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its values during a given time interval, a text by the frequency of occurrence
of the significant words that it contains, etc. Typically, the questions whose
answer a classifier is expected to contribute to are: is this unknown character a
a ,a b ,a c , etc.? is this observed signal normal or anomalous? is this company
a safe investment? is this text relevant to a given topic of interest? will there
be a pollution alert to-morrow?
The classifier is not necessarily expected to give a full answer to such a
question: it may make a contribution to the answer. Actually, it is often the
case that the classifier is expected to be a decision aid only, the decision being
made by the expert himself. In the first applications of neural networks to
classification, the latter were expected to give a definite answer to the clas-
sification problem. Since significant advances have been made in the under-
standing of neural network operation, we know that they are able to provide
a much richer information than just a binary decision as to the class of the
pattern of interest: neural networks can provide an estimation of the proba-
bility of a pattern to belong to a class (also termed posterior probability of the
class). This is extremely valuable in complex pattern recognition applications
that implement several classifiers, each of which providing an estimate of the
posterior probability of the class. The final decision is made by a “supervi-
sor” system that assigns the class to the pattern in view of the probability
estimates provided by the individual classifiers (committee machines).
Similarly, information filtering is an important problem in the area of
data mining: find, in a large text data base, the texts that are relevant to
a prescribed topic, and rank these texts by order of decreasing relevance, so
that the user of the system can make a choice e ciently among the suggested
documents. Again, the classifier does not provide a binary answer, but it
estimates the posterior probability of the class “relevant.” Feedforward neural
networks are more and more frequently used for data mining applications.
Chapter 6 of the present topic is fully devoted to feedforward neural
networks and support vector machines for discrimination.
1.1.5 Feedforward Neural Networks with Unsupervised Training
for Data Analysis and Visualization
Due to the development of powerful data processing and storage systems, very
large amounts of information are available, whether in the form of numbers
(intensive data processing of experimental results) or in the form of symbols
(text corpuses). Therefore, the ability of retrieving information that is known
to be present in the data, but that is di cult to extract, becomes crucial.
Computer graphics facilitates greatly user-friendly presentation of the data,
but the human operator is unable to visualize high-dimensionality data in an
e cient way. Therefore, it is often desired to project high-dimensionality data
onto a low-dimensionality space (typically dimension 2) in which proximity re-
lations are preserved. Neural networks with unsupervised learning, especially
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