Which statement about hierarchical and k-means clustering is true?

k-means clustering is characterized as a greedy algorithm due to its iterative approach that seeks to minimize the within-cluster variance, also known as the inertia. The algorithm begins by randomly initializing a set number of cluster centroids. It then assigns each data point to the nearest centroid, forming clusters based on these assignments. After the initial assignment, it recalculates the centroids by taking the mean of all points allocated to each cluster, and repeats this process of assignment and re-calculation iteratively until the centroids no longer move significantly or the assignments do not change.

This greedy nature manifests in the sense that at every step, the algorithm makes a locally optimal choice (assigning points to the nearest centroids) that may not lead to the globally optimal arrangement of clusters. As a result, the final clustering outcome can depend on the initial placement of centroids, which means that k-means can sometimes converge to a local minima instead of the best possible solution.

In contrast, hierarchical clustering does not follow the same iterative or greedy steps; it builds clusters based on a specified linkage criterion and can result in different clusters depending on the distance metrics and methods chosen. Standardizing variables is indeed important for both methods, as differences in scale among variables could lead