Databases Reference
In-Depth Information
methods, where the approaches like black-box concepts, connectionism and
induction concepts can be applied.
120
The black-box method is a principal
approach to analyze systems on the basis of input-output samples. And the
method of connection and induction can be thought of as representation
of complex functions through network of elementary functions. Thus the
GMDH algorithm has the ability to trace all input-output relationship
through an entire system that is too complex. The GMDH-type Polynomial
Neural Networks are multilayered model consisting of the neurons/active
units/Partial Descriptions (PDs) whose transfer function is a short-term
polynomial described in equation (9.11). At the first layer
L
=1,an
algorithm, using all possible combinations by two from
m
inputs variables,
generates the first population of PDs. Total number of PDs in first layer is
n
=
m
(
m
1)
/
2.
The outputs of each PDs in layer
L
= 1 is computed by applying the
Equation (9.11). Let the outputs of first layer be denoted as
y
1
,y
2
,...,y
n
.
The vector of coecients of the PDs are determined by least square
estimation approach.
The architecture of a PNN
122,123
with four input features is shown in
Fig. 9.4. The input and output relationship of the above data by PNN
algorithm can be described in the following manner:
−
y
=
f
(
x
1
,x
2
,...,x
m
)
,
where
m
is the number of features in the dataset.
This process is repeated till error decreases. Overall framework of the
design procedure
6,115,124-128
of the GMDH-type PNN comes as a sequence
of the following steps:
(1)
Determine system's input variables.
(2)
Form training and testing data.
Fig. 9.4.
Basic PNN model
