Direct factorization by similarity of fuzzy concept lattices by factorization of input data

  • Authors:

  • Radim Belohlavek;Jan Outrata;Vilem Vychodil

  • Affiliations:

  • Dept. Systems Science and Industrial Engineering, T. J. Watson School of Engineering and Applied Science, Binghamton University-SUNY, Binghamton, NY and Dept. Computer Science, Palacky University, ...;Dept. Computer Science, Palacky University, Olomouc, Czech Republic;Dept. Systems Science and Industrial Engineering, T. J. Watson School of Engineering and Applied Science, Binghamton University-SUNY, Binghamton, NY and Dept. Computer Science, Palacky University, ...

  • Venue:
  • CLA'06 Proceedings of the 4th international conference on Concept lattices and their applications
  • Year:
  • 2006

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Abstract

The paper presents additional results on factorization by similarity of fuzzy concept lattices. A fuzzy concept lattice is a hierarchically ordered collection of clusters extracted from tabular data. The basic idea of factorization by similarity is to have, instead of a possibly large original fuzzy concept lattice, its factor lattice. The factor lattice contains less clusters than the original concept lattice but, at the same time, represents a reasonable approximation of the original concept lattice and provides us with a granular view on the original concept lattice. The factor lattice results by factorization of the original fuzzy concept lattice by a similarity relation. The similarity relation is specified by a user by means of a single parameter, called a similarity threshold. Smaller similarity thresholds lead to smaller factor lattices, i.e. to more comprehensible but less accurate approximations of the original concept lattice. Therefore, factorization by similarity provides a trade-off between comprehensibility and precision. We first recall the notion of factorization. Second, we present a way to compute the factor lattice of a fuzzy concept lattice directly from input data, i.e. without the need to compute the possibly large original concept lattice.