Discrimination - Neural Networks: Methodology and Applications - page 333

Fig. 6.1. Examples belonging to two classes in dimension N = 2. The lines represent
the discriminant surfaces. ( a ) linearly separable training set, showing two separations
without training errors but giving different answers for the class of a new input
( empty circle ). ( b ) A general case

• if one just needs to classify the patterns x , the discriminant surface only is

needed. Since the classifier performs a binary function of its inputs, in this
chapter we will show how the discriminant surface may be represented us-
ing binary neurons only. That cannot be done if we transform the problem
into a regression problem;

• if the probability that the input pattern belongs to a given class is neces-

sary, in order to make a posterior decision (such is the case for instance
when the classification is performed after comparison of the outputs of
different classifiers) we may use either continuous output units (e.g., sig-
moidal neurons), but also binary neurons. In this chapter we show that
the latter can also be assigned a probabilistic interpretation.

Fig. 6.2. Examples in dimension 2. Black points stand for patterns of class +1; white
denote those of class − 1. The shadowed surface is the regression; the discriminant
surface (a line in that case) is shown as a dotted line