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taught from labelled patterns how to perform the classification. If the classifier is
efficiently designed it will be able to perform well on new patterns.
There are variants of the statistical classification approach, which depend on
whether a known, parametrizable, distribution model is being used or not. There
are also important by-products of statistical classification such as decision trees
and tables.
The statistical classification approach is adequate when the patterns are
distributed in the features space, among the several classes, according to simple
topologies and preferably with known probabilistic distributions.
Example of statistical classification system: A machine is given the task of
separating cork stoppers into several categories according to the type of defects
they present. For that purpose defects are characterized by several features, which
can be well modelled by the normal distribution. The machine uses a statistical
classifier based on these features in order to achieve the separation.

1.4.3 Neural Networks

Neural networks (or neural nets) are inspired by physiological knowledge of the
organization of the brain. They are structured as a set of interconnected identical
units known as neurons. The interconnections are used to send signals from one
neuron to the others. in either an enhanced or inhibited way. This enhancement or
inhibition is obtained by adjusting connection weights.
Neural nets can perform classification and regression tasks in either a supervised
or non-supervised way. They accomplish this by appropriate methods of weight
adjustment, whereby the outputs of the net hopefully converge to the right target
values.
Contrary to statistical classification, neural nets have the advantage of being
model free machines, behaving as universal approximators, capable of adjusting to
any desired output or topology of classes in the feature space. One disadvantage of
neural nets compared with statistical classification is that its mathematics are more
intricate and, as we will see later on, for some important decisions the designer has
often little theoretically based guidance, and has to rely on trial-and-error
heuristics. Another disadvantage, which can be important in some circumstances,
is that practically no semantic information is available from a neural net. In order
to appreciate this last point, imagine that a physician performs a diagnostic task
aided by a neural net and by a statistical classifier, both fed with the same input
values (symptoms) and providing the correct answer, maybe contrary to the
physician's knowledge or intuition. In the case or the statistical classifier the
physician is probably capable of perceiving how the output was arrived at, given
the distribution models. In the case of the neural net this perception is usually
impossible.
Neural nets are preferable to classic statistical model-free approaches, especially
when the training set size is small compared with the din~ensionality of the
problem to be solved. Model-free approaches, either based on classic statistical
classification or on neural nets, have a common body of analysis provided by the
Statistical Learning Theory (see e.g. Cherkassky and Mulier, 1998).