Which of the following statements is true regarding hierarchical clustering but not K-means clustering?

Hierarchical clustering is characterized by its approach of building a hierarchy of clusters, where the choice of linkage method (such as single, complete, or average linkage) significantly influences the resulting clusters. The linkage method determines how the distance between clusters is calculated, which is essential in forming the cluster hierarchy.

In contrast, K-means clustering involves assigning data points to a predetermined number of clusters, which is set before running the algorithm. This requirement of a set number of clusters is not present in hierarchical clustering, making this choice irrelevant for hierarchical methods.

Moreover, while distance calculations are integral to both techniques, hierarchical clustering can produce a dendrogram that visualizes the clustering structure at multiple levels of granularity, which is not possible in K-means without deciding on the number of clusters first.

Thus, the necessity to choose a linkage in hierarchical clustering highlights an important distinction that makes this option the correct answer for the scenario described.