Neural Networks Approach - Computational Intelligence in Time Series Forecasting - page 83

neuron in the hidden layer the centre c and the spread around the centre V ; this is
mostly done using the k-means clustering algorithm , which is capable of
determining the optimal position of centres. In addition, the value of the spread
parameter V should be selected small enough in order to restrict the basis
function spreading, but also large enough to enable a smooth network output
through the joint effect with the neighbouring functions.
The network training process mainly includes two training phases:

x initialization of RBF centres, for instance using unsupervised clustering
methods (Moody and Darken, 1989), linear vector quantization
(Schwenker et al , 1994), or decision trees (Kubat, 1998)
x output weight training of the RBF using an adaptive algorithm to estimate
its appropriate values.

Radial Basis Function Network

Gaussian
Function (RBF)

x 1

Input
neuron-1

w 11 y 1

Sum

:
:

w 21

Input
neuron-2

x 2

w 1m

w 2m

:
:

:
:

:
: w h1

Sum

y m Input

neuron- n

x n

w hm

Inputs

outputs

Input Layer RBF hidden Layer Output Layer

Figure 3.5. Configuration of an RBF network

In some cases, it is recommended to add a third training phase (Schwenker et al.
2001) in which the entire network architecture is adjusted using an optimization
method.

3.3.3 Recurrent Networks

Research in the area of sequential and time-varying patterns recognition has
created the need for time-dependent nonlinear input-output mapping using neural
networks. To achieve this extended network capability, the time dimension has to
be introduced into the network topology, for instance by introducing short-term
memory features , that would enable network to perform time-dependent mappings.
Elman (1990) proposed a kind of globally feedforward, locally recurrent network
using the context nodes as the principal processing elements of the network. Such
nodes have also been the principal processing elements of the network proposed by
Jordan (1986) for providing the networks with the dynamic memory. Both Jordan
and Elman networks belong to the category of simple recurrent networks .