Hierarchical Clustering, merge by merge


Dataset
Data points 10 to 30 — press Enter or click away to redraw
Linkage
Run
Cluster threshold

The one step:
There is no k to choose and nothing to initialize. Every point starts as its own cluster, and the only move is: find the two closest clusters and join them. Do that n−1 times and everything is in one cluster. Distance between two points is obvious. Distance between two groups is a choice — that choice is the linkage, and it is the only thing that ever changes.

Reading the height scale.
The number at the top right of the tree panel is the cheapest merge the current cut is refusing — the scale grows as you merge, so the tree always fills the panel. Watch it jump when two whole groups finally join: that is the same tall gap you are looking for when you decide where to cut.

Which linkage does what?
All three run the identical loop — they differ only in how the distance between two groups is defined. That one line is the entire difference between these methods.

LinkageDistance between groups A and B
Single the closest pair: min d(a, b)
Complete the farthest pair: max d(a, b)
Average the mean over all: cross pairs