C++ Neural Networks and Fuzzy Logic: Preface

Another Example of Backpropagation Calculations

You have seen, in the preceding sections, the details of calculations for one particular neuron in the hidden

layer in a feedforward backpropagation network with five input neurons and four neurons in the output layer,

and two neurons in the hidden layer.

You are going to see all the calculations in the C++ implementation later in this chapter. Right now, though,

we present another example and give the complete picture of the calculations done in one completed iteration

or cycle of backpropagation.

Consider a feedforward backpropagation network with three input neurons, two neurons in the hidden layer,

and three output neurons. The weights on connections from the input neurons to the neurons in the hidden

layer are given in Matrix M−1, and those from the neurons in the hidden layer to output neurons are given in

Matrix M−2.

We calculate the output of each neuron in the hidden and output layers as follows. We add a bias or threshold

value to the activation of a neuron (call this result x) and use the sigmoid function below to get the output.

     f(x) = 1/ (1 + e

−x 

)

Learning parameters used are 0.2 for the connections between the hidden layer neurons and output neurons

and 0.15 for the connections between the input neurons and the neurons in the hidden layer. These values as

you recall are the same as in the previous illustration, to make it easy for you to follow the calculations by

C++ Neural Networks and Fuzzy Logic:Preface

Adjustments to Threshold Values or Biases

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comparing them with similar calculations in the preceding sections.

The input pattern is ( 0.52, 0.75, 0.97 ), and the desired output pattern is ( 0.24, 0.17, 0.65). The initial weight

matrices are as follows: