Jolliffe I. Principal Component Analysis (2ed., Springer, 2002)(518s)

218 9. Principal Components Used with Other Multivariate TechniquesFigure 9.4. English counties: complete-linkage four-cluster solution superimposedon a plot of the first two PCs.the diagram is Greater London and the four-county cluster at the top leftconsists of other metropolitan counties. The counties at the right of thediagram are more rural, confirming the interpretation of the first PC givenearlier. The split between the larger groups at the right of the plot is rathermore arbitrary but, as might be expected from the interpretation of thesecond PC, most of the retirement areas have similar values in the verticaldirection; they are all in the bottom part of the diagram. Conversely, manyof the counties towards the top have substantial urban areas within them,and so have somewhat lower values on the first PC as well.The clusters are rather nicely located in different areas of the figure,although the separation between them is not particularly clear-cut, exceptfor Greater London. This behaviour is fairly similar to what occurs for otherclustering methods in this example, and for different numbers of clusters.For example, in the eight-cluster solution for complete-linkage clustering,one observation splits off from each of the clusters in the top left and bottomright parts of the diagram to form single-county clusters. The large 27-