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ly-shaped triangle in the two configurations. Because we are interest-

ed in the aspects of shape that change the least, we need to define a

statistic that measures the degree of shape difference. We can then

look at all possible triangles and select the one (not necessarily unique)

where the shape difference is minimum. Once the seed triangle is iden-

tified, we expand the clique by adding a landmark to the seed triangle,

so that the clique has four landmarks. Which landmark should be

added? We search through all possible four-landmark cliques (condi-

tional on the three landmarks already included), and we add the

landmark that creates the four-landmark clique where the shape dif-

ference is again minimal. We then add a fifth landmark using the same

criterion, and so on. When do we stop adding landmarks? The clique

will eventually grow to the size where the addition of any remaining

landmark will result in shapes that will be too different to be consid-

ered shape-conservative. We define “too different” by specifying some
a

priori
tolerance that the shape-difference statistic cannot exceed. Once

the tolerance is exceeded, the clique has reached its maximum size. We

then begin a search for a new clique, providing there are enough land-

marks left over and that there is some remaining triangle that will

meet the criterion for being shape-conservative. At most, the new

clique can share only one (for two-dimensional data) or two (for three-

dimensional data) landmarks with any preexisting clique. Once the

second clique reaches its maximum size (beyond which the addition of

any new landmark will produce configurations that are too different),

the search for a new clique starts over. The analysis concludes when all

possible cliques (given the tolerance) have been found.

The
T
statistic, defined by Lele and Richtsmeier (1991; see
Chapter

4
), as a coordinate-system- and scale-invariant measure of shape

difference that can be used for clique formation. Recall that

and that
T
has a minimum possible value of 1.0, obtained when two

landmark configurations have identical shapes. The
a priori
choice of

a tolerance value for
T
is arbitrary, and we can vary the tolerance to

examine its effect on how the cliques form. In many cases, a reasonable

starting tolerance might be 5 to 10% of the
T
statistic that is observed

in a form comparison that uses all of the landmarks.

To illustrate, we can again compare the structures of the mutant

and normal insulins. The results of the analysis are shown in
Figures

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