Page 304 - Introduction to Statistical Pattern Recognition

286 Introduction to Statistical Pattern Recognition

E% A
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100

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80

60 -

40 -

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20
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0.0 0.2 0.4 0.6 0.8 1 .o 1.2
Fig. 6-6 Errors for a large number of classes.

Figure 6-6 indicates that, when cVIEXE(d~~(X)) is larger than 0.2 for a
large number of classes, it may not be feasible to identify individual classes.
Therefore, before trying to design any classifier, it is advisable to confirm that
the classes are well separated pairwise. One way to evade this difficulty is to
assemble the classes into a smaller number (L) of groups, and to treat it as an
L-class problem. The errors, which occur among classes within the same
group, are considered as correct classification. Only the error from a class of
one group to a class of another group is treated as the error between groups.
Thus, the error between groups is normally much smaller than the error
between classes.
It has been found experimentally that E,, and E, are very roughly related
by E, E(2 + 0.2n)~,, for small CY. That is, E, is about equivalent to the errors
due to 4 and 6 neighbors for n = 10 and 20 respectively, assuming all distances