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42 2 Pattern Discrimination

in many textbooks on Statistics, namely Hoe1 (1975). and Siegel and Castellan
(1998).

2.5.1 Graphic Inspection

Graphic inspection allows one to compare feature distributions for the several
classes of the problem at hand, and therefore to obtain some insight into their
usefulness for the class discrimination task. There are several types of graphic
representations that can be used depending on the insight one wishes to obtain.
Particularly useful in PR problems, besides histogra~ns, are box plots and scatter
plots.

,800

two
4000
E
800
200

,200
a
Figure 2.18. Box plots for the 3 classes of cork stopper& and features PRT (a) and
PRTG (b): - median position; I - exfremes, exceeding above or below the box
1.5 times the interquartile distance; o - oufliers, exceeding above or below the box
3 times the interquartile d~stance.

A box plot depicts for each feature and each class a box representing the
interquartile range of the distribution, i.e., covering 50% of the central feature
values. Figure 2.18 shows box plots for features PRT and PRTG of the cork
stoppers data. As shown in this figure, the box plot usually includes further
infonnation.
As can be appreciated from Figure 2.18, box plots give a clear indication of the
discrimination capability of each feature and the amount of overlap of the several
classes. In this example we see that feature PRT seems to discriminate the three
classes well, meanwhile feature PRTG seems to be useful only in the
discrimination of class y from classes wl and Q.
Features with largely overlapped distributions are, of course, of little help for
classification or regression purposes.