The aim of pattern recognition is the design of a classifier, a mechanism which takes features of objects as its input and which results in a classification , a label or value indicating to which class the object belongs.

This is done on the basis of a learning set: a set of objects with a known labelling. The classifier's performance is usually tested using a set of objects independent of the learning set, called the test set.

The error a classifier makes is usually defined as the number (or percentage) of objects classified wrong. Errors can have one of two causes:

• wrong classification, or
• class overlap: some range of feature-values occurring for more than one class. If the probability density functions of the classes' features overlap, no classifier can flawlessly discriminate objects belonging to them.

Numerous functions can be used to implement a classifier:

• the Bayes' optimal classifier presented in the following section,
• linear classifiers,
• quadratic classifiers,
• the k-nearest neighbour classifier,
• artificial neural networks, and so on.