Computing iceberg concept lattices with TITANIC

  • Authors:

  • Gerd Stumme;Rafik Taouil;Yves Bastide;Nicolas Pasquier;Lotfi Lakhal

  • Affiliations:

  • Institut für Angewandte Informatik und Formale Beschreibungsverfahren (AIFB), Universität Karlsruhe (TH), D-76128 Karlsruhe, Germany;INRIA Lorraine, LORIA, BP 239, F-54506 Vandæuvre-lès-Nancy, France;Laboratoire d'Informatique (LIMOS), Université Blaise Pascal, Complexe Scientifique des Cézeaux, 24 Avenue des Landais, F-63177 Aubière Cedex, France;Université de Nice, I3S--CNRS UPRESA 6070-UNSA, Les Algorithmes--Euclide B, 2000 route des Lucioles, BP 121, F-06903 Sophia Antipolis, France;LIM, CNRS FRE-2246, Université de la Méditerranée, Case 90, 163 Avenue de Luminy, F-13288 Marseille Cedex 9, France

  • Venue:
  • Data & Knowledge Engineering
  • Year:
  • 2002

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Abstract

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.