Page 92 -

4 Statistical Classification

4.1 Linear Discriminants

In previous chapters, several distance metrics were presented and used to assess
pattern similarity relative to a prototype. In the present chapter, we further explore
this way of thought, taking into account the specificity of the pattern distributions.

4.1.1 Minimum Distance Classifier

Let us consider the cork stoppers classification problem (see the Cork Stopperxxls
dataset description in Appendix A). Assume that the main goal was to design a
classifier for classes 1 (w,) and 2 (w~), having only feature N (number of defects)
available (see A.3). Therefore, a feature vector with only one element represents
each pattern: x = [N].
Let us first inspect the pattern distributions in the feature space (d=l)
represented by the histograms of Figure 4.1. The distributions have a similar shape
with some amount of overlap. The sample means are ml=55.28 for q and
m2=79.74 for w2.

Figure 4.1. Feature N histograms for the first two classes of the cork stoppers data.