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complex network. On the other hand, if a small number of input variables
are available, PNN does not maintain good performance.
In addition to input variables, the type or order of polynomial used for
the PDs plays an important role in construction of the network model and
its performance. These parameters must be chosen in advance before the
architecture of the PNN is constructed. In most cases, they are determined
by trial and error method, leading to heavy computational load and low
eciency. Evolutionary techniques may be used to determine the number
of input variables to be optimally chosen among many input variables for
each node and to determine the appropriate type of polynomials for each
PD.
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The rest of the chapter is organized as follows. Section 3.2 gives
a brief overview of the evolving neural network. Section 3.3 discusses
how swarm intelligence can be used for evolving neural network. Further,
the application of swarm intelligence for evolving polynomial network is
discussed in Section 3.4. This chapter is concluded at Section 3.5.
3.2. Evolving Neural Network
In evolving neural network (ENN) evolution is the fundamental form of
adaptation in addition to learning.
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Evolutionary algorithms (EA)
has been used successfully to perform various tasks, such as connection
weight training, architecture design, learning rule adaptation, input feature
selection, connection weight initialization, rule extraction from ANN, etc.
One important feature of ENN is its adaptability to a dynamic environment.
Evolution and learning are the basic two forms of adaptation required in
general for developing an evolving network. ENN adapts to the dynamic
environment much more effectively and eciently. ENN may be considered
as a general framework for adaptive systems, where the system changes its
architecture and learning rule without involvement of the designer/user.
Figure 3.1 illustrates a feed forward ANN architecture consisting of
a set of processing elements called neurons or nodes performs a transfer
function
f
i
of the form:
n
y
i
=
f
i
w
ij
x
j
−
θ
i
(3.1)
i
=1
where
y
i
is the output of the node
i
,
x
j
is the
j
th input to the node, and
w
ij
is the connection weight between nodes
i
and
j
.Θ
i
is the threshold (or bias)
