Biology Reference
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FIGURE 2.5 Landmarks that switch positions. (A) The
landmarks that switch position; (B) the third principal com-
ponent, in the absence of any switch in position; (C) the third
principal component when the landmarks are switched.
differs is only those two points that switch their positions. Figure 2.5 shows a manufac-
tured example, highlighting two landmarks that switch their position ( Figure 2.5A ). In
this case, the coordinates of the landmarks for four of the 28 specimens were simply
exchanged in the data matrix. The effect is fairly subtle; instead of the component that
accounts for approximately 13% of the variation in the actual sample ( Figure 2.5B ), there
is another that also accounts for approximately 13% of the variance ( Figure 2.5C ). The
effects, however, can be far larger, just like digitizing points out of order can produce
dramatic outliers.
Landmarks that switch position may seem to be a rather trivial problem, one that arises
rarely. Yet, when densely sampling a landmark-rich structure, it can become a real issue,
especially when many of the landmarks are located on sutures and foramina. You may
find this kind of variation interesting, but if not, you have two choices. The first is to
exclude one of the two landmarks from the analysis, and the other is to exclude some of
the individuals from the analysis.
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