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

5.3. Biplots 101Figure 5.5. Biplot using α = 1 2finishing position in race).for 100 km running data (numbers indicateple, consider the outlying observation at the top of Figures 5.4 and 5.5. Thispoint corresponds to the 54th finisher, who was the only competitor to runthe final 10 km faster than the first 10 km. To put this into perspective itshould be noted that the average times taken for the first and last 10 kmby the 80 finishers were 47.6 min, and 67.0 min respectively, showing thatmost competitors slowed down considerably during the race.At the opposite extreme to the 54th finisher, consider the two athletescorresponding to the points at the bottom left of the plots. These are the65th and 73rd finishers, whose times for the first and last 10 km were 50.0min and 87.8 min for the 65th finisher and 48.2 min and 110.0 min for the73rd finisher. This latter athlete therefore ran at a nearly ‘average’ pacefor the first 10 km but was easily one of the slowest competitors over thelast 10 km.5.3.2 Variations on the BiplotThe classical biplot described above is based on the SVD of X, the columncentreddata matrix. This in turn is linked to the spectral decomposition