation between distinct clusters.

Therefore, BCSS serves as a clear and direct measure of the separation between clusters, making it the most appropriate choice in this context.