CSCE 470 Lecture 18

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Clustering Review

• Top-down: Bisecting k-means
• Bottom-up: Hierarchical Agglomerative Clustering (HAC)

Hierarchical Agglomerative Clustering

Measure distance between point and every other point and put in a lower triangular matrix:

Constructing this thing takes $O(n^2)$

	1	2	3	4	5	6	7	8	9	10
1	0	—	—	—	—	—	—	—	—	—
2		0	—	—	—	—	—	—	—	—
3			0	—	—	—	—	—	—	—
4				0	—	—	—	—	—	—
5					0	—	—	—	—	—
6						0	—	—	—	—
7							0	—	—	—
8								0	—	—
9									0	—
10										0

Calculating distance between points is as easy as looking them up in the table!

Merge the smallest distance in the table.

Now we have a way to calculate distance between:

• point and point: dist(p,q) = sqrt(sum((i-j)**2 for i,j in zip(p,q))
• point and cluster: dist(p,c) = min(dist(p,q) for q in c) (or max(); design choice)
• cluster to cluster: dist(c1,c2) = min(dist(p,q) for p in c1 for q in c2) (or max(); design choice)