C++ Neural Networks and Fuzzy Logic: Preface

C++ Neural Networks and Fuzzy Logic

by Valluru B. Rao

MTBooks, IDG Books Worldwide, Inc.

ISBN: 1558515526   Pub Date: 06/01/95

Previous Table of Contents Next

C++ Implementation of Kohonen’s Approach

Our C++ implementation of this algorithm (described above) is with small modifications. We create but do

not destroy neurons explicitly. That is, we do not count the number of consecutive iterations in which a

neuron is not selected for modification of weights. This is a consequence of our not defining a neighborhood

of a neuron. Our example is for a problem with five neurons, for illustration, and because of the small number

of neurons involved, the entire set is considered a neighborhood of each neuron.

When all but one neuron are created, the remaining neuron is created without any more work with the

algorithm, and it is assigned to the input, which isn’t corresponded yet to a neuron. After creating n – 1

neurons, only one unassigned input should remain.

In our C++ implementation, the distance matrix for the distances between neurons, in our example, is given as

follows, following the stipulation in the algorithm that these values should be integers between 0 and n – 1.

         0 1 2 3 4

         1 0 1 2 3

d =    2 1 0 1 2

         3 2 1 0 1

         4 3 2 1 0

We also ran the program by replacing the previous matrix with the following matrix and obtained the same

solution. The actual distances between the cities are about four times the corresponding values in this matrix,

more or less. We have not included the output from this second run of the program.

        0 1 3 3 2

        1 0 3 2 1

d =   3 3 0 4 2

        3 2 4 0 1

        2 1 2 1 0

In our implementation, we picked a function similar to the Gaussian density function as the squashing

function. The squashing function used is:

f(d,») = exp( −d

2

/») /  (2 )