POLITECHNIKA WARSZAWSKA

3. Basics of Artificial Neural Network (ANN)
square difference between the desired output and the actual output of the feedforward
ANN. In order to minimize this error function, the backpropagation algorithm uses a
gradient search technique.
3.4.2.1. The Widrow-Hoff (standard delta) learning rule
Learning rule for one linear neuron
Let us consider the simplest case of ANN. It means, that the Neural Network consists
of one linear neuron with N inputs. We will study supervized learning process of this
network. So, it is convenient to introduce so-called teaching sequence. We can define
this sequence as follows:
T
( 1) (1) (2) (2) ( P)
( P)
= {{ X , z },{ X , z }, K ,{ X , z }} (3.11)
( j)
( j)
where each element { X , z }, consists of input vector X in the j-th step of learning
process, and appropriate desired output signal z.
In order to show the learning algorithm, we define the error function as:
Q =
1
2
P
( j)
( j)
2
∑(
z − y )
j=
1
(3.12)
We can rewrite this equation in the following form:
Q =
P
( j)
∑Q
j=
1
(3.13)
where:
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