Which statements are true regarding K-means and hierarchical clustering?

When considering the characteristics of K-means and hierarchical clustering, the statement that K-means requires random assignments while hierarchical clustering does not is accurate.

K-means clustering involves an initial random assignment of centroids to start the clustering process. This randomness is integral because it can significantly affect the final clusters produced by the algorithm. The algorithm iteratively assigns data points to the nearest centroid and then recalculates the centroids based on these assignments until convergence is reached. The reliance on this initial random assignment means that different runs of K-means can yield different cluster outcomes, especially if the data set is not well-separated.

In contrast, hierarchical clustering does not require a random assignment process. This method builds a hierarchy of clusters by either merging or splitting existing clusters in a systematic way, based on the distance between points or clusters. The output of hierarchical clustering is a dendrogram, which illustrates the arrangement of clusters and the distances at which they merge. As a result, its outcome is more stable compared to K-means in terms of initial conditions.

Understanding these distinctions helps clarify why the implications of random assignments differ markedly between the two clustering methods, thus supporting the correctness of the answer.