Classification and Clustering Applications - An Invariant Approach to Statistical Analysis of Shapes - page 243

CHAPTER 6
Classification and Clustering
Applications
Traditionally quantification of the morphology of biological organisms
has played an important role in Numerical Taxonomy (e.g., Sneath and
Sokal, 1973, Reyment et al., 1984). A chief objective of many studies in
Numerical Taxonomy is to find groups in the data such that the organ-
isms within a group are more similar to other members of the group
than they are to the members of alternate groups. A related but dis-
tinct issue of substantial interest to the clinical sciences is the
classification of new patients into already defined groups. This practice
is clearly relevant to the field of medical diagnostics, but it is also use-
ful in evolutionary biology where a scientist may want to assign a
newly found individual to a group; e.g., a clade, a species, a family. In
this chapter, we discuss the ways in which the invariant approach to
the quantitative analysis of forms can be applied towards the problem
of forming groups (clustering) and the assignment of individuals to
known groups (classification). In standard statistical terminology, the
classification approach is used when the groups are known and the
goal is to determine the group membership of a new individual. The
goal of the clustering approach is to find the groups in the data. There
exist a vast array of statistical procedures that can be applied to attain
either goal. We start with the problem of classification, in part, because
it provides a relatively clean statistical answer. We then turn to clus-
tering, although with less enthusiasm due to the fact that clustering is
inherently subjective. This is because the results of a clustering proce-
dure can depend more on the method than on the signal in the data. In
this chapter, we propose algorithms for classification and clustering of
individuals represented by landmark coordinate data.