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observed that two best PDs does not join to produce better result, rather
a PD giving better result joins with another inferior result giving PD
yields the best result in the next layer. As the number of PDs grow
exponentially over the layers, preserving all the PDs are not practicable.
Further a substantial number of PDs need to be preserved to obtain
better performance. As a result the program implementation requires large
memory and computation time.
PNN layers are grown based on the error at each level. Performance
of the model is evaluated at each level of the generation of the layers. At
times the error level decreases gradually even up to the 10th layer. However,
while evaluating the performance of the model with unknown input data
results drop off beyond 3rd or 4th layer. This is due to overtraining by
the chosen training data. Moreover, the growth of the layers beyond 3rd or
4th requires a lot of memory and computational time. However obtaining
a suitable trade off is hard to determine, as it is not an iterative method.
3.4.2.
Evolving polynomial network (EPN) using PSO
Evolution has been introduced to PNN at different levels by different
researchers.
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Some of them have tried to evolve the optimal set of inputs
to each PD, some of them have evolved optimal type of the polynomial
required, selection of PDs for the next layer, optimal architecture
design, etc.
In most of these cases the polynomial used to develop the PDs are of
Ivakhnenko's model. Generally the PDs are developed from a predefined
set of standard polynomials. These standard polynomial may take two or
three input and may be linear, quadratic or cubic. The combinations of
these standard polynomials may not always be a good choice to generate
the optimal model.
To alleviate these problems, in this section we suggest an evolving
technique that will not take any standard polynomial input, the number
and structure of PDs will be evolved. In addition to the number of inputs
to each neuron, what are the inputs to each neuron, what are the degrees
of each input in a neuron; along with the required biased weights will be
evolved.
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In this approach we have used particle swarm optimization technique to
evolve polynomials to classify the data set. The representation of a particle
is shown at Fig. 3.5.
