FORMAL CONCEPT ANALYSIS

A

A formal concept of (G,M,I) is a pair (A,B) of sets satisfying :

A G, B M, A'= B, A = B'

where A' et B' are the operators :

A' := {m M | (g,m) I for all g A} (A' is the set of attributes which are possessed by all the objects of A)

B' := {g G | (g,m) I for all m B} (B' is the set of objects which possess all the attributes of B)

The set A is called the

Concepts are ordered by:

(A1,B1) (A2,B2) : A1 A2 ( B2 B1 )

The set

NB:

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**Concept Approximation by a similarity index** (see Saquer and Deogun)

Another method based on Rough Set Theory has been proposed by the same authors (see RST).

Alpha Galois Lattices

A method to reduce the size of the lattice when the number of nodes is very large. The method is based on a preliminary partition of the full BD in "types" (basic concepts)

A list of the Association Rules (

{D,F} => {H} (12/12) 100

means that, when an object has features D and F, it has also feature H in 100% of the 12 occurrences in the formal context. Such a rule, observed without exception within the formal context, is called

**References**

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PERNELLE N., M.-C.ROUSSET , H. SOLDANO H., V. VENTOS (2002). ZOOM: a nested Galois lattices-based system for conceptual clustering.* J. of Experimental and Theoretical Artificial Intelligence*, 1 (14), 157-187.

PERNELLE N., V. VENTOS, H. SOLDANO (2003). ZooM: Alpha Galois lattices for conceptual clustering *MASPEGHI 2003, 2nd International Workshop on MAnaging SPEcialization/ Generalization HIerarchies, Montréal, Québec, Canada*.

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