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Towards a Generalisation of Formal Concept Analysis for Data Mining Purposes

  • Francisco J. Valverde-Albacete
  • Carmen Peláez-Moreno
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3874)

Abstract

In this paper we justify the need for a generalisation of Formal Concept Analysis for the purpose of data mining and begin the synthesis of such theory. For that purpose, we first review semirings and semimodules over semirings as the appropriate objects to use in abstracting the Boolean algebra and the notion of extents and intents, respectively. We later bring to bear powerful theorems developed in the field of linear algebra over idempotent semimodules to try to build a Fundamental Theorem for \(\mathcal{K}\)-Formal Concept Analysis , where \(\mathcal{K}\) is a type of idempotent semiring. Finally, we try to put Formal Concept Analysis in new perspective by considering it as a concrete instance of the theory developed.

Keywords

Boolean Algebra Complete Lattice Natural Order Concept Lattice Formal Context 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Francisco J. Valverde-Albacete
    • 1
  • Carmen Peláez-Moreno
    • 1
  1. 1.Dpto. de Teoría de la Señal y de las ComunicacionesUniversidad Carlos III de MadridLeganésSpain

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