Multidimensional scaling and nonlinear biplots - Understanding Biplots - page 242

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Figure 5.30 Nonlinear biplot based on Clark's distance for aircraft data with circle
projection prediction biplot trajectories.

Although we currently do not know how to obtain predictions from back-projection
nonlinear prediction trajectories, we can construct such a biplot by assigning predic-
tion.type = "back" in the above call. The resulting biplot is shown in Figure 5.31.

5.7.5 Nonlinear predictive biplot with square root
of Manhattan distance

Finally, we give an example of predictive biplots when square root of Manhattan distances
are used. This distance function differs from our previous examples in that (a) it has a
discontinuity at zero and (b) its second-order derivative vanishes. The last property means
that normal projection prediction trajectories cannot be constructed with Nonlinbipl .
We again use the aircraft data to obtain circle and back-projection prediction trajec-
tories. The function calls are similar to those encountered in Section 5.7.4 except for
the changes dist = "SqrtL1", prediction.type = "circle" or "back" .The
biplots are shown in Figure 5.32. The effect of the absolute value can clearly be seen.