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(4,10)
(7,10)
(4.7, 8.7)
(4,9)
(4,8)
(6,8)
(12,6)
(10,5)
(11,4)
(10.5, 3.8)
(3,4)
(2.5, 3)
(9,3)
(12,3)
(2,2)
(5,2)
Figure 7.5: Three more steps of the hierarchical clustering
1. Take the distance between two clusters to be the minimum of the distances
between any two points, one chosen from each cluster. For example, in
Fig. 7.3 we would next chose to cluster the point (10,5) with the cluster of
two points, since (10,5) has distance
√
2, and no other pair of unclustered
points is that close. Note that in Example 7.2, we did make this combi-
nation eventually, but not until we had combined another pair of points.
In general, it is possible that this rule will result in an entirely different
clustering from that obtained using the distance-of-centroids rule.
2. Take the distance between two clusters to be the average distance of all
pairs of points, one from each cluster.
(2,2) (3,4) (5,2) (4,8) (4,10) (6,8) (7,10) (11,4) (12,3) (10,5) (9,3) (12,6)
Figure 7.6: Tree showing the complete grouping of the points of Fig. 7.2
