Abstract
There are many approaches and tools which deal with conceptual structures in datasets and their main goal is to support user in understanding of data and structure. One of methods is formal concept analysis (FCA) which is suitable for processing and analyzing input data of object-attributes models based on their relationship. One from FCA family is model of generalized one-sided concept lattice (GOSCL). It is suitable to work with different type of attributes. While generating one-sided concept lattices in FCA improved understanding and interpretation of analysis, one of the lasting problem is to provide the users a result of FCA in appropriate form, if there is large number of concept lattices and generated structure is complex. This is one of the main topics in the FCA and solution can be reached with the reduction methods. In this paper we propose some of the reduction techniques and their combinations.
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Wille, R.: Restructuring Lattice Theory: An Approach Based on Hierarchies of Concepts. Springer, Netherlands (1982)
Birkhoff, G.: Lattice Theory. American Mathematical Soc. (1940)
Thomas, J., Cook, K.: Illuminating the path: research and development agenda for visual analytics. In: National Visualization and Analytics Ctr. (2005)
Keim, D.A.: Information visualization and visual data mining. IEEE Trans. Vis. Comput. Graph. 8(1), 1–8 (2002)
Hamrouni, T., Yahia, S.B., Slimani, Y.: Avoiding the itemser clousure computation pitfall. In: Belohlavek, R., Snasel, V. (eds.) CLA (2005)
Hermann, M., Sertkaya, B.: On the complexity of computing generators of closed sets. In: ICFCA, LNAI 4933, pp. 158–168, Springer, Berlin (2008)
Belohlavek, R.: Introduction to Formal Concept Analysis. Palacky University, Department of Computer Science, Olomouc (2008)
Borchmann, D.: A Generalized Next-Closure Algorithm–Enumerating Semilattice Elements from a Generating Set. arXiv (2011)
Butka, P., Pocs, J.: Generalization of one-sided concept lattices. Comput. Informat. 32(2), 355–370 (2013)
Butka, P., Pocs, J., Pocsova, J.: On equivalence of conceptual scaling and generalized one-sided concept lattices. Inform. Sci. 259, 57–70 (2014)
Pocs, J., Pocsova, J.: Basic theorem as representation of heterogeneous concept lattices. Front. Comput. Sci. 9(4), 636–642 (2015)
Pocs, J., Pocsova, J.: Bipolarized extension of heterogeneous concept lattices. Appl. Math. Sci. 8(125–128), 6359–6365 (2014)
Butka, P., Pocs, J., Pocsová, J.: Reduction of concepts from generalized one-sided concept lattice based on subsets quality measure. Adv. Intell. Syst. Comput. 314, 101–111 (2015)
Antoni, L., Krajci, S., Kridlo, O.: Randomized fuzzy formal contexts and relevance of one-sided concepts. In: LNAI (Subseries of LNCS) 9113, pp. 183–199 (2014)
Melo, C., Le-Grand, B., Aufaure, A.: Browsing large concept lattices through tree extraction and reduction methods. Int. J. Intell. Inf. Technol. (IJIIT) 9(4), 16–34 (2013)
Pensa, R., Boulicaut, J.-F.: Towards fault-tolerant formal concept analysis. In: Proceedings of 9th Congress of the Italian Association for Artificial Intelligence, LNAI, pp. 212–223, Springer (2005)
Gajdos, P., Moravec, P., Snasel, V.: Concept lattice generation by singular value decomposition. In: Proceedings of CLA (2004)
Snasel, V., Polovincak, M., Abdulla, H.: Concept lattice reduction by singular value decomposition. In: Proceedings of the SYRCoDIS, Moscow, Russia (2007)
Ganter, B. Stumme, G. Wille, R.: Formal Concept Analysis: Foundations and Applications. Springer (2005)
Kuznetsov, S.O.: Stability as an estimate of the degree of substantiation of hypotheses derived on the basis of operational similarity. In: Automatic Documentation and Mathematical Linguistics (1990)
Ganter, B. Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer Science & Business Media (2012)
Acknowledgments
The work presented in this paper was partially supported by the Slovak Cultural and Educational Grant Agency of Ministry of Education, Science, Research and Sport of the Slovak Republic (KEGA) under grant No. 025TUKE-4/2015 and also by the Slovak Grant Agency of Ministry of Education and Academy of Science of Slovak Republic (VEGA) under grant No. 1/0493/16.
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Smatana, M., Butka, P., Cöveková, L. (2017). Tree Based Reduction of Concept Lattices Based on Conceptual Indexes. In: Borzemski, L., Grzech, A., Świątek, J., Wilimowska, Z. (eds) Information Systems Architecture and Technology: Proceedings of 37th International Conference on Information Systems Architecture and Technology – ISAT 2016 – Part I. Advances in Intelligent Systems and Computing, vol 521. Springer, Cham. https://doi.org/10.1007/978-3-319-46583-8_17
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