Neural Networks: An Overview - Neural Networks: Methodology and Applications - page 2

Fig. 1.1. A neuron is a nonlinear bounded function y = f ( x 1 ,x 2 ,...x n ; w 1 ,w 2 , ...,
w p ) where the {x i } are the variables and the {w j } are the parameters (or weights)
of the neuron

Finally, various applications will be described that illustrate the variety
of areas where neural networks can provide e cient and elegant solutions to
engineering problems, such that pattern recognition, nondestructive testing,
information filtering, bioengineering, material formulation, modeling of in-
dustrial processes, environmental control, robotics, etc. Further applications
(spectra interpretation, classification of satellite images, classification of sonar
signals, process control) will be either mentioned or described in detail in sub-
sequent chapters.

1.1 Neural Networks: Definitions and Properties

A neuron is a nonlinear, parameterized, bounded function.
For convenience, a linear parameterized function is often termed a linear
neuron.
The variables of the neuron are often called inputs of the neuron and
its value is its output. A neuron can be conveniently represented graphically
as shown on Fig. 1.1. This representation stems from the biological inspira-
tion that prompted the initial interest in formal neurons, between 1940 and
1970 [McCulloch 1943; Minsky 1969].
Function f can be parameterized in any appropriate fashion. Two types
of parameterization are of current use.
• The parameters are assigned to the inputs of the neurons; the output of

the neuron is a nonlinear combination of the inputs { x i } ,weightedbythe

parameters , which are often termed weights, or, to be reminiscent of

the biological inspiration of neural networks, synaptic weights. Following
the current terminology, that linear combination will be termed potential
in the present topic, and, more specifically, linear potential in Chap. 5. The

{ w i }