Cheatsheet: Building a hierarchy: hierarchical clustering

The procedure (agglomerative)

Step	Action
1	every point is its own cluster
2	merge the two closest clusters
3	repeat until one cluster remains
output	the full merge history (a tree), no k chosen up front

Reading the dendrogram

Feature	Meaning
Leaves (bottom)	individual points
A merge connector	two clusters joining
Height of a merge	distance between them when merged
Low merge	very similar
High merge	quite different
Left-right order	meaningless (branches rotate freely)

Cutting it into clusters

Cut	Result
Horizontal line	branches crossed = number of clusters
Cut low	many small, tight clusters
Cut high	few broad clusters
Best cut	across the tallest gap (no merges) = most natural split

Linkage (cluster-to-cluster distance)

Type	Distance used
Single	the two nearest points (can chain)
Complete	the two farthest points (compact)
Average	mean over all pairs
Ward’s	least increase in within-cluster spread

Hierarchical vs k-means

	K-means	Hierarchical
Choose k first	yes	no (cut later)
Output	flat groups	a tree (dendrogram)
Multi-scale view	no	yes
Speed / scale	fast, scalable	slower, poor on large data