Classification and Clustering Applications - An Invariant Approach to Statistical Analysis of Shapes - page 246

classify the individual to class 2. This type of classification
rule corresponds to what is called 'likelihood classification'.

Unfortunately, calculation of the likelihood classification is compu-
tationally difficult when landmark coordinate data are used because of
the presence of the nuisance parameters of translation, rotation and
reflection. The difficulty in computing the likelihood rule is explained
in Chapter 3 , Part 2 .

2. Dissimilarity measures-based classification

Fortunately, likelihood method is not the only approach to
classification. Another classification tool uses a dissimilarity
measure. In this approach, the first step is to calculate a dis-
tance, or dissimilarity measure between the observation of
interest and each of the defined classes. This distance, repre-
sented by a single number, quantifies the resemblance (or
lack of resemblance) between the new observation and the
class under consideration. We classify the new observation as
belonging to the class that it resembles most closely according
to the chosen measure.

The choice of the measure, be it a dissimilarity metric or a distance,
is subjective. For each distance measure, there exists a corresponding
classification rule. As we noted earlier, every probabilistic classification
rule has the potential to lead to a wrong decision. Given two different
classification rules, we choose that rule that on average leads to a
smaller number of wrong decisions. Unfortunately, in practice, no sin-
gle classification rule turns out to be uniformly the best, in the sense
that it has the smallest error rate under every possible situation. It is
unfortunate, but true, that some classification rules are good for some
situations whereas others work well under different conditions. This
feature makes classification more an art than science. There seldom is
a single classification rule that is best under every situation. It is futile
to argue for one classification rule over others based on a few, simple,
specific situations.
There will certainly be some situations where an alternate classifi-
cation rule works better than the rule we are proposing here.
Presentation of situations where one rule provides superior outcomes
does not prove the superiority of a given approach. Instead this demon-
strates that one classification rule should not be used in every possible