Which of these clustering approaches does not scale well when applied to large data sets?
Hierarchical clustering builds a full dendrogram by repeatedly merging (or splitting) clusters, which requires computing and maintaining a pairwise distance matrix of size O(n²) and has overall time complexity ranging from O(n²) to O(n³) depending on the linkage method used. This quadratic-to-cubic growth in both computation and memory makes hierarchical clustering impractical for very large datasets, unlike density-based methods (which can leverage spatial indexing for near-linear performance) or fuzzy clustering methods (which scale similarly to iterative partitioning algorithms like k-means).
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