C++ Neural Networks and Fuzzy Logic: Preface

i

, Y

i

), i ranging from 1 to k. Note that T in the superscript of a matrix stands for the

transpose of the matrix. While you interchange the rows and columns to get the transpose of a matrix, you

write a column vector as a row vector, and vice versa to get the transpose of a vector. The following equations

refer to the vector pairs after their components are changed to bipolar values, only for obtaining the weight

matrix W. Once W is obtained, further use of these exemplar vectors is made in their original form.

W =  X

1T

 Y

1

 + ... + X

kT

 Y

k

and

W

T

 =  Y

1T

X

1

 + ... + Y

kT

 X

k

Example

Suppose you choose two pairs of vectors as possible exemplars. Let them be:

     X

1

 = (1, 0, 0, 1), Y

1

= (0, 1, 1)

and

     X

2

 = (0, 1, 1, 0), Y

2

 = (1, 0, 1)

These you change into bipolar components and get, respectively, (1, –1, –1, 1), (–1, 1, 1), (–1, 1, 1, –1), and

(1, –1, 1).

C++ Neural Networks and Fuzzy Logic:Preface

Weights and Training

153

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      1 [−1 1 1]   −1 [1 −1 1]   −1  1  1     −1  1 −1    −2  2 0

 W = −1           + 1          =  1 −1 −1  +   1 −1  1  =  2 −2 0

     −1             1             1 −1 −1      1 −1  1     2 −2 0

      1            −1            −1  1  1     −1  1 −1    −2  2 0

and

       −2    2    2    −2

W

T

 =    2   −2   −2     2

        0    0    0     0

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C++ Neural Networks and Fuzzy Logic:Preface

Weights and Training

154

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