Figure 8.12 Ward's minimum variance clustering of the ponds from Ecological application 8.2. The scale of dendrogram (a) is the square root of the squared distances computed in Table 8.7; in dendrogram (b), it is the Ek (or TESS) statistic.

distances in Ward's method. So, unless the descriptors are such that Euclidean distances (D1 in Chapter 7) are an appropriate model for the relationships among objects, one should not use a Ward's algorithm based or raw data. It is preferable in such cases to compute a distance matrix using an appropriate coefficient (Tables 7.3 to 7.5), followed by clustering of the resemblance matrix in A-space by a distance-based Ward algorithm. Section 9.2 will show that resemblance matrices can also be used for plotting the positions of objects in A-space, "as if" the distances were Euclidean.

Because of the squared error criterion used as the objective function to minimize, clusters produced by the Ward minimum variance method tend to be hyperspherical, i.e. spherical in multidimensional A-space, and to contain roughly the same number of objects if the observations are evenly distributed through A-space. The same applies to the centroid methods of the previous subsections. This may be seen as either an advantage or a problem, depending on the researcher's conceptual model of a cluster.

Combinatorial method

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