Discrimination - Neural Networks: Methodology and Applications - page 329

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Discrimination

M. B. Gordon

The task of assigning patterns to classes based on their characteristics is
called discrimination. For example, medical diagnosis, handwritten character
recognition, non-destructive tests of defects, are particular cases of pattern
discrimination.
In Chap. 1, a general introduction to the problem of discrimination was
provided. A general methodology for the design of statistical classifiers was
described, and was illustrated by detailed presentations of actual applications.
That methodology is based on considerations developed in the present chapter.
We have already pointed out that the problem of automatic classification
may be considered from different viewpoints, depending on the application.
We may consider the classifier training problem as a regression problem, and
view the continuous output as an estimate of the probability that the patterns
belong to a given class. Conversely, in other applications, we may just need the
frontiers between classes, called discriminant surfaces; those may be obtained
using neural networks of binary neurons, as was suggested already in the
sixties, and further developed from the eighties up to the present.
This chapter is mainly devoted to the second approach: we provide detailed
explanations of the modern techniques allowing linear separations between
classes using binary neurons, and, if necessary, how to go beyond and deter-
mine more complex separations. A probabilistic interpretation of the results
is also presented.
We also introduce many theoretical justifications, stemming mainly from
work due to physicists, as well as from recent developments in learning theory.
However, it should be borne in mind that in any application, the time devoted
to the following tasks should not be underestimated:

• The choice of the data representation requires a careful analysis, because

the quality of the results depends critically on that issue. An appropriate
representation is both compact (the dimension of the input vectors should
be as small as possible) and discriminant (it allows e cient separation of
patterns belonging to different classes).