Cluster Analysis 9

Stability

Stability is evaluated by using different clustering procedures on the same data and considering the differences that occur. For example, you may first run a hierarchical clustering procedure, followed by k-means clustering to check whether the cluster affiliations of the objects change. Alternatively, running a hierarchical clustering procedure, you can use different distance measures and evaluate their effect on the stability of the results. However, note that it is common for results to change even when your solution is adequate. As a rule of thumb, if more than 20% of the cluster affiliations change from one technique to the other, you should reconsider the analysis and use, for example, a different set of clustering variables, or reconsider the number of clusters. Note, however, that this percentage is likely to increase with the number of clusters used.
When the data matrix exhibits identical values (referred to as ties), the ordering of the objects in the dataset can influence the results of the hierarchical clustering procedure. For example, the distance matrix based on the city-block distance in Table 9.8 shows the distance of 56 for object pairs (D,E), (E,F), and (F,G). Ties can prove problematic when they occur for the minimum distance in a distance matrix, as the decision about which objects to merge then becomes ambiguous (i.e., should we merge objects D and E, E and F, or F and G if 56 was the smallest distance in the matrix?). To handle this problem, van der Kloot et al. (2005) recommend re-running the analysis with a different input order of the data. The downside of this approach is that the labels of a cluster may change from one analysis to the next. This issue is referred to as label switching. For example, in the first analysis, cluster 1 may correspond to cluster 2 in the second analysis. Ties are, however, more the exception than the rule in practical applications—especially when using (squared) Euclidean distances—and generally don’t have a pronounced impact on the results. However, if changing the order of the objects also drastically changes the cluster compositions (e.g., in terms of cluster sizes), you should reconsider the set-up of the analysis and, for example, re-run it with different clustering variables.

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