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14 1 Basic Notions

There are two distinct ways such hypotheses can be obtained:
Supervised, concept driven or indzrctive hypotheses: find in the representation
space a hypothesis corresponding to the structure of the interpretation space.
This is the approach of the previous examples, where given a set of patterns we
hypothesise a solution. In order to be useful, any hypothesis found to
approximate the target values in the training set must also approximate
unobserved patterns in a similar way.
Unsupervised, dutu-driven or clehictive hypotheses: find a structure in the
interpretation space corresponding to the structure in the representation space.
The unsupervised approach attempts to find a useful hypothesis based only on
the similarity relations in the representation space.

The hypothesis is derived using learning methods which can be of statistical,
approximation (error minimization) or structural nature.
Taking into account how the hypothesis is derived and pattern similarity is
measured, we can establish the hierarchical categorization shown in Figure1 .l 1.
We proceed to briefly describe the main characteristics and application scope of
these approaches, to be explained in detail in the following chapters.

1.4.1 Data Clustering

The objective of data clustering is to organize data (patterns) into meaningful or
useful groups using some type of similarity measure. Data clustering does not use
any prior class information. It is therefore an unsupervised classification method,
in the sense that the solutions arrived at are data-driven, i.e., do not rely on any
supervisor or teacher.
Data clustering is useful when one wants to extract some meaning from a pile of
unclassified information or in an exploratory phase of pattern recognition research
for assessing internal data similarities. I11 section 5.9 we will also present a neural
network approach that relies on a well-known data clustering algorithm as a first
processing stage.
Example of data clustering: Given a table containing crop yields per hectare for
several soil lots the objective is to cluster these lots into meaningful groups.

1.4.2 Statistical Classification

Statistical classification is a long-established and classic approach of pattern
recognition whose matheniatics dwell on a solid body of methods and formulas. It
is essentially based on the use of probabilistic models for the feature vector
distributions in the classes in order to derive classifying functions. Estimation of
these distributions is based on a training set of patterns whose classification is
known beforehand (e.g. assigned by human experts). It is therefore a supervised
method of pattern recognition, in the sense that the classifier is concept-driven,