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1.3 Classes. Patterns and Features 13

In what follows we assume a set of d features or primitives. In classification or
regression problems we consider features represented by real numbers; a pattern is,
therefore, represented by a feature vector:

where X is the d-dimensional domain of the feature vectors.
For description problems a pattern is often represented by a string of symbolic
primitives x,:

where S is the set of all possible strings built with the primitives. We will see in
Chapter 6 other representational alternatives to strings.
The feature space is also called the representation space. The representation
space has data-driven properties according to the defined similarity measure.

1.4 PR Approaches

There is a multiplicity of PR approaches and no definite consensus on how to
categorize them. The objective of a PR system is to perform a mapping between
the representation space and the interpretation space. Such mapping, be it a
classification, a regression or a description solution, is also called a hypothesis.

Similarity

Distance Matching score Syntactic rule
(feature vector) (primitive slructure) (primitive structure)
I I
Description / Descriplion /
Classiticalion Regression Classification Classificalion

Figure 1.11. PR approaches: S - supervised; U - unsupervised; SC - statistical
classification; NN - neural networks; DC - data clustering; SM - structural
matching; SA - syntactic analysis; GI - grammatical inference.