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

100 5. Graphical Representation of Data Using Principal ComponentsFigure 5.4. Biplot using α = 0 for 100 km running data (V1, V2, ...,V10indicatevariables measuring times on first, second, ..., tenth sections of the race).more likely to be similar to those in adjacent parts than to those which aremore distant.Turning to the positions of the observations, the points near the righthandside of the diagrams correspond to the fastest athletes and those onthe left to the slowest. To illustrate this, the first five and last five of the 80finishers are indicated on Figure 5.5. Note that competitors 77 and 78 rantogether throughout the race; they therefore have identical values for all tenvariables and PCs, and hence identical positions on the plot. The positionsof the athletes in this (horizontal) direction tally with the directions of thevectors: observations with large values on all variables, that is slow runners,will be in the direction of the vectors, namely towards the left.Similarly, the observations near the top of the diagram are of athleteswho maintained a fairly steady pace, while those at the bottom correspondto athletes who slowed down considerably during the race. Again this correspondswith the directions of the vectors: those observations at the bottomof the diagram tend to have large values of V10, V9, V8, etc. comparedwith V1, V2, V3, etc., meaning that these runners slow down a lot, whereasthose at the top have more nearly equal values for all variables. For exam-