Neural Networks: An Overview - Neural Networks: Methodology and Applications - page 50

• For each pair of classes, test the pairwise linear separability of the examples

with the Ho and Kashyap algorithm.

• For all pairwise linearly separable classes, make use of linear separation

methods (described in Chap. 6) and derive an estimate of the posterior
probabilities.

• For nonlinearly separable classes, design small multilayer Perceptrons, or

spherical perceptrons as described in Chap. 6, with probability estima-
tions; use leave-one-out or cross-validation techniques for model selection
(see Chap. 2).

• Estimate the global posterior probabilities of each class from the pairwise

probabilities estimated at the previous steps, using the relation indicated
in Sect. 1.3.5.2, subsection “pairwise classification” above.

• Determine the decision thresholds in order to define rejection classes.

That strategy is a variant of the STEPNET procedure [Knerr 1990, 1991],
which allowed the design of several industrial applications.
In the planning of a classification project, the time required by the first and
the last steps of the above strategy should definitely not be underestimated;
for nontrivial applications, those are frequently the lengthiest and most painful
steps.
The applicability of that strategy is limited by the fact that the number
of pairwise classifiers grows as the square of the number of classes. However,
each classifier is usually very simple, so that the procedure can be applied
with up to a few tens of classes. For larger number of classes, hierarchical
strategies must be resorted to.

1.4 Some Applications of Neural Networks to Various
Areas of Engineering

1.4.1 Introduction

The present topic is intended to assist the engineer or researcher in answering
the following question: can neural networks solve my problem, and can they do
it more e ciently (in terms of accuracy, computation time, etc.) than other
techniques?
Contributions to a rational answer were provided at the beginning of the
present chapter, where we explained the mathematical foundations and prin-
ciples underlying the operation of neural networks. Although some elements
may look somewhat technical, they are mandatory for getting an in-depth un-
derstanding of what one can and cannot do with neural networks. Since the
software implementation of neural networks is straightforward with present-
time tools, one might be tempted to apply neural networks without prior
thinking, which may lead to disappointing results.
In addition to mathematical arguments, it may be helpful, in order to il-
lustrate the use and limitations of neural networks, to describe some typical