Russel-Research-Method-in-Anthropology

Multivariate Analysis 691
6, 1, 4. The two clustering solutions (again, done with Anthropac) are shown
in figure 21.7.
a. SINGLE LINK
b. COMPLETE LINK
1 3 7 9 14 20 21 25
Level
1
x x x
1
2 x x x x x x x x x
2
4
5
6
x x x x x x x x x x x x
x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x
1 3 7 9 14 20 21 25
Level
5
7
13
Figure 21.7. Cluster analysis of data in table 21.27.
x x x
x x x
x x x
x x x
x x x x x
x x x
x x x x x x x x x
x x x
x x x
x x x x x
x x x x x
x x x x x
24 x x x x x x x x x x x x x x x
In the single-link solution, the two closest neighbors are 20 and 21. They
are exactly one unit of distance apart, and there is a 1 adjacent to the diagonal
of the original matrix where 20 and 21 come together. In figure 21.7a, 20 and
21 are shown joined at level 1. The numbers 1,3 and the numbers 7,9 are the
next closest neighbors. They are both two units apart. Figure 21.7a shows
them joined at level 2.
Once a pair is joined, it is considered a unit. The pairs 1,3 and 7,9 are joined
together at level 4 because they are four units apart (the nearest neighbor to
the pair 1,3 is 7, which is four units from 3). The pair 21,25 are also four units
apart. However, 20,21 are already joined, so 25 joins this pair at level 4. The
connections are built up to form a tree.
Figure 21.7b shows the complete-link (or farthest neighbor) clustering solution
for the data in table 21.29. In complete-link clustering, all the numbers in
table 21.29 are used. Once again, the pair 20,21 is joined at level 1 because
the pair is just one unit apart. The pairs 1,3 and 7,9 join at level 2.
At this point, the complete-link and single-link solutions are identical. At
the next level, though, things change. The neighbors of 20,21 are 14 and 25.
The farthest neighbor from 14 to 20,21 is 21. The distance is seven units. The
farthest neighbor from 25 to 20,21 is 20. The distance is five units. Since five
is less than seven, 25 joins 20,21 at level 5. But the two pairs 1,3 and 7,9 are
not joined at this level.
The only number not yet joined to some other number is 14. It is compared
to its farthest neighbors in the adjacent clusters: 14 is 11 units away from 25
(which is now part of the 20,21,25 cluster) and it’s seven units away from the
7,9 cluster. So, at level 7, 14 is joined to 7,9. The same game is played out
with all the clusters to form the tree in figure 21.7b.