Association rules are a popular knowledge discovery technique for
rehouse basket analysis. They indicate which items of the
rehouse are frequently bought together. The problem of association
le mining has first been stated in 1993. Five years later, several
search groups discovered that this problem has a strong connection
Formal Concept Analysis (FCA). In this survey, we will first
troduce some basic ideas of this connection along a specific
gorithm, and show how FCA helps in reducing the number
resulting rules without loss of information, before giving a
neral overview over the history and state of the art of applying
A for association rule mining.

Association rules are a popular knowledge discovery technique for
rehouse basket analysis. They indicate which items of the
rehouse are frequently bought together. The problem of association
le mining has first been stated in 1993. Five years later, several
search groups discovered that this problem has a strong connection
Formal Concept Analysis (FCA). In this survey, we will first
troduce some basic ideas of this connection along a specific
gorithm, and show how FCA helps in reducing the number
resulting rules without loss of information, before giving a
neral overview over the history and state of the art of applying
A for association rule mining.

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.