What unique characteristic distinguishes K-means clustering from hierarchical clustering?

The characteristic that distinguishes K-means clustering from hierarchical clustering is that a defined number of clusters must be chosen prior to running the algorithm. In K-means, the user specifies the number of clusters (k) to be formed, and the algorithm partitions the dataset based on this predetermined number. This requirement for a pre-specified number of clusters is a fundamental aspect of K-means.

In contrast, hierarchical clustering does not require a predefined number of clusters; it creates a dendrogram that illustrates how data points can be grouped at various levels of similarity. Thus, one can choose the number of clusters after observing the dendrogram.

While other aspects mentioned in the options relate to clustering methods, they do not highlight the essential difference between K-means and hierarchical clustering regarding the specification of clusters. This makes the uniqueness of having a pre-defined number of clusters in K-means the correct characteristic to note.