Classification and Clustering Applications - An Invariant Approach to Statistical Analysis of Shapes - page 252

correctness of classification and record the outcome (classified
correctly or not).
STEP 5: Go back to Step 1, replace the individual that was
removed in this step in the previous iteration, remove a dif-
ferent individual and repeat steps 2 to 4. Continue until each
individual has been removed once and classified.

This method of studying the error rates of a particular procedure is a
cross-validation procedure (Efron and Tibshirani, 1991). We repeated
the cross-validation procedure for other dissimilarity measures. Table
6.1 provides the number of times an individual was classified incor-
rectly. This table suggests that different dissimilarity measures have
about the same misclassification rates and that landmark coordinate
data from the cranial base may not be sufficient for diagnostic classifi-
cation of certain craniofacial phenotypes. Interestingly, the unicoronal
synostosis class, which is characterized by marked asymmetry of the
calvarium and premature closure of a unilateral suture, has the lowest
misclassification rate. Posterior plagiocephaly is also identified by
asymmetry of the calvarium, but not by premature closure of a unilat-
eral suture, and it shows a higher misclassification rate. Both sagittal
and metopic craniosynostosis involve fusion of a midline suture, dis-
play cranial symmetry, and show relatively high percentages of
misclassification.
Table 6.1 Cross-validation based misclassification rates for various dissimi-
larity measures and four known classes. The smaller percentage indicates
a more correct classification. All four dissimilarity measures seem to be
equally effective in classifying individuals in different categories of
craniofacial anomalies.

Unicoronal Sagittal Posterior Metopic

Synotosis Synotosis Plagiocephaly Synotosis

n = 4 n = 25 n = 9 n = 11

Procrustes 0% 40% 22% 18%

Arithmetic 0% 36% 33% 18%

form difference
Relative form 0% 36% 33% 18%

difference
Logarithmic form

0% 32% 33% 27%

difference