A Fixed Point Theorem for Stronger Association Rules and Its Computational Aspects

  title={A Fixed Point Theorem for Stronger Association Rules and Its Computational Aspects},
  author={G{\'a}bor Cz{\'e}dli},
  journal={Acta Cybern.},
Each relation induces a new closure operator, which is (in the sense of data mining) stronger than or equal to the Galois one. The goal is to give some evidence that the new closure operator is often properly stronger than the Galois one. An easy characterization of the new closure operator as a largest fixed point of an appropriate contraction map leads to a (modest) computer program. Finally, various experimental results obtained by this program give the desired evidence. 

Tables from this paper

The goal of this paper is to introduce a more general pair of closure operators, smaller than the Galois one, such that the corresponding stronger association rules take into account that not all the attributes are positive.
Some new closures on orders
For each of the relations “less than or equal to”, “less than”, “covered by”, and “covered by or equal to”, we characterize finite orders (also called posets) with the property that the pair of


Functional Dependencies in Relational Databases: A Lattice Point of View
Efficient Mining of Association Rules Based on Formal Concept Analysis
This survey will first introduce some basic ideas of this connection along a specific algorithm, Titanic, and show how FCA helps in reducing the number of resulting rules without loss of information, before giving a general overview over the history and state of the art of applying FCA for association rule mining.
2-uniform congruences in majority algebras and a closure operator
Abstract.A ternary term m(x, y, z) of an algebra is called a majority term if the algebra satisfies the identities m(x, x, y) = x, m(x, y, x) = x and m(y, x, x) = x. A congruence α of a finite
Mining association rules between sets of items in large databases
An efficient algorithm is presented that generates all significant association rules between items in the database of customer transactions and incorporates buffer management and novel estimation and pruning techniques.
Restructuring Lattice Theory: An Approach Based on Hierarchies of Concepts
Restructuring lattice theory is an attempt to reinvigorate connections with the authors' general culture by interpreting the theory as concretely as possible, and in this way to promote better communication between lattice theorists and potential users of lattices theory.
Formal Concept Analysis: Mathematical Foundations
From the Publisher: This is the first textbook on formal concept analysis. It gives a systematic presentation of the mathematical foundations and their relation to applications in computer science,
The mathematics of juggling Springer-Verlag
  • New York,
  • 2003
The lattice of all 1-meet-subsemilattices of a finite lattice
  • The lattice of all 1-meet-subsemilattices of a finite lattice
  • 1987