Lindig's Algorithm for Concept Lattices over Graded Attributes

  • Authors:

  • Radim Belohlavek;Bernard Baets;Jan Outrata;Vilem Vychodil

  • Affiliations:

  • Dept. Systems Science and Industrial Engineering, T. J. Watson School of Engineering and Applied Science, Binghamton University---SUNY, PO Box 6000, Binghamton, NY 13902---6000, USA and Dept. Comp ...;Dept. Appl. Math., Biometrics, and Process Control, Ghent University, Coupure links 653, B-9000 Gent, Belgium;Dept. Computer Science, Palacky University, Olomouc, Tomkova 40, CZ-779 00 Olomouc, Czech Republic;Dept. Computer Science, Palacky University, Olomouc, Tomkova 40, CZ-779 00 Olomouc, Czech Republic

  • Venue:
  • MDAI '07 Proceedings of the 4th international conference on Modeling Decisions for Artificial Intelligence
  • Year:
  • 2007

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Abstract

Formal concept analysis (FCA) is a method of exploratory data analysis. The data is in the form of a table describing relationship between objects (rows) and attributes (columns), where table entries are grades representing degrees to which objects have attributes. The main output of FCA is a hierarchical structure (so-called concept lattice) of conceptual clusters (so-called formal concepts) present in the data. This paper focuses on algorithmic aspects of FCA of data with graded attributes. Namely, we focus on the problem of generating efficiently all clusters present in the data together with their subconcept-superconcept hierarchy. We present theoretical foundations, the algorithm, analysis of its efficiency, and comparison with other algorithms.