Formal concept analysis

In information science, formal concept analysis (FCA) is a principled way of deriving a concept hierarchy or formal ontology from a collection of objects and their properties. Each concept in the hierarchy represents the set of objects sharing the same values for a certain set of properties; and each sub-concept in the hierarchy contains a subset of the objects in the concepts above it. The term was introduced by Rudolf Wille in 1984, and builds on applied lattice and order theory that was developed by Garrett Birkhoff and others in the 1930s.

Formal concept analysis finds practical application in fields including data mining, text mining, machine learning, knowledge management, semantic web, software development, chemistry and biology.

The original motivation of formal concept analysis was the concrete representation of complete lattices and their properties by means of formal contexts, data tables that represent binary relations between objects and attributes, thus tabulating pairs of the form "object g has attribute m." In this theory, a formal concept is defined to be a pair (A, B), where A is a set of objects (called the extent) and B is a set of attributes (the intent) such that

In this way, formal concept analysis formalizes the semantic notions of extension and intension.

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