Lindig’s Algorithm for Concept Lattices over Graded Attributes
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.
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- 3.Belohlavek, R.: Algorithms for fuzzy concept lattices. In: Proc. Fourth Int. Conf. on Recent Advances in Soft Computing. Nottingham, United Kingdom, pp. 200–205 (December 12–13, 2002)Google Scholar
- 5.Belohlavek, R., Vychodil, V.: Reducing the size of fuzzy concept lattices by fuzzy closure operators. In: Proc. SCIS & ISIS 2006, pp. 309–314. Tokyo Institute of Technology, Japan, (September 20–24, 2006), ISSN 1880–3741Google Scholar
- 7.Ganter, B.: Two basic algorithms in concept analysis. FB4-Preprint No. 831, TH Darmstadt (1984)Google Scholar
- 10.Goguen, J.A.: The logic of inexact concepts. Synthese 18, 325–373 (1968-1969)Google Scholar
- 11.Gratzer, G.A.: General Lattice Theory, 2nd edn. Birkhauser (1998)Google Scholar
- 18.Lindig, C.: Fast concept analysis. In: Ganter, B., Mineau, G.W. (eds.) ICCS 2000. LNCS, vol. 1867, pp. 152–161. Springer, Heidelberg (2000)Google Scholar
- 20.Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival, I. (ed.) Ordered Sets, pp. 445–470. Reidel, Dordrecht, Boston (1982)Google Scholar