C++ Neural Networks and Fuzzy Logic: Preface


Figure 1.3   Layout of a Hopfield network. The two patterns we want the network to recall are A



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Figure 1.3

  Layout of a Hopfield network.

The two patterns we want the network to recall are A = (1, 0, 1, 0) and B = (0, 1, 0, 1), which you can verify

to be orthogonal. Recall that two vectors A and B are orthogonal if their dot product is equal to zero. This is

true in this case since

     A


1

B

1



 + A

2

 B



2

 + A


3

B

3



 + A

4

B



4

 = (1x0 + 0x1 + 1x0 + 0x1) = 0

The following matrix W gives the weights on the connections in the network.

      0   −3    3   −3

     −3    0   −3    3

W =   3   −3    0   −3

     −3    3   −3    0

We need a threshold function also, and we define it as follows. The threshold value [theta] is 0.

            1  if t >= [theta]

f(t) = 


{

            0  if t < [theta]

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C++ Neural Networks and Fuzzy Logic:Preface

Example—A Feed−Forward Network

23




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