By G Dunn; Brian Everitt
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3 Mathematical account 49 fit in rdimensions (r being less than p) is obtained by projecting the observations into the subspace defined by the first r principal components. How well this r-dimensional configuration of the n taxonomic units describes the configuration in the original p-dimensional space may be measured by the proportion of the variance in the data accounted for by the first r principal components (see next section). To summarize, one may say that a principal components analysis refers the original data to a new set of orthogonal axes.
4. However, with this approach no allowance is made for the possibility that a match in a four-state character is less likely than in a two-state character. A more elaborate treatment of qualitative characters with more than two states which considers the probability of a given match taking place is given by Smirnov (1960, 1969). He suggests that the similarity based upon anyone character is weighted as a function of the probability of the simultaneous occurrence of such a character state in two separate OTUs; if these C;::>TUs share a rare character state, this is given large weight; if, however, they share a commonly occurring state, then this is given lower weight.
As a second example, a set of data described by Jeffers (1967) of 40 individual winged aphids will be considered. 2. 3. 50 Component Cumulative . 4. Latent vectors for first four components of winged aphid variables (Jeffers, 1967) Latent vectors for component Variable Length Width Fore-wing Hind-wing Spiracles Antenna! segment Antenna! segment Antennal segment Antenna! segment Antenna! 4. Note that the latent vectors have been rescaled by Jeffers after the analysis, so that 'the maximum coefficient (weighting) in each column is + 1.