By G. Dunn

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Appxp (b) The coefficients defining each linear transformation are such that the sum of their squares is unity; that is, p L a~ = l,i = 1, ... ,p j= 1 (c) Of all the possible transformations of this type, YI has greatest variance. 2 Geometrical interpretation (d) Of all possible transformations of this type which are uncorrelated with Yl' Y2 has the gi-eatest variance. Similarly Y3 has the greatest variance amongst linear transformations uncorrelated with Yl and Y2' and so on, until the complete set of p transformed variables has been defined.

4) a more satisfactory measure of the similarity in shape of two OTUs. Although Euclidean distance has been the dissimilarity measure most widely used in numerical taxonomy, as we shall illustrate by examples given in later chapters, a number of other measures have been employed in particular applications. ) This has been used in anthropology by Czekanowski (1909, 1932), and by Haltenorth (1937) in a study of eight species of the large cats. Carmichael & Sneath (1969) also prefer this coefficient to Euclidean distance in their T AXMAP clustering procedure.

5 Note that the values for the first principal component are all positive and are clearly related to the size of the buttercup flowers. 4). the best-fitting straight line in this p-dimensional character space. Similarly, the first two principal components describe the best-fitting plane in this space, and so on. 1. (a) Plot of mean petal length against mean petal width for four hypothetical buttercups. (b) Plot of first principal component score derived from measurements of petal length and width.