Abstract
One of the key problems of knowledge discovery is knowledge reduction. Concept lattice is an effective tool for data analysis and knowledge processing. The existing works on attribute reduction in concept lattice have mainly been focused on static database. This paper presents an incremental approach to identify reductions from dynamic database. The properties of attributes are discussed within the framework of equivalence classes and the determinant theorem of attribute reduction is presented. Based on the theorem, the reductions can be easily derived. The experimental results validate the effectiveness of the approach.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Wille, R.: Restructuring Lattice theory: An Approach Based on Hierarchies of Concepts. In: Rival, I. (ed.) Ordered Sets, pp. 445–470. Reidel, Dordrecht (1982)
Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, Heidelberg (1999)
Godin, R., Missaoui, R., Alaoui, H.: Incremental Concept Formation Algorithms Based on Galois Lattices. Computational Intelligence 2(11), 246–267 (1995)
Chen, Y.H., Yao, Y.Y.: Formal Concept Analysis and Hierarchical Classes Analysis. In: Annual Meeting of the North American Fuzzy Information Processing Society, pp. 276–281 (2005)
Burmeister, P.: Formal Concept Analysis with ConImp: Introduction to The Basic Features. Technical Report (2003)
Shao, M.W.: The Reduction for Two Kind of Generalized Concept Lattice. In: Proceedings of International Conference on Machine Learning and Cybernetics, pp. 2217–2222 (2005)
Li, H.R., Zhang, W.X., Wang, H.: Classification and Reduction of Attributes in Concept Lattices. In: IEEE International Conference on Granular Computing, pp. 142–147 (2006)
Kent, R.: Rough Concept Analysis: A synthesis of Rough Sets and Formal Concept Analysis. Fund. Information 27(2), 169–181 (1996)
Yao, Y.: A Comparative Study of Formal Concept Analysis and Rough Set Theory in Data Analysis. In: Tsumoto, S., et al. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 59–68. Springer, Heidelberg (2004)
Yao, Y.Y.: Concept Lattices in Rough Set Theory. In: NAFIPS2004, pp. 796–801. IEEE Catalog Number: 04TH8736 (2004)
Jin, J.Y., Qin, K., Pei, Z.: Reduction-Based Approaches Towards Constructing Galois (Concept) Lattice. In: Wang, G.-Y., et al. (eds.) RSKT 2006. LNCS (LNAI), vol. 4062, pp. 107–113. Springer, Heidelberg (2006)
Eisenbarth, T., Koschke, R.: Locating Features in Source Code. IEEE Transactions on Software Engineering 29(3), 195–209 (2003)
Snelting, G., Tip, F.: Reengineering Class Hierarchies Using Concept Analysis. In: Proc. Sixth Int’l Symp. Foundations of Software Eng. (1998)
Siff, M., Reps, T.: Identifying Modules via Concept Analysis. IEEE Transactions on Software Engineering 25(6) (1999)
Zhang, W.X., Liu, W., Qi, J.J.: The Theory and Approach of Attribute Reduction in Concept Lattice. China Science, Informational Science 35(6), 628–639 (2005)
Stumme, G., et al.: Intelligent Structuring and Reducing of Association Rules with Formal Concept Analysis. In: Baader, F., Brewka, G., Eiter, T. (eds.) KI 2001. LNCS (LNAI), vol. 2174, pp. 335–350. Springer, Heidelberg (2001)
Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991)
Zhang, W.X., Liu, W., Qi, J.J.: Attribute Reduction in Concept Lattice Based on Discernibility Matrix. In: Ślęzak, D., et al. (eds.) RSFDGrC 2005. LNCS (LNAI), vol. 3642, pp. 157–165. Springer, Heidelberg (2005)
Godin, R., Missaoui, R., April, A.: Experimental Comparison of Navigation in Galois Lattice with Conventional Information Retrieval Methods. International Journal of Man-Machine Studies 38 (1993)
Skowron, A., Rauszwer, C.: The Discernibility Matrices and Functions in Information Systems. In: Intelligent Decision Support: Handbook of Applications and Advances of the Rough Set Theory, pp. 331–362. Kluwer Academic Publishers, Dordrecht (1992)
Pagliani, P.: From Concept Lattices to Approximation Spaces: Algebraic Structures of Some Spaces of Partial Objects. Fundamental Information 18, 1–25 (1993)
Hu, K.: Concept Approximation in Concept Lattice. In: Cheung, D., Williams, G.J., Li, Q. (eds.) PAKDD 2001. LNCS (LNAI), vol. 2035, pp. 167–173. Springer, Heidelberg (2001)
Deogun, J.S., Saquer, J.: Concept Approximations for Formal Concept Analysis. In: Stumme, G. (ed.) Working with Conceptual Structures, ICCS, pp. 73–83 (2000)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Yang, B., Xu, B., Li, Y. (2007). An Incremental Approach for Attribute Reduction in Concept Lattice. In: Yao, J., Lingras, P., Wu, WZ., Szczuka, M., Cercone, N.J., Ślȩzak, D. (eds) Rough Sets and Knowledge Technology. RSKT 2007. Lecture Notes in Computer Science(), vol 4481. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72458-2_56
Download citation
DOI: https://doi.org/10.1007/978-3-540-72458-2_56
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72457-5
Online ISBN: 978-3-540-72458-2
eBook Packages: Computer ScienceComputer Science (R0)