Jolliffe I. Principal Component Analysis (2ed., Springer, 2002)(518s)

11.1. Rotation of Principal Components 275Figure 11.1. Loadings of first rotated autumn components for three normalizationconstraints based on (a) A m; (b) Ãm; (c)à mtated PC has no clear meaning, as there is no longer a successive variancemaximization property after rotation, but these three rotated componentsare matched in the sense that they all have large loadings in the EasternMediterranean. The rotated loadings are rescaled after rotation for conveniencein making comparisons, so that their sums of squares are equal tounity. The numbers given in Figure 11.1 are these rescaled loadings multipliedby 100. The darker shading in the figure highlights those grid boxesfor which the size of their loadings is at least 50% of the largest loading (inabsolute value) for that component.In can be seen that the loadings in the first two plots of Figure 11.1are similar, although those corresponding to Ãm emphasize a larger areaof the Eastern Mediterranean than those derived from A m . The rotatedloadings corresponding to à m show more substantial differences, with aclear negative area in the centre of the Mediterranean and the extremewestern grid-box having a large positive loading.For the normalization based on A m , the vectors of rotated loadings areorthogonal, but the correlations of the displayed component with the other