C++ Neural Networks and Fuzzy Logic: Preface

Normalizing the Range

We now have values in the original five data columns that have a very large range. We would like to reduce

the range by some method. We use the following function:

new value = (old value − Mean)/ (Maximum Range)

This relates the distance from the mean for a value in a column as a fraction of the Maximum range for that

column. You should note the value of the Maximum range and Mean, so that you can un−normalize the data

when you get a result.

The Target

We’ve taken care of all our inputs, which number 15. The final piece of information is the target. The

objective as stated at the beginning of this exercise is to predict the percentage change 10 weeks into the

future. We need to time shift the S&P 500 close 10 weeks back, and then calculate the value as a percentage

change as follows:

Result = 100 X ((S&P 10 weeks ahead) − (S&P this week))/(S&P this week).

This gives us a value that varies between −14.8 to and + 33.7. This is not in the form we need yet. As you

recall, the output comes from a sigmoid function that is restricted to 0 to +1. We will first add 14.8 to all

values and then scale them by a factor of 0.02. This will result in a scaled target that varies from 0 to 1.

scaled target = (result + 14.8) X 0.02

The final data file with the scaled target shown along with the scaled original six columns of data is shown in

Table 14.4.

Table 14.4 Normalized Ranges for Original Columns and Scaled Target