C++ Neural Networks and Fuzzy Logic: Preface

Notation for ART1 Calculations

Let us list the various symbols we will use to describe the operation of a neural network for an ART1 model:

w

ij

Weight on the connection from the ith neuron in the F

1

 layer to the jth neuron in the F

2

 layer

v

ji

Weight on the connection from the jth neuron in the F

2

 layer to the ith neuron on the F

1

 layer

a

i

Activation of the ith neuron in the F

1

 layer

b

j

Activation of the jth neuron in the F

2

 layer

x

i

Output of the ith neuron in the F

1

 layer

y

j

Output of the jth neuron in the F

2

 layer

z

i

Input to the ith neuron in F

1

 layer from F

2

 layer

C++ Neural Networks and Fuzzy Logic:Preface

A Simplified Diagram of Network Layout

200

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Á

Vigilance parameter, positive and no greater than 1 (0<Á d 1)

m

Number of neurons in the F

1

 layer

n

Number of neurons in the F

2

 layer

I

Input vector

S

i

Sum of the components of the input vector

S

x

Sum of the outputs of neurons in the F

1

 layer

A, C, D

Parameters with positive values or zero

L

Parameter with value greater than 1

B

Parameter with value less than D + 1 but at least as large as either D or 1

r

Index of winner of competition in the F

2

 layer

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Copyright ©

 IDG Books Worldwide, Inc.

C++ Neural Networks and Fuzzy Logic:Preface

A Simplified Diagram of Network Layout

201

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C++ Neural Networks and Fuzzy Logic

by Valluru B. Rao

MTBooks, IDG Books Worldwide, Inc.

ISBN: 1558515526   Pub Date: 06/01/95

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Algorithm for ART1 Calculations

The ART1 equations are not easy to follow. We follow the description of the algorithm found in James A.

Freeman and David M. Skapura. The following equations, taken in the order given, describe the steps in the

algorithm. Note that binary input patterns are used in ART1.