85.85. Hierarchical Clustering

Implement **Agglomerative Hierarchical Clustering** (bottom-up approach).

Algorithm:

1. Start with each point as its own cluster

2. Compute distances between all pairs of clusters

3. Merge the two closest clusters

4. Repeat until the desired number of clusters is reached

Linkage Methods:

Single: min distance between any two points in different clusters

Complete: max distance between any two points in different clusters

Average: mean distance between all pairs of points in different clusters

Example:

hc = AgglomerativeClustering(n_clusters=2, linkage='single')

hc.fit(X)

print(hc.labels_) # Cluster assignment for each point

**Explanation:** Unlike K-Means, hierarchical clustering doesn't require specifying k upfront (you can cut the dendrogram at any level). Single linkage tends to create elongated clusters, complete linkage creates compact clusters.

Constraints: