By G Dunn; Brian Everitt
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Additional info for A introduction to mathematical taxonomy
This scaling is arbitrary and is only useful if it helps the reader to assess the relative importance of each of the original measurements in the composition of the calculated orthogonal components. In this example the ftrst component is again clearly a measure of the overall size of the aphids. Jeffers (1967) interpreted the second component as a measure of the number of ovipositor spines, the third as a measure of the number of antennal spines and the fourth as a measure of the number of spiracles.
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.
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. This scaling is arbitrary and is only useful if it helps the reader to assess the relative importance of each of the original measurements in the composition of the calculated orthogonal components.
A introduction to mathematical taxonomy by G Dunn; Brian Everitt