Classification and Clustering Applications - An Invariant Approach to Statistical Analysis of Shapes - page 244

The use of these algorithms is illustrated using datasets involving
craniosynostosis patients.
6.1 Classification analysis
The activity of allocating individuals to one of a set of existing groups
is usually referred to as classification, assignment or discrimination.
The term classification has two complementary meanings in the sta-
tistical literature (Gower, 1998). First, classification involves assigning
an observation to one of a set of previously known classes. Secondly,
classification is concerned with the construction and description of the
classes themselves. In this topic, we define classification in the first
sense; i.e., assigning a new observation to one of the known classes.
Gower (1998) suggests that this is better described as discrimination
and we agree that the theory of discriminant analysis plays an impor-
tant role in this activity. Here, a discrimination or classification
problem concerns the identification of the sample of interest as belong-
ing to one group within a set of known groups. Using a combination of
features that are held in common by the individuals in the same group,
an individual is identified as belonging or not belonging to the group.
The features may be based solely on landmark data or additional infor-
mation; e.g., life history information, ecological variables, phylogenetic
information. In this topic, we restrict ourselves to the exclusive use of
landmark data. However, modification of the classification procedure
to accommodate other variables is straightforward and may be partic-
ularly valuable in specific research situations.
Classification involves specification of a rule that determines the
class to which a new observation is assigned. There are two kinds of
classification rules: “probabilistic” and “non-probabilistic.” In a
research situation of living organisms, classification based on gender
(which is observable from the organism) is non-probabilistic because
the membership of a new individual to the class 'male' or 'female' can
be done with certainty . On the other hand, probabilistic classification
involves the assignment of specimens into groups with the possibility
for misclassification. For example, classification of an organism into
the groups male and female is usually probabilistic when the specimen
has been skeletonized (or fossilized), and observable features do not
include genitalia; i.e., there is uncertainty inherent to the classifica-
tion. The main difference between a non-probabilistic and probabilistic
classification, then, is that a non-probabilistic classification rule does