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Fig. 6.6.
Input space, with two examples
x
1
and
x
2
, of class +; the hyperplane
corresponding to a perceptron of weights
w
(with
w
= 1) is shown, together with
the stabilities
γ
1
and
γ
2
of the examples
6.4 Training Algorithms for the Perceptron
There are many learning algorithms that allow to determine the perceptron
weights based on the training set
L
M
(
x
k
,y
k
)
,
k
=1to
M
. Historically,
the oldest one is the “perceptron algorithm”. Although it is seldom used in
practice, it has interesting properties. We will see that the alternative training
algorithms may be considered as generalizations of it.
=
{
}
Remark.
If the examples of the training set are linearly separable, a percep-
tron should be able to learn the classification.
6.4.1 Perceptron Algorithm
The following algorithm was proposed by Rosenblatt to train the perceptron:
Perceptron Algorithm
•
Initialization
1.
t
= 0 (counter of updates)
2. either
w
(0) = 0 (tabula rasa initialization) or each component of
w
(0)
is initialized at random.
•
Test
1.
if z
k
≡
x
k
>
0 for all examples
k
=1
,
2
,...,M
(they are
correctly learned)
then
stop
.
2.
else go to
learning
•
Learning
1. select an example
k
of the training set
L
M
, either at random or follow-
ing a pre-established order.
y
k
w
(
t
)
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