Normalized-scale Relations and Their Concept Lattices in Relational Databases

  • Authors:

  • Yuxia Lei;Yuefei Sui;Cungen Cao

  • Affiliations:

  • (Correspd.) Key Laboratory of Intelligent Information Processing, Inst. of Computing Technology, Chinese Academy of Sciences, Beijing 100190, PRC and Graduate University of Chinese Academy of Scie ...;Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100190, P.R.China;Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100190, P.R.China

  • Venue:
  • Fundamenta Informaticae
  • Year:
  • 2009

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Abstract

Formal Concept Analysis (FCA) is a valid tool for data mining and knowledge discovery, which identifies conceptual structures from (formal) contexts. As many practical applications involve non-binary data, non-binary attributes are introduced via a many-valued context in FCA. In FCA, conceptual scaling provides a complete framework for transforming any many-valued context into a context, in which each non-binary attribute is given a scale, and the scale is a context. Each relation in relational databases is a many-valued context of FCA. In this paper, we provide an approach toward normalizing scales, i.e., each scale can be represented by a nominal scale and/or a set of statements. One advantage of normalizing scales is to avoid generating huge (binary) derived relations. By the normalization, the concept lattice of a derived relation is reduced to a combination of the concept lattice of a derived nominal relation and a set of statements. Hence, without transforming a relation into a derived relation, one can not only determine concepts of the derived relation from concepts of given scales, but also determine concepts of the derived relation from concepts of a derived nominal relation and a set of statements. The connection between the concept lattice of a derived nominal relation and the concept lattice of a derived relation is also considered.