Biomedical Engineering Reference
In-Depth Information
1RW
$QG
2U
J
3
J
3
J
3
3
[
3
[
[
3
[
[
[
[
[
[
[
1RW
$QG
2U
8
8
8
8
8
Figure 7.8:
Perceptrons computing logical NOT, AND, and OR.
2
w
i
a
i
=
θ
=
w
1
a
1
+
w
2
a
2
.
(7.5)
i
=
1
If we solve for
a
2
w
1
w
2
a
1
+
θ
w
2
a
2
=−
.
(7.6)
Equation (7.6) is in the form of a decision line, with a slope of
w
1
/w
2
and intercept of
θ/w
2
, that
separates the inputs into two categories.These two categories are assigned the output of 1 or 0 depending
upon whether they are above or below the decision line. A decision line is therefore the most simple form
of pattern recognition. Figure 7.8 shows the decision lines for the AND, OR, and NOT gates where the
thresholds have been set to 1.
Although the math will not be presented here, given some set of inputs that need to be classified,
the appropriate decision line may be created as in the left panel of Fig. 7.9. Finding the decision line is a
very simple
learning rule
by which the weights and thresholds are adjusted. Graphically, this is equivalent
to changing the slope and intercept of the line in an iterative process until the line effectively separates
to two inputs.
The right panel of Fig. 7.9b demonstrates a case where a simple line is not capable of separating
two sets of points. Here, open squares represent inputs which should be classified together and closed
−
