Dendrogram
Study guide: Exam MAS-II
A dendrogram is the tree that records a hierarchical clustering. Each fusion is drawn as a horizontal bar at the height of the dissimilarity at which it happened, so cutting the tree at a chosen height reads off a set of clusters.
\text{cut at height } h \;\Longrightarrow\; \text{the clusters joined below } h
- Height is the only thing that means anything. The lower two observations fuse, the more similar they are
- Horizontal position means nothing. There are
2^{n-1}ways to draw the same tree by swapping branches at each node, so two leaves being side by side says nothing about their similarity — read down to where they fuse - One tree gives every
Kat once: cutting high gives few clusters, cutting low gives many - A long vertical stretch with no fusions is the natural place to cut — the analogue of a Scree Plot elbow
- Cluster-level structure depends on the Linkage choice: single linkage produces long straggly chains and unbalanced trees, complete and average linkage more even, more interpretable ones
Which Pair Is More Similar? On a dendrogram, leaves A and B sit next to each other but fuse only at height 9; leaves A and C are drawn far apart but fuse at height 3. Which pair is more similar?
Answer A and C. They fuse at height 3 — the clusters containing them merge at a dissimilarity of 3, against 9 for A and B. Being adjacent on the page is an artefact of how the branches happened to be drawn: any node can be flipped without changing the clustering. The classic misreading, and a routine exam trap.