Formal Concept Analysis Note
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Basic:
A concept consists of an object and its relative attributes.Concept={Objects, Attributes}. The set of objects is the extension of the concept, the set of attributes is the intension of the concept.
Formal context: is a group(G,M,I) of objects G, attributes M and arelation I is called a formal context. It is usually presented by a contexttable.
Using mathematical definition of formal concepts we introduce thederivation operators “ ^ “. For a set of objects A, A^ is defined as :
A^ = {all attributes shared by the objects of A}
For a set of attributes B, B^ is defined as:
B^= {all objects that have all attributes of B}
A formal concept is a pair of set (A,B) of objects and attributes thatfulfils the conditions that A^=B and B^=A. Searching a concept in a formalcontext is looking for a pair set (A^^, A^).
A formal concept (A^^,A^) is called subconcept of (B^^,B^) and (B^^,B^)is called superconcept of (A^^,A^),provided that the set of objects A^^ is a subset of B^^. In mathematicaldefinition:
(A,B) <= (C,D) ó A subsets C and Dsubset B.
Concept Lattice: Objects structure from top to bottom joining theattributes, attributes structure formbottom to top meeting the objects. A diagram based on a subset of attributes ofa formal context is called a conceptual scale.
Find the attribute concepts having a1 and a2 as intent and follow thelines down to the concept where they meet.
Find the concepts having O1 and O2 as extent and follow the lines up tothe concept they join.
Algorithms:
The methods exist to derive all formal concepts: Ganter’s algorithm, cutover extents, Lindig’s algorithm etc.
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