Which statement regarding clustering algorithms is true?

The statement that k-means clustering is a greedy algorithm is accurate. K-means clustering operates through a process that iteratively refines the placement of cluster centroids based on the data points assigned to each cluster. The algorithm starts with a random selection of centroids and, in each iteration, reassigns data points to the nearest centroid before recalculating the centroid locations. This process continues until the centroids stabilize or the assignments no longer change.

Because each step only chooses the next nearest points without considering the global best configuration but rather focuses on local optimization, it embodies the characteristics of a greedy algorithm. It seeks to minimize within-cluster variance at each iteration, often leading to suboptimal solutions because it does not backtrack or consider earlier decisions once made.

Other statements can be misunderstood. For instance, hierarchical and k-means clustering apply different methodologies to cluster data and typically do not yield the same results due to their distinct approaches to forming clusters. Additionally, while standardizing variables can influence the results in clustering scenarios, especially given the sensitivity of distance metrics used in k-means, it isn't universally applicable to all clustering methods. Therefore, the confirmation that k-means is a greedy algorithm provides clarity and an accurate understanding of one such clustering