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Figure 5.19
Illustration of circle projection prediction axis for the original variable Y .
In Figure 5.22 the markers µ = 2, 3 and 4 on the intersection spaces L N are
shown for the original variable Y .As µ varies along the embedded original variable
axis, a nonlinear biplot trajectory is traced in the approximation space, as shown in
Figure 5.23. The shortest distance property is attractive but unfortunately there is currently
no known way of predicting from a back-projection trajectory. In the linear case, however,
prediction axes derived from circle projection, normal projection and back-projection
are identical.
Although we do not have a method for predicting the values of a point P from the
back-projection prediction biplot trajectories, the biplot is shown in Figure 5.24 and the
procedure is also implemented in the function Nonlinbipl .
5.5 A PCA biplot as a nonlinear biplot
When the matrix D is based on Pythagorean distances, then the nonlinear biplot reduces
to a PCA biplot and the nonlinear biplot trajectories become linear. All three methods of
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