Trees in Concept Lattices

  • Radim Belohlavek
  • Bernard De Baets
  • Jan Outrata
  • Vilem Vychodil
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4617)

Abstract

The paper presents theorems characterizing concept lattices which happen to be trees after removing the bottom element. Concept lattices are the clustering/classification systems provided as an output of formal concept analysis. In general, a concept lattice may contain overlapping clusters and need not be a tree. On the other hand, tree-like classification schemes are appealing and are produced by several classification methods as the output. This paper attempts to help establish a bridge between concept lattices and tree-based classification methods. We present results presenting conditions for input data which are sufficient and necessary for the output concept lattice to form a tree after one removes its bottom element. In addition, we present illustrative examples and several remarks on related efforts and future research topics.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Radim Belohlavek
    • 1
    • 3
  • Bernard De Baets
    • 2
  • Jan Outrata
    • 3
  • Vilem Vychodil
    • 3
  1. 1.Dept. Systems Science and Industrial Engineering, T. J. Watson School of Engineering and Applied Science, Binghamton University–SUNY, PO Box 6000, Binghamton, NY 13902–6000USA
  2. 2.Dept. Appl. Math., Biometrics, and Process Control, Ghent University, Coupure links 653, B-9000 GentBelgium
  3. 3.Dept. Computer Science, Palacky University, Olomouc, Tomkova 40, CZ-779 00 OlomoucCzech Republic

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