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4.1 Linear Discriminants 81

I=[ ] or X=[N PRTIO]'.
PRTlO

We use PRTlO instead of PRT for the scaling reason already explained at the
beginning of section 2.3. There is also another reason: although statistical
classification is in principle independent of the feature measurement scales, as we
will have to compute later the inverse of a covariance matrix, numerical
considerations recommend that, for this calculation to be performed in the best
conditions, the value ranges should not be too different. The scatter diagram of the
feature vectors is shown in Figure 4.3.
In this two-dimensional feature space, the minimum distance classifier using
Euclidian metrics is implemented as follows:

I. Draw the straight line (decision surface) equidistant from the sample means (see
Figure 4.3), i.e., perpendicular to the segment linking the means and passing at
half distance.
2. Any pattern above the straight line is assigned to a. Any sample below is
assigned to w,. The assignment is arbitrary if the pattern falls on the straight line
boundary.

Figure 4.3. Scatter diagram for two classes of cork stoppers (features N, PRT10)
with the linear discriminant at half distance from the means (solid line).