Neural Networks: An Overview - Neural Networks: Methodology and Applications - page 26

cost function) is minimum. As a consequence, the design of a neural network
requires

• finding the relevant inputs, i.e., the factors that have a significant influence

on the quantity to be modeled (i.e., an influence that is larger than the
measurement noise),

• collecting the data that is necessary for training and testing the neural

network,

• finding the appropriate complexity of the model, i.e., the appropriate num-

ber of hidden neurons,

• estimating the parameters for which the cost function is minimum, i.e.,

training the network,

• assessing the generalization ability of the neural network after training.

In view of the results, it may be necessary to iterate the whole procedure, or
part of it.
These points will be considered in detail in the next sections.

1.2.2.1 Relevant Inputs

The selection of relevant inputs may have various requirements, depending on
the application that is considered.
If the process to be modeled is an industrial problem that has been care-
fully engineered, the relevant factors and the causal relations between them
are usually known. Consider, as an example, the industrial process of spot
welding, which will be described in detail in a subsequent section: the metal
sheets to be welded are melted together locally by passing a very large current
(a few kiloamperes) during a few milliseconds, through two electrodes that are
pressed onto the metal surfaces (Fig. 1.13). The quality of the joint is assessed
from the diameter of the melted zone; it depends on the current intensity, on
the duration of the current flow, on the stress applied to the electrodes while
current flows and during cooling, on the surface state of the electrodes, on
the nature of the metal sheets, and on a few additional factors. Thus, the
desirable model inputs are essentially known from physics: however, it may
be important to make a choice between these factors, so that only those fac-
tors that have a significant influence on the spot weld diameter, i.e., whose
influence is larger than the uncertainty on the measurement of the diameter,
are taken into account.
By contrast, if the process of interest is a complex natural process (e.g., in
biology or ecology), or if it is an economic, financial or social process, the choice
of the relevant inputs may be more di cult. An example of a complex natural
process (the solubility of molecules in solvents), where the determination of
the relevant factors is not trivial, will be described in a subsequent section.
Similarly, great care must be exercised in the choice of relevant inputs for
credit rating, an example that will also be described below.