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5.3 The Perceptron Concept 161

Let us consider formula (5-7e) for the particular case of 77 = ?h and use the
activation step function applied to the linear discriminant:

For correct decisions the output h(w'x,) is identical to ti and no increment is
obtained. For wrong decisions the increment obtained is exactly the same as in
(5-16). Hence, the perceptron rule is identical to the LMS rule, using the step
function and a learning rate 77 = %.
Note that what the perceptron produces are class labels, therefore it is adequate
for classijkation problems. It is interesting to compare how the perceptron
performs in the case of the one-dimensional data of Figure 5.2a. In this case the
perceptron learning rule can be written:

-a+b if -a+b>_O
if a+bcO
other cases

Figure 5.12. Energy surface for the perceptron learning rule in a one-dimensional
two-class situation.

Figure 5.12 shows this error surface, exemplifying the piecewise linear nature of
the error energy surface for the perceptron learning rule, with jumps whenever a
pattern changes from class label.