Answer: Four general characteristics of hierarchical clustering

Hierarchical clustering methods build a nested hierarchy (dendrogram) of clusters. Their general characteristics include:

1. No requirement to specify the number of clusters $k$ in advance — the $k$ is chosen afterwards by "cutting" the dendrogram at a chosen similarity/distance level.

2. Agglomerative (bottom-up) or divisive (top-down) — agglomerative starts with each object in its own cluster and repeatedly merges the two most similar clusters (e.g., AGNES/AGNES), while divisive starts with all objects in one cluster and repeatedly splits (e.g., DIANA).

3. Merge/split decisions are based on inter-cluster proximity (distance or similarity between clusters), using linking criteria such as:

   • single-link — distance between the closest members,
   • complete-link — distance between the farthest members,
   • average-link — average inter-cluster distance.

4. The hierarchy is represented by a dendrogram — a tree diagram that records the sequences of merges/splits and the similarity levels at which they occur.

5. They do not backtrack / are irreversible — once two clusters are merged (agglomerative) they are never separated; once a cluster is split (divisive) it is never re-merged.

6. They are deterministic and non-linear — no centroid optimisation; no iterative refinement (unlike k-means).

7. Complexity: typically $O(n^2)$ or more (no need for $k$) — less noisy/sensitive to initial conditions if stable, but costlier than partitioning.

(At least four of the above are usually quoted — e.g., 1, 2, 3, 4.)