Pasquier, N.; Taouil, R.; Bastide, Y.; Stumme, G. & Lakhal, L. (2005),
'Generating a Condensed Representation for Association Rules', * Journal Intelligent Information Systems (JIIS)*
**24**
(1)
, 29-60
.

[BibTeX]
[Endnote]

Pasquier, N.; Taouil, R.; Bastide, Y.; Stumme, G. & Lakhal, L. (2005),
'Generating a Condensed Representation for Association Rules', * Journal Intelligent Information Systems (JIIS)*
**24**
(1)
, 29-60
.

[BibTeX]
[Endnote]

Stumme, G.; Taouil, R.; Bastide, Y.; Pasquier, N. & Lakhal, L. (2002),
'Computing iceberg concept lattices with TITANIC', * Data & Knowledge Engineering*
**42**
(2)
, 189--222
.

[BibTeX]
[Endnote]

We introduce the notion of iceberg concept lattices and show their use in knowledge discovery in databases. Iceberg lattices are a conceptual clustering method, which is well suited for analyzing very large databases. They also serve as a condensed representation of frequent itemsets, as starting point for computing bases of association rules, and as a visualization method for association rules. Iceberg concept lattices are based on the theory of Formal Concept Analysis, a mathematical theory with applications in data analysis, information retrieval, and knowledge discovery. We present a new algorithm called TITANIC for computing (iceberg) concept lattices. It is based on data mining techniques with a level-wise approach. In fact, TITANIC can be used for a more general problem: Computing arbitrary closure systems when the closure operator comes along with a so-called weight function. The use of weight functions for computing closure systems has not been discussed in the literature up to now. Applications providing such a weight function include association rule mining, functional dependencies in databases, conceptual clustering, and ontology engineering. The algorithm is experimentally evaluated and compared with Ganter's Next-Closure algorithm. The evaluation shows an important gain in efficiency, especially for weakly correlated data.