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The types of clusters formed in these five playing card examples are disjoint in that a single partitioning splits the cards into two or more final clusters. There is another approach which allows for clusters to be further subdivided. An obvious example would be to initially split the cards into red and black clusters. Each of these could then be split into their suits (four clusters) and then into face and non-face cards (eight clusters). This is known as hierarchical clustering and the method creates a taxonomy of cluster relatedness.

If the mean for each variable is used the niche becomes a single point in p-dimensional space. Similarly, the state of the genome can be represented by a single point that represents the expression values for each of p genes. A complete description of either requires that all p variables are recorded. However, once p exceeds the trivial value of three it is difficult to represent this state unless it can be mapped onto fewer dimensions. It would certainly be very difficult to compare two niches or two gene expression states visually in their original p-dimensional space.

The first is an iterative algorithm that gives the method its alternative name of reciprocal averaging. The iterative procedure uses the row scores to adjust the column scores which are then used to adjust the row scores and so on until the change in scores is below some preset minimum criterion. The result is a set of row and column scores that have the maximum possible correlation. This must then be repeated for all other axes but with a constraint that betweenaxis scores must be uncorrelated.

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