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Cluster analysis
There are many forms of cluster analysis. The form most commonly applied to grid data is known as hierarchical cluster analysis. It is hierarchical in the sense, that at the lowest level, every element1 is deemed to be in its own cluster. In the first step the similarity (which may be any kind of measure, such as distances or correlations) between each pair of clusters is considered and the most similar pair of clusters are merged (to form a cluster containing two elements). The second step is to compute2 the  similarity between this new cluster and the other (single element) clusters and again merge most similar pair is chosen to form the next cluster. Here the first cluster (of two elements) is considered along with the other clusters (of one element). The third step is to form a new cluster from the next most similar pair of clusters. This continues until the clusters are gradually merged into one cluster. There is one less step or level in the hierarchical clustering than there are elements. The process is often represented by connecting lines in what is known as a dendogram. Cluster analysis is the basis of the FOCUS procedure.

1 Wherever elements appear, constructs could.
2 There are many methods of hierarchical clustering. The methods differ chiefly with respect to how the similarity between a recently merged pair and the the other clusters is computed. Two simple ways is to either take the similarity of the more similar member of the merged pair (often called ‘single-linkage’ or nearest-neighbour and used by FOCUS) or to take the similarity of the less similar member of the merged pair (often called ‘complete-linkage’ or furthest-neighbour). And obviously there are various ways of taking averages. More detail about these can be found in Everitt, Landau, and Leese (2001)


  • Everitt, B.S., Landau, S., and Leese, M. (2001) Cluster analysis (4th edition) London: Arnold.

Richard C. Bell

Establ. 2003
Last update: 15 February 2004