Page 963 - The Mechatronics Handbook

0066_Frame_C32.fm Page 13 Wednesday, January 9, 2002 7:54 PM

UNIPOLAR NEURON BIPOLAR NEURON
+1 −0.5 +1
x 1 +1 OUTPUT x 1 OUTPUT
−0.5
+1
x 2 XOR x 2 XOR
−3
+1
x x x x
1 2 1 2
(a) (b)
FIGURE 32.12 Functional link networks for solution of the X OR problem: (a) using unipolar signals, (b) using
bipolar signals.

GROSSBERG
KOHONEN 0
LAYER LAYER

1

NORMALIZED INPUTS 0 0 OUTPUTS

0
SUMMING
CIRCUITS
UNIPOLAR
NEURONS

FIGURE 32.13 The counterpropagation network.

Feedforward Version of the Counterpropagation Network
The counterpropagation network was originally proposed by Hecht-Nilsen (1987). In this section a mod-
ified feedforward version as described by Zurada (1992) is discussed. This network, which is shown in
Fig. 32.13, requires numbers of hidden neurons equal to the number of input patterns, or more exactly,
to the number of input clusters. The first layer is known as the Kohonen layer with unipolar neurons.
In this layer only one neuron, the winner, can be active. The second is the Grossberg outstar layer. The
Kohonen layer can be trained in the unsupervised mode, but that need not be the case. When binary
input patterns are considered, the input weights must be exactly equal to the input patterns. In this case,

(
net = x w = [ n 2HD x, w)] (32.34)
t
–
where
n = number of inputs,
w = weights,
x = input vector,
HD (w, x) = Hamming distance between input pattern and weights.

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