Which of the following statements about cluster numbering in k-Means is true?

• A. The cluster numbers indicate the order in which clusters were created.
• B. The cluster numbers are arbitrary labels and do not indicate any inherent ranking of clusters.
• C. The cluster numbers reflect the distance of each cluster center to the origin.
• D. The cluster numbers are used to measure cluster quality.

Answer: (B)

In this context, cluster numbers are just arbitrary labels. The k-Means algorithm assigns each data point to the nearest centroid, and while the centroids themselves are updated during iterations, there’s no inherent meaning attached to which centroid gets labeled as 1, 2, or 3. Re-running the algorithm with a different initialization or data order can swap these labels without changing the actual grouping. So the numbers do not indicate any order, creation sequence, distance to the origin, or a measure of cluster quality. Cluster quality is assessed with metrics like within-cluster sum of squares or silhouette scores, not by the cluster labels themselves.