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

82 5. Graphical Representation of Data Using Principal ComponentsFigure 5.1. (a). Student anatomical measurements: plot of the first two PC for28 students with convex hulls for men and women superimposed.ning tree (MST) on the diagram, as in Figure 5.1(b). The MST is a set oflines drawn between pairs of points such that(i) each point is connected to every other point by a sequence of lines;(ii) there are no closed loops;(iii) the sum of ‘lengths’ of lines is minimized.If the ‘lengths’ of the lines are defined as distances in seven-dimensionalspace, then the corresponding MST will give an indication of the closenessof-fitof the two-dimensional representation. For example, it is seen thatobservations 5 and 14, which are very close in two dimensions, are joinedvia observation 17, and so must both be closer to observation 17 in sevendimensionalspace than to each other. There is therefore some distortionin the two-dimensional representation in the vicinity of observations 5 and14. Similar remarks apply to observations 12 and 23, and to the group ofobservations 19, 22, 25, 27, 28. However, there appears to be little distortionfor the better-separated observations.